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This talk considers approximation algorithms for embedding: constructing a global geometry that is approximately consistent with a given local geometry, which is typically represented by distances between some or all pairs of points in a point set. Such problems arise, for example, in the contexts of sensor networks and structural analysis of proteins. The first half of the talk is about embedding when given more information than just distances. In many cases, such information makes it possible to design efficient algorithms that embed with approximately minimum possible distortion. One example of extra information, available in some practical scenarios, is approximate angles between pairs of edges of known distance. We give efficient approximation algorithms for embedding in this and several other cases. In particular, one type of extra information, an “extremum oracle,” can be guessed in quasipolynomial time, leading to the first such algorithm for embedding into 2D given only distances. This is joint work with Mihai Badoiu, MohammadTaghi Hajiaghayi, and Piotr Indyk (SoCG 2004). The second half of the talk is about relaxed ordinal embedding, where the goal is to find an embedding in which the distances do not match the specified values but have roughly the correct relative order. Although exact ordinal embeddings have been studied before, we introduce the idea of getting the correct relative order for distances that are substantially different (have a large ratio), but violate the order when distances are close, for the minimum possible value of “close.” The minimum possible relaxation is related to the minimum possible distortion of regular metric embeddings, and we show that in some cases these two notions differ substantially. Minimum relaxation ordinal embeddings open the door for efficient approximation algorithms where such algorithms are impossible or difficult for minimum-distortion metric embedding, and may lead to better approximation algorithms for various geometric and graph problems. This is joint work with Mihai Badoiu, Martin Farach-Colton, MohammadTaghi Hajiaghayi, and Anastasios Sidiropoulos (2004). ©2004 Microsoft Corporation. All rights reserved.

We study the applicability of distributed, local algorithms to 0/1 max-min LPs where the objective is to maximise ${\min_k \sum_v c_{kv} x_v}$ subject to ${\sum_v a_{iv} x_v \le 1}$ for each $i$ and ${x_v \ge 0}$ for each $v$. Here $c_{kv} \in \{0,1\}$, $a_{iv} \in \{0,1\}$, and the support sets ${V_i = \{v : a_{iv} > 0 \}}$ and ${V_k = \{v : c_{kv}>0 \}}$ have bounded size; in particular, we study the case $|V_k| \le 2$. Each agent $v$ is responsible for choosing the value of $x_v$ based on information within its constant-size neighbourhood; the communication network is the hypergraph where the sets $V_k$ and $V_i$ constitute the hyperedges. We present a local approximation algorithm which achieves an approximation ratio arbitrarily close to the theoretical lower bound presented in prior work.

This write-up contains some minor results and notes related to our work [HQ15] (some of them already known in the literature). In particular, it shows the following: - We show that a graph with polynomial expansion have sublinear separators. - We show that hereditary sublinear separators imply that a graph have small divisions. - We show a natural condition on a set of segments, such that they have low density. This might be of independent interest in trying to define a realistic input model for a set of segments. Unlike the previous two results, this is new. For context and more details, see the main paper.

We consider the problem of approximating the girth, $g$, of an unweighted and undirected graph $G=(V,E)$ with $n$ nodes and $m$ edges. A seminal result of Itai and Rodeh [SICOMP'78] gave an additive $1$-approximation in $O(n^2)$ time, and the main open question is thus how well we can do in subquadratic time. In this paper we present two main results. The first is a $(1+\varepsilon,O(1))$-approximation in truly subquadratic time. Specifically, for any $k\ge 2$ our algorithm returns a cycle of length $2\lceil g/2\rceil+2\left\lceil\frac{g}{2(k-1)}\right\rceil$ in $\tilde{O}(n^{2-1/k})$ time. This generalizes the results of Lingas and Lundell [IPL'09] who showed it for the special case of $k=2$ and Roditty and Vassilevska Williams [SODA'12] who showed it for $k=3$. Our second result is to present an $O(1)$-approximation running in $O(n^{1+\varepsilon})$ time for any $\varepsilon > 0$. Prior to this work the fastest constant-factor approximation was the $\tilde{O}(n^{3/2})$ time $8/3$-approximation of Lingas and Lundell [IPL'09] using the algorithm corresponding to the special case $k=2$ of our first result.

In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing problem for which there is no known algorithm with approximation ratio $\alpha$, and a parameter $k$. If the value of an optimal solution is at least $k$, we seek a solution of value at least $\alpha k$; otherwise, we seek an arbitrary solution. Clearly, if the best known parameterized algorithm that finds a solution of value $t$ runs in time $O^*(f(t))$ for some function $f$, we are interested in running times better than $O^*(f(\alpha k))$. We present tradeoffs between running times and approximation ratios for the $P_2$-Packing, $3$-Set $k$-Packing and $3$-Dimensional $k$-Matching problems. Our tradeoffs are based on combinations of several known results, as well as a computation of "approximate lopsided universal sets."

Unique games are constraint satisfaction problems that can be viewed as a generalization of MAX CUT to a larger domain: We are given a graph G = (V,E) on n vertices and a permutation P uv on the set of labels {1,...,k} for every edge (u, v). Our goal is to assign a label X u in {1,..., k} to each vertex u, so as to maximize the number of satisfied constraints P uv (X u ) = X v . This problem has recently attracted a lot of attention since hardness of approximation for many problems, such as Sparsest Cut and Vertex Cover, was proved assuming the Unique Games Conjecture. Roughly speaking, this conjecture says that even if almost all constraints in a unique game are satisfiable it is NP-hard to satisfy a small constant fraction of constraints.Unique games pose a great challenge for our existing techniques:Typically, semidefinite programming (SDP) relaxations are well suited for optimization problems involving boolean variables (e.g. MAX CUT). But little is known about how to analyze SDP solutions for problems with larger domains. We present three approximation algorithms for Unique Games that satisfy roughly k -epsilon/2 , 1 - O(sqrt{epsilon log k}) and 1 - epsilon * O(sqrt{log k log n}) fraction of all constraints if a (1-epsilon) fraction of all constraints is satisfiable. This talk is based on joint papers with Moses Charikar, Eden Chlamtac, and Konstantin Makarychev. ©2007 Microsoft Corporation. All rights reserved.

Unique games are constraint satisfaction problems that can be viewed as a generalization of MAX CUT to a larger domain: We are given a graph G = (V,E) on n vertices and a permutation P uv on the set of labels {1,...,k} for every edge (u, v). Our goal is to assign a label X u in {1,..., k} to each vertex u, so as to maximize the number of satisfied constraints P uv (X u ) = X v . This problem has recently attracted a lot of attention since hardness of approximation for many problems, such as Sparsest Cut and Vertex Cover, was proved assuming the Unique Games Conjecture. Roughly speaking, this conjecture says that even if almost all constraints in a unique game are satisfiable it is NP-hard to satisfy a small constant fraction of constraints.Unique games pose a great challenge for our existing techniques:Typically, semidefinite programming (SDP) relaxations are well suited for optimization problems involving boolean variables (e.g. MAX CUT). But little is known about how to analyze SDP solutions for problems with larger domains. We present three approximation algorithms for Unique Games that satisfy roughly k -epsilon/2 , 1 - O(sqrt{epsilon log k}) and 1 - epsilon * O(sqrt{log k log n}) fraction of all constraints if a (1-epsilon) fraction of all constraints is satisfiable. This talk is based on joint papers with Moses Charikar, Eden Chlamtac, and Konstantin Makarychev. ©2007 Microsoft Corporation. All rights reserved.

This paper gives a lower bound on the complexity of epsilon-approximately solving a packing or covering problem using a certain class of ``Lagrangian-relaxation'' algorithms: any such algorithm, given a problem formed by a random {0,1}-matrix, requires (with high probability) a number of iterations proportional to (rho/epsilon)^2 log m iterations. (Here rho is a technical parameter, the "width" of the problem instance.) The class of algorithms in question includes Dantzig-Wolfe decomposition, Benders' decomposition, the Lagrangian-relaxation method developed by Held and Karp for lower-bounding TSP, and algorithms recently studied by many authors including Plotkin, Shmoys, and Tardos. The lower bound matches the known upper bounds within a constant factor. The lower bound is useful because, in practice, the dependence on epsilon limits the applicability of these algorithms. The lower bound provides some insight into what is necessary to surmount this dependence.

The projection games (aka Label-Cover) problem is of great importance to the field of approximation algorithms, since most of the NP-hardness of approximation results we know today are reductions from Label-Cover. In this paper we design several approximation algorithms for projection games: 1. A polynomial-time approximation algorithm that improves on the previous best approximation by Charikar, Hajiaghayi and Karloff. 2. A sub-exponential time algorithm with much tighter approximation for the case of smooth projection games. 3. A polynomial-time approximation scheme (PTAS) for projection games on planar graphs and a tight running time lower bound for such approximation schemes.

The projection games (aka Label-Cover) problem is of great importance to the field of approximation algorithms, since most of the NP-hardness of approximation results we know today are reductions from Label-Cover. In this paper we design several approximation algorithms for projection games: 1. A polynomial-time approximation algorithm that improves on the previous best approximation by Charikar, Hajiaghayi and Karloff. 2. A sub-exponential time algorithm with much tighter approximation for the case of smooth projection games. 3. A polynomial-time approximation scheme (PTAS) for projection games on planar graphs and a tight running time lower bound for such approximation schemes.

We will survey recent work in the design of approximation algorithms for several discrete stochastic optimization problems, with a particular focus on 2-stage problems with recourse. In each of the problems we discuss, we are given a probability distribution over inputs, and the aim is to find a feasible solution that minimizes the expected cost of the solution found (with respect to the input distribution); an approximation algorithm finds a solution that is guaranteed to be nearly optimal. Among the specific problems that we shall discuss are stochastic generalizations of the traditional deterministic facility location problem, a simple single-machine scheduling problem, and the traveling salesman problem.These results build on techniques initially developed in the context of deterministic approximation, including rounding approaches, primal-dual algorithms, as well as a simple random sampling technique. Furthermore, although the focus of this stream of work was for discrete optimization problems, new insights for solving 2-stage stochastic linear programming problems were gained along the way. ©2008 Microsoft Corporation. All rights reserved.

Speaker: Timothy Chan Date: October, 2003

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor clustering [8,34]. Like k-means, these more general problems also suffer from the NP-hardness of the associated optimization. Researchers have developed approximation algorithms of varying degrees of sophistication for k-means, k-medians, and more recently also for Bregman clustering [2]. However, there seem to be no approximation algorithms for Bregman co- and tensor clustering. In this paper we derive the first (to our knowledge) guaranteed methods for these increasingly important clustering settings. Going beyond Bregman divergences, we also prove an approximation factor for tensor clustering with arbitrary separable metrics. Through extensive experiments we evaluate the characteristics of our method, and show that it also has practical impact.

A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many such algorithms have now been proven to have optimal-order uniform recovery guarantees using the ubiquitous Restricted Isometry Property (RIP). However, it is unclear when the RIP-based sufficient conditions on the algorithm are satisfied. We present a framework in which this task can be achieved; translating these conditions for Gaussian measurement matrices into requirements on the signal's sparsity level, length, and number of measurements. We illustrate this approach on three of the state-of-the-art greedy algorithms: CoSaMP, Subspace Pursuit (SP), and Iterative Hard Thresholding (IHT). Designed to allow a direct comparison of existing theory, our framework implies that, according to the best known bounds, IHT requires the fewest number of compressed sensing measurements and has the lowest per iteration computational cost of the three algorithms compared here.

Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and initiate its study. We present two main results. The first shows that a non-trivial approximation ratio can be obtained in the class NP using product states. The second result (which builds on the first one), gives a polynomial time (classical) algorithm providing a similar approximation ratio for dense instances of the problem. The latter result is based on an adaptation of the "exhaustive sampling method" by Arora et al. [J. Comp. Sys. Sci. 58, p.193 (1999)] to the quantum setting, and might be of independent interest.

The link scheduling in wireless multi-hop networks is addressed. Different from most of work that adopt the protocol interference model which merely take consideration of packet collisions, our proposed algorithms use the physical interference model to reflect the aggregated signal to interference and noise ratio (SINR), which is a more accurate abstraction of the real scenario. We first propose a centralized scheduling method based on the Integer Linear Programming (ILP) and resolve it by an approximate solution based on the randomized rounding method. The probability bound of getting a guaranteed approximate factor is given. We then extend the centralized algorithm to a distributed solution, which is favorable in wireless networks. It is proven that with the distributed scheduling method, all links can transmit without interference, and the approximate ratio of the algorithm is also given.

Unique games are constraint satisfaction problems that can be viewed as a generalization of MAX CUT to a larger domain: We are given a graph G = (V,E) on n vertices and a permutation P uv on the set of labels {1,...,k} for every edge (u, v). Our goal is to assign a label X u in {1,..., k} to each vertex u, so as to maximize the number of satisfied constraints P uv (X u ) = X v . This problem has recently attracted a lot of attention since hardness of approximation for many problems, such as Sparsest Cut and Vertex Cover, was proved assuming the Unique Games Conjecture. Roughly speaking, this conjecture says that even if almost all constraints in a unique game are satisfiable it is NP-hard to satisfy a small constant fraction of constraints.Unique games pose a great challenge for our existing techniques:Typically, semidefinite programming (SDP) relaxations are well suited for optimization problems involving boolean variables (e.g. MAX CUT). But little is known about how to analyze SDP solutions for problems with larger domains. We present three approximation algorithms for Unique Games that satisfy roughly k -epsilon/2 , 1 - O(sqrt{epsilon log k}) and 1 - epsilon * O(sqrt{log k log n}) fraction of all constraints if a (1-epsilon) fraction of all constraints is satisfiable. This talk is based on joint papers with Moses Charikar, Eden Chlamtac, and Konstantin Makarychev. ©2007 Microsoft Corporation. All rights reserved.

We give the first combinatorial approximation algorithm for Maxcut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an O(n^{b}) algorithm that outputs a (0.5+delta)-approximation for Maxcut, where delta = delta(b) is some positive constant. One of the components of our algorithm is a weak local graph partitioning procedure that may be of independent interest. Given a starting vertex $i$ and a conductance parameter phi, unless a random walk of length ell = O(log n) starting from i mixes rapidly (in terms of phi and ell), we can find a cut of conductance at most phi close to the vertex. The work done per vertex found in the cut is sublinear in n.

We consider various {\em multi-vehicle versions of the minimum latency problem}. There is a fleet of $k$ vehicles located at one or more depot nodes, and we seek a collection of routes for these vehicles that visit all nodes so as to minimize the total latency incurred, which is the sum of the client waiting times. We obtain an $8.497$-approximation for the version where vehicles may be located at multiple depots and a $7.183$-approximation for the version where all vehicles are located at the same depot, both of which are the first improvements on this problem in a decade. Perhaps more significantly, our algorithms exploit various LP-relaxations for minimum-latency problems. We show how to effectively leverage two classes of LPs---{\em configuration LPs} and {\em bidirected LP-relaxations}---that are often believed to be quite powerful but have only sporadically been effectively leveraged for network-design and vehicle-routing problems. This gives the first concrete evidence of the effectiveness of LP-relaxations for this class of problems. The $8.497$-approximation the multiple-depot version is obtained by rounding a near-optimal solution to an underlying configuration LP for the problem. The $7.183$-approximation can be obtained both via rounding a bidirected LP for the single-depot problem or via more combinatorial means. The latter approach uses a bidirected LP to obtain the following key result that is of independent interest: for any $k$, we can efficiently compute a rooted tree that is at least as good, with respect to the prize-collecting objective (i.e., edge cost + number of uncovered nodes) as the best collection of $k$ rooted paths. Our algorithms are versatile and extend easily to handle various extensions involving: (i) weighted sum of latencies, (ii) constraints specifying which depots may serve which nodes, (iii) node service times.

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks. Here three approximation algorithms are examined; the linear-programming relaxation, the loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using the statistical-mechanical technique while the average-case analysis of the last one is studied by the generating function method. These algorithms have a threshold in the typical performance with increasing the average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases determined by the order of the typical-performance thresholds. We provide some conditions for classifying the graph ensembles and demonstrate explicitly examples for the difference in the threshold.

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks. Here three approximation algorithms are examined; the linear-programming relaxation, the loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using the statistical-mechanical technique while the average-case analysis of the last one is studied by the generating function method. These algorithms have a threshold in the typical performance with increasing the average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases determined by the order of the typical-performance thresholds. We provide some conditions for classifying the graph ensembles and demonstrate explicitly examples for the difference in the threshold.

Recent advances in the study of voting classification algorithms have brought empirical and theoretical results clearly showing the discrimination power of ensemble classifiers. It has been previously argued that the search of this classification power in the design of the algorithms has marginalized the need to obtain interpretable classifiers. Therefore, the question of whether one might have to dispense with interpretability in order to keep classification strength is being raised in a growing number of machine learning or data mining papers. The purpose of this paper is to study both theoretically and empirically the problem. First, we provide numerous results giving insight into the hardness of the simplicity-accuracy tradeoff for voting classifiers. Then we provide an efficient "top-down and prune" induction heuristic, WIDC, mainly derived from recent results on the weak learning and boosting frameworks. It is to our knowledge the first attempt to build a voting classifier as a base formula using the weak learning framework (the one which was previously highly successful for decision tree induction), and not the strong learning framework (as usual for such classifiers with boosting-like approaches). While it uses a well-known induction scheme previously successful in other classes of concept representations, thus making it easy to implement and compare, WIDC also relies on recent or new results we give about particular cases of boosting known as partition boosting and ranking loss boosting. Experimental results on thirty-one domains, most of which readily available, tend to display the ability of WIDC to produce small, accurate, and interpretable decision committees.

We initiate the study of approximating the largest induced expander in a given graph $G$. Given a $\Delta$-regular graph $G$ with $n$ vertices, the goal is to find the set with the largest induced expansion of size at least $\delta \cdot n$. We design a bi-criteria approximation algorithm for this problem; if the optimum has induced spectral expansion $\lambda$ our algorithm returns a $\frac{\lambda}{\log^2\delta \exp(\Delta/\lambda)}$-(spectral) expander of size at least $\delta n$ (up to constants). Our proof introduces and employs a novel semidefinite programming relaxation for the largest induced expander problem. We expect to see further applications of our SDP relaxation in graph partitioning problems. In particular, because of the close connection to the small set expansion problem, one may be able to obtain new insights into the unique games problem.

Consider a setting where selfish agents are to be assigned to coalitions or projects from a fixed set P. Each project k is characterized by a valuation function; v_k(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.

This article presents a short and concise description of stochastic approximation algorithms in reinforcement learning of Markov decision processes. The algorithms can also be used as a suboptimal method for partially observed Markov decision processes.

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic formulation of the fixed-point algorithm we show that it converges to the minimum of the convex envelope of the original objective function along with its structured matrix constraint. It often happens that this solution agrees with the solution to the original minimization problem, and we provide a simple criterium for when this is true. We also provide more general fixed-point algorithms that can be used to treat the problems of making weighted approximations by sums of exponentials given equally or unequally spaced sampling. We apply the method to the case of missing data, although optimal convergence of the fixed-point algorithm is not guaranteed in this case. However, it turns out that the method often gives perfect reconstruction (up to machine precision) in such cases. We also discuss multidimensional extensions, and illustrate how the proposed algorithms can be used to recover sums of exponentials in several variables, but when samples are available only along a curve.

We propose two finite difference two-timescale simultaneous perturbation stochastic approximation (SPSA) algorithms for simulation optimization of hidden Markov models. Stability and convergence of both the algorithms is proved. Numerical experiments on a queueing model with high dimensional parameter vectors demonstrate orders of magnitude faster convergence using these algorithms over related (N + 1)-Simulation finite difference analogues and another Two-Simulation finite difference algorithm that updates in cycles.

Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number of additional (relay) nodes so that the induced communication graph is k-connected. The problem is NP-hard. We develop algorithms that find close to optimal solutions for both edge and vertex connectivity. For k-connectivity between sensor nodes, we prove the algorithms have an approximation ratio of O(k2) for vertex connectivity and O(k) for edge connectivity. In addition, our methods extend with the same approximation guarantees to a generalization when the locations of relays are required to avoid certain polygonal regions (obstacles). We prove that the algorithms for k-connectivity between sensor and relay nodes have an approximation ratio of O(k3) for vertex connectivity and O(k2) for edge connectivity.

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

We study the prize-collecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. PATH-TSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V,E) with costs on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle (for PCTSP), or stroll (for PCS) that minimizes the sum of the edge costs in the tree/cycle/stroll and the penalties of the nodes not spanned by it. In addition to being a useful theoretical tool for helping to solve other optimization problems, PCST has been applied fruitfully by AT&T to the optimization of real-world telecommunications networks. The most recent improvements for the first two problems, giving a 2-approximation algorithm for each, appeared first in 1992. (A 2-approximation for PCS appeared in 2003.) The natural linear programming (LP) relaxation of PCST has an integrality gap of 2, which has been a barrier to further improvements for this problem. We present (2 - epsilon)-approximation algorithms for all three problems, connected by a unified technique for improving prize collecting algorithms that allows us to circumvent the integrality gap barrier. ©2009 Microsoft Corporation. All rights reserved.

The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the context of large-scale monitoring of communication networks. We consider the problem of selecting the "best" subset of links so as to optimally predict the quantity of interest at the remaining ones. This is a well know NP-hard problem, and algorithms seeking the exact solution are prohibitively expensive. We present a number of approximation algorithms that: 1) their computational complexity gains a significant improvement over existing greedy algorithms; 2) exploit the geometry of principal component analysis, which also helps us establish theoretical bounds on the prediction error; 3) are amenable for randomized implementation and execution in parallel or distributed fashion, a process that often yields the exact solution. The new algorithms are demonstrated and evaluated using real-world network data.

Orienteering is the following optimization problem: given an edge-weighted graph (directed or undirected), two nodes s,t and a time limit T, find an s-t walk of total length at most T that maximizes the number of distinct nodes visited by the walk. One obtains a generalization, namely orienteering with time-windows (also referred to as TSP with time-windows), if each node v has a specified time-window [R(v), D(v)] and a node v is counted as visited by the walk only if v is visited during its time-window. For the time-window problem, an O(\log \opt) approximation can be achieved even for directed graphs if the algorithm is allowed quasi-polynomial time. However, the best known polynomial time approximation ratios are O(\log^2 \opt) for undirected graphs and O(\log^4 \opt) in directed graphs. In this paper we make some progress towards closing this discrepancy, and in the process obtain improved approximation ratios in several natural settings. Let L(v) = D(v) - R(v) denote the length of the time-window for v and let \lmax = \max_v L(v) and \lmin = \min_v L(v). Our results are given below with \alpha denoting the known approximation ratio for orienteering (without time-windows). Currently \alpha = (2+\eps) for undirected graphs and \alpha = O(\log^2 \opt) in directed graphs. 1. An O(\alpha \log \lmax) approximation when R(v) and D(v) are integer valued for each v. 2. An O(\alpha \max{\log \opt, \log \frac{\lmax}{\lmin}}) approximation. 3. An O(\alpha \log \frac{\lmax}{\lmin}) approximation when no start and end points are specified. In particular, if \frac{\lmax}{\lmin} is poly-bounded, we obtain an O(\log n) approximation for the time-window problem in undirected graphs.

In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NP-hard. In this paper, we present new approximation results for the TSPN, including (1) a constant-factor approximation algorithm for the case of arbitrary connected neighborhoods having comparable diameters; and (2) a PTAS for the important special case of disjoint unit disk neighborhoods (or nearly disjoint, nearly-unit disks). Our methods also yield improved approximation ratios for various special classes of neighborhoods, which have previously been studied. Further, we give a linear-time O(1)-approximation algorithm for the case of neighborhoods that are (infinite) straight lines.

he segment minimization problem consists of finding the smallest set of integer matrices that sum to a given intensity matrix, such that each summand has only one non-zero value, and the non-zeroes in each row are consecutive. This has direct applications in intensity-modulated radiation therapy, an effective form of cancer treatment. We develop three approximation algorithms for matrices with arbitrarily many rows. Our first two algorithms improve the approximation factor from the previous best of $1+\log_2 h $ to (roughly) $3/2 \cdot (1+\log_3 h)$ and $11/6\cdot(1+\log_4{h})$, respectively, where $h$ is the largest entry in the intensity matrix. We illustrate the limitations of the specific approach used to obtain these two algorithms by proving a lower bound of $\frac{(2b-2)}{b}\cdot\log_b{h} + \frac{1}{b}$ on the approximation guarantee. Our third algorithm improves the approximation factor from $2 \cdot (\log D+1)$ to $24/13 \cdot (\log D+1)$, where $D$ is (roughly) the largest difference between consecutive elements of a row of the intensity matrix. Finally, experimentation with these algorithms shows that they perform well with respect to the optimum and outperform other approximation algorithms on 77% of the 122 test cases we consider, which include both real world and synthetic data.

We present approximation algorithms with O(n^3) processing time for the minimum vertex and edge guard problems in simple polygons. It is improved from previous O(n^4) time algorithms of Ghosh. For simple polygon, there are O(n^3) visibility regions, thus any approximation algorithm for the set covering problem with approximation ratio of log(n) can be used for the approximation of n vertex and edge guard problems with O(n^3) visibility sequence. We prove that the visibility of all points in simple polygons is guaranteed by covering O(n^2) sinks from vertices and edges : It comes to O(n^3) time bound.

The radius and diameter are fundamental graph parameters. They are defined as the minimum and maximum of the eccentricities in a graph, respectively, where the eccentricity of a vertex is the largest distance from the vertex to another node. In directed graphs, there are several versions of these problems. For instance, one may choose to define the eccentricity of a node in terms of the largest distance into the node, out of the node, the sum of the two directions (i.e. roundtrip) and so on. All versions of diameter and radius can be solved via solving all-pairs shortest paths (APSP), followed by a fast postprocessing step. Solving APSP, however, on $n$-node graphs requires $\Omega(n^2)$ time even in sparse graphs, as one needs to output $n^2$ distances. Motivated by known and new negative results on the impossibility of computing these measures exactly in general graphs in truly subquadratic time, under plausible assumptions, we search for \emph{approximation} and \emph{fixed parameter subquadratic} algorithms, and for reasons why they do not exist. Our results include: - Truly subquadratic approximation algorithms for most of the versions of Diameter and Radius with \emph{optimal} approximation guarantees (given truly subquadratic time), under plausible assumptions. In particular, there is a $2$-approximation algorithm for directed Radius with one-way distances that runs in $\tilde{O}(m\sqrt{n})$ time, while a $(2-\delta)$-approximation algorithm in $O(n^{2-\epsilon})$ time is unlikely. - On graphs with treewidth $k$, we can solve the problems in $2^{O(k\log{k})}n^{1+o(1)}$ time. We show that these algorithms are near optimal since even a $(3/2-\delta)$-approximation algorithm that runs in time $2^{o(k)}n^{2-\epsilon}$ would refute the plausible assumptions.

A graph $G$ is called B$_k$-VPG (resp., B$_k$-EPG), for some constant $k\geq 0$, if it has a string representation on a grid such that each vertex is an orthogonal path with at most $k$ bends and two vertices are adjacent in $G$ if and only if the corresponding strings intersect (resp., the corresponding strings share at least one grid edge). If two adjacent strings of a B$_k$-VPG graph intersect exactly once, then the graph is called a one-string B$_k$-VPG graph. In this paper, we study the Maximum Independent Set and Minimum Dominating Set problems on B$_1$-VPG and B$_1$-EPG graphs. We first give a simple $O(\log n)$-approximation algorithm for the Maximum Independent Set problem on B$_1$-VPG graphs, improving the previous $O((\log n)^2)$-approximation algorithm of Lahiri et al. (COCOA 2015). Then, we consider the Minimum Dominating Set problem. We give an $O(1)$-approximation algorithm for this problem on one-string B$_1$-VPG graphs, providing the first constant-factor approximation algorithm for this problem. Moreover, we show that the Minimum Dominating Set problem is APX-hard on B$_1$-EPG graphs, ruling out the possibility of a PTAS unless P=NP. Finally, we give constant-factor approximation algorithms for this problem on two non-trivial subclasses of B$_1$-EPG graphs. To our knowledge, these are the first results for the Minimum Dominating Set problem on B$_1$-EPG graphs, partially answering a question posed by Epstein et al. (WADS 2013).

The expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut. We study the Hypergraph Small Set Expansion problem, which, for a parameter $\delta \in (0,1/2]$, asks to compute the cut having the least expansion while having at most $\delta$ fraction of the vertices on the smaller side of the cut. We present two algorithms. Our first algorithm gives an $\tilde O(\delta^{-1} \sqrt{\log n})$ approximation. The second algorithm finds a set with expansion $\tilde O(\delta^{-1}(\sqrt{d_{\text{max}}r^{-1}\log r\, \phi^*} + \phi^*))$ in a $r$--uniform hypergraph with maximum degree $d_{\text{max}}$ (where $\phi^*$ is the expansion of the optimal solution). Using these results, we also obtain algorithms for the Small Set Vertex Expansion problem: we get an $\tilde O(\delta^{-1} \sqrt{\log n})$ approximation algorithm and an algorithm that finds a set with vertex expansion $O\left(\delta^{-1}\sqrt{\phi^V \log d_{\text{max}} } + \delta^{-1} \phi^V\right)$ (where $\phi^V$ is the vertex expansion of the optimal solution). For $\delta=1/2$, Hypergraph Small Set Expansion is equivalent to the hypergraph expansion problem. In this case, our approximation factor of $O(\sqrt{\log n})$ for expansion in hypergraphs matches the corresponding approximation factor for expansion in graphs due to ARV.

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the Kullback-Leibler divergence as a distance and find the best Gaussian approximation by minimizing this distance. It then follows that the approximate Gaussian must be equivalent to the Gaussian reference measure, defining a natural function space setting for the underlying calculus of variations problem. We introduce a computational algorithm which is well-adapted to the required minimization, seeking to find the mean as a function, and parameterizing the covariance in two different ways: through low rank perturbations of the reference covariance; and through Schr\"odinger potential perturbations of the inverse reference covariance. Two applications are shown: to a nonlinear inverse problem in elliptic PDEs, and to a conditioned diffusion process. We also show how the Gaussian approximations we obtain may be used to produce improved pCN-MCMC methods which are not only well-adapted to the high-dimensional setting, but also behave well with respect to small observational noise (resp. small temperatures) in the inverse problem (resp. conditioned diffusion).

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further.

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further.

We consider the problem of finding a lowest cost dominating set in a given disk graph containing $n$ disks. The problem has been extensively studied on subclasses of disk graphs, yet the best known approximation for disk graphs has remained $O(\log n)$ -- a bound that is asymptotically no better than the general case. We improve the status quo in two ways: for the unweighted case, we show how to obtain a PTAS using the framework recently proposed (independently)by Mustafa and Ray [SoCG 09] and by Chan and Har-Peled [SoCG 09]; for the weighted case where each input disk has an associated rational weight with the objective of finding a minimum cost dominating set, we give a randomized algorithm that obtains a dominating set whose weight is within a factor $2^{O(\log^* n)}$ of a minimum cost solution, with high probability -- the technique follows the framework proposed recently by Varadarajan [STOC 10].

In the stochastic knapsack problem, we are given a knapsack of size B, and a set of jobs whose sizes and rewards are drawn from a known probability distribution. However, we know the actual size and reward only when the job completes. How should we schedule jobs to maximize the expected total reward? We know O(1)-approximations when we assume that (i) rewards and sizes are independent random variables, and (ii) we cannot prematurely cancel jobs. What can we say when either or both of these assumptions are changed? The stochastic knapsack problem is of interest in its own right, but techniques developed for it are applicable to other stochastic packing problems. Indeed, ideas for this problem have been useful for budgeted learning problems, where one is given several arms which evolve in a specified stochastic fashion with each pull, and the goal is to pull the arms a total of B times to maximize the reward obtained. Much recent work on this problem focus on the case when the evolution of the arms follows a martingale, i.e., when the expected reward from the future is the same as the reward at the current state. What can we say when the rewards do not form a martingale? In this paper, we give constant-factor approximation algorithms for the stochastic knapsack problem with correlations and/or cancellations, and also for budgeted learning problems where the martingale condition is not satisfied. Indeed, we can show that previously proposed LP relaxations have large integrality gaps. We propose new time-indexed LP relaxations, and convert the fractional solutions into distributions over strategies, and then use the LP values and the time ordering information from these strategies to devise a randomized adaptive scheduling algorithm. We hope our LP formulation and decomposition methods may provide a new way to address other correlated bandit problems with more general contexts.

We parallelize several previously proposed algorithms for the minimum routing cost spanning tree problem and some related problems.

Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and Kelly-width are some such notions which generalize treewidth, whereas directed pathwidth generalizes pathwidth. Each of these digraph width measures have an associated decomposition structure. In this paper, we present approximation algorithms for all these digraph width parameters. In particular, we give an O(sqrt{logn})-approximation algorithm for directed treewidth, and an O({\log}^{3/2}{n})-approximation algorithm for directed pathwidth, DAG-width and Kelly-width. Our algorithms construct the corresponding decompositions whose widths are within the above mentioned approximation factors.

We consider the Generalized Bin Covering (GBC) problem: We are given $m$ bin types, where each bin of type $i$ has profit $p_i$ and demand $d_i$. Furthermore, there are $n$ items, where item $j$ has size $s_j$. A bin of type $i$ is covered if the set of items assigned to it has total size at least the demand $d_i$. In that case, the profit of $p_i$ is earned and the objective is to maximize the total profit. To the best of our knowledge, only the cases $p_i = d_i = 1$ (Bin Covering) and $p_i = d_i$ (Variable-Sized Bin Covering (VSBC)) have been treated before. We study two models of bin supply: In the unit supply model, we have exactly one bin of each type, i.\,e., we have individual bins. By contrast, in the infinite supply model, we have arbitrarily many bins of each type. Clearly, the unit supply model is a generalization of the infinite supply model. To the best of our knowledge the unit supply model has not been studied yet. Our results for the unit supply model hold not only asymptotically, but for all instances. This contrasts most of the previous work on \prob{Bin Covering}. We prove that there is a combinatorial 5-approximation algorithm for GBC with unit supply, which has running time $\bigO{nm\sqrt{m+n}}$. Furthermore, for VSBC we show that the natural and fast Next Fit Decreasing ($\NFD$) algorithm is a 9/4-approximation in the unit supply model. The bound is tight for the algorithm and close to being best-possible. We show that there is an AFPTAS for VSBC in the \emph{infinite} supply model.

In this paper we investigate quasi-stationary distributions {\mu}_N of stochastic approximation algorithms with constant step size which can be viewed as random perturbations of a time-continuous dynamical system. Inspired by ecological models these processes have a closed absorbing set corresponding to extinction. Under some large deviation assumptions and the existence of an interior attractor for the ODE, we show that the weak* limit points of the QSD {\mu}_N are invariant measures for the ODE with support in the interior attractors.

Network applications, such as multimedia streaming and video conferencing, impose growing requirements over Quality of Service (QoS), including bandwidth, delay, jitter, etc. Meanwhile, networks are expected to be load-balanced, energy-efficient, and resilient to some degree of failures. It is observed that the above requirements could be better met with multiple disjoint QoS paths than a single one. Let $G=(V,\, E)$ be a digraph with nonnegative integral cost and delay on every edge, $s,\, t\in V$ be two specified vertices, and $D\in\mathbb{Z}_{0}^{+}$ be a delay bound (or some other constraint), the \emph{$k$ Disjoint Restricted Shortest Path} ($k$\emph{RSP})\emph{ Problem} is computing $k$ disjoint paths between $s$ and $t$ with total cost minimized and total delay bounded by $D$. Few efficient algorithms have been developed because of the hardness of the problem. In this paper, we propose efficient algorithms with provable performance guarantees for the $k$RSP problem. We first present a pseudo-polynomial-time approximation algorithm with a bifactor approximation ratio of $(1,\,2)$, then improve the algorithm to polynomial time with a bifactor ratio of $(1+\epsilon,\,2+\epsilon)$ for any fixed $\epsilon>0$, which is better than the current best approximation ratio $(O(1+\gamma),\, O(1+\frac{1}{\gamma})\})$ for any fixed $\gamma>0$ \cite{orda2004efficient}. To the best of our knowledge, this is the first constant-factor algorithm that almost strictly obeys the constraint for the $k$RSP problem.

Given an undirected graph on a node set $V$ and positive integers $k$ and $m$, a $k$-connected $m$-dominating set ($(k,m)$-CDS) is defined as a subset $S$ of $V$ such that each node in $V \setminus S$ has at least $m$ neighbors in $S$, and a $k$-connected subgraph is induced by $S$. The weighted $(k,m)$-CDS problem is to find a minimum weight $(k,m)$-CDS in a given node-weighted graph. The problem is called the unweighted $(k,m)$-CDS problem if the objective is to minimize the cardinality of a $(k,m)$-CDS. These problems have been actively studied for unit disk graphs, motivated by the application of constructing a virtual backbone in a wireless ad hoc network. However, constant-approximation algorithms are known only for $k \leq 3$ in the unweighted $(k,m)$-CDS problem, and for $(k,m)=(1,1)$ in the weighted $(k,m)$-CDS problem. In this paper, we consider the case in which $m \geq k$, and we present a simple $O(5^k k!)$-approximation algorithm for the unweighted $(k,m)$-CDS problem, and a primal-dual $O(k^2 \log k)$-approximation algorithm for the weighted $(k,m)$-CDS problem. Both algorithms achieve constant approximation factors when $k$ is a fixed constant.

We determine the jet vertex for Mueller-Navelet jets and forward jets in the small-cone approximation for two particular choices of jet algoritms: the kt algorithm and the cone algorithm. These choices are motivated by the extensive use of such algorithms in the phenomenology of jets. The differences with the original calculations of the small-cone jet vertex by Ivanov and Papa, which is found to be equivalent to a formerly algorithm proposed by Furman, are shown at both analytic and numerical level, and turn out to be sizeable. A detailed numerical study of the error introduced by the small-cone approximation is also presented, for various observables of phenomenological interest. For values of the jet "radius" R=0.5, the use of the small-cone approximation amounts to an error of about 5% at the level of cross section, while it reduces to less than 2% for ratios of distributions such as those involved in the measure of the azimuthal decorrelation of dijets.

1Oscar Wilde: Art and Morality

By Stuart Mason

“Who can help laughing when an ordinary journalist seriously proposes to limit the subject-matter at the disposal of the artist?”<br><br>“We are dominated by journalism.... Journalism governs for ever and ever.”[/i]<br><br>One of the nastiest of the British tabloids was founded a year too late to join in the moral panic generated to accompany Oscar Wilde’s court appearances in 1895. Yet there was no shortage of hypocritical journalists posing as moral arbiters to the nation, then as now.<br><br>This compendium work - skillfully assembled by the editor, Stuart Mason - ends with transcript of Wilde’s first appearance in the Old Bailey, when he was cross-examined on the alleged immorality of his novel The Picture of Dorian Gray. The disastrous outcome of these trials provides an ironic conclusion to the earlier knockabout exchanges between Oscar and his reviewers. In these he is at his flamboyant best, revelling in the publicity he pretends to disdain. His brave performances in the dock did nothing, however, to save him from hard labour, the treadmill and complete physical and moral breakdown which the law found it necessary to inflict on him.<br><br>In contrast to the hacks and lawyers, two refreshingly open-minded Americans write perceptively about the novel, as does Walter Pater, the grand old man of Aestheticism.<br><br>This solo Librivox project complements a new dramatised reading of The Picture of Dorian Gray, currently in preparation, featuring the present reader as Narrator. (Introduction by Martin Geeson)

2Four Feathers

By A. E. W. Mason

The Four Feathers is a 1902 adventure novel by British writer A.E.W. Mason that has inspired many films of the same title. The novel tells the story of British officer, Harry Feversham, who resigns his commission in the East Surrey Regiment just prior to Sir Garnet Wolseley's 1882 expedition to Egypt to suppress the rising of Urabi Pasha. He is faced with censure from three of his comrades for cowardice, signified by the delivery of three white feathers to him, from Captain Trench and Lieutenants Castleton and Willoughby, and the loss of the support of his Irish fiancée, Ethne Eustace, who presents him with the fourth feather. His best friend in the regiment, Captain Durrance becomes his rival for Ethne.<br>(Summary extracted from Wikipedia)

3Running Water

By A. E. W. Mason

Although A.E.W. Mason is best known for The Four Feathers, an adventure novel of 1902 set in Egypt and the Sudan (and filmed several times), he was a prolific and popular writer of the period. Running Water, published in 1907, is, like its predecessor, a tale of romantic adventure. Though much of the story takes place in England, the real setting here is in the high Alps, in the range of Mont Blanc near Chamonix and Courmayeur. Here it is that Captain Hilary Chayne arrives, having spent the prior four years of his army service on the shores of the Red Sea, dreaming all the time of his return to the Alps, to the world of rock, ice, and snow, to mountaineering with all its challenges and joys, and to its comradeship. And here it is too that he meets the young and beautiful Sylvia Thesiger, a girl already in love with the high mountains, and seeking in them an escape, as far as possible, from her unpleasant and domineering mother.<br>Is it necessary to add that disappointments. problems, misunderstandings, and outright villainies, ensue to complicate the course of true love? After the twists and turns of novel's English midsection, the setting shifts back to the high Alps, and the final, climactic scene is played out on the heights of the Italian face of the Mont Blanc. This is the Brenva -- where thousands of feet of rock and glacier sweep steeply up to reach the highest point in western Europe. It is an Alpine route that today, over century later, even experienced climbers still find a challenge. There are not many novels given over to mountaineering, and some consider Mason's descriptions of climbing among the finest in fiction. Unlike The Four Feathers, Running Water has never been filmed – though given the quality of some of Hollywood's mountaineering movies, that may actually be a blessing.<br> Finally, for those unfamiliar with the teminology, several French terms are customarily used by alpinists and appear in Mason's book. An aiguille (needle) is a peak, usually sharp pointed, often of rock, sometimes of ice and snow. The Chamonix aiguilles, many of which are mentioned here, are famous among climbers and lovers of alpine scenery. A col is a pass between two mountains, or ranges, and in the High Alps often of steep ice and snow, sometimes of rock. And an arête is a ridge, or spur, of a mountain, sometimes of ice or snow, sometimes of rock, and often of all three. Historical note: The first ascent of the Brenva face was made by A.W. Moore and a party of three other British climbers and two Swiss alpine guides, in July, 1865. The account was published in Moore's book, The Alps in 1864, and it is this book that Garratt Skinner is reading in Chapter XII, as he lies in his Dorsetshire hammock. In 1943, another great British climber, T. Graham Brown published his Brenva, describing the various routes on the great southern face, on two of which had had made first ascents. Brown credits Running Water as first turning his attention to the face, and has high praise for its descriptions of mountaineering. (The second ascent for the Brenva route was made by W.A.P. Coolidge and others in 1870).<br>A further note: in Chapter XIII, Mason twice refers to Switzerland when he means France. Perhaps he was dozing; or perhaps he was drawing some of his material from Baedeker's Guide to Switzerland, whose earlier editions included the range of Mont Blanc, a chain shared by France, Italy, and Switzerland.

4At the Villa Rose

By A. E. W. Mason

Harry Wethermill, the brilliant young scientist, a graduate of Oxford and Munich, has made a fortune from his inventions, and is taking a vacation at Aix-les-Bains. There he meets, and immediately falls in love with, the young and beautiful Celia Harland, who serves as companion to the aging but warm-hearted Madam Dauvray of Paris. All this is observed by Julius Ricardo, a retired financier from the City of London, who spends every August at Aix, expecting there to find a pleasant and peaceful life. Imagine his consternation when he learns that Mme. Dauvray has been brutally murdered, and imagine Harry Wethermill's consternation when he learns that every finger of suspicion is pointed at the now vanished Celia Harland.<br>Implored to do so by Wethermill, Ricardo asks his friend Inspector Hanaud, the great detective of the Paris Sûreté (who is also vacationing in Aix) to involve himself in the case so that the truth may come out. Hanaud agrees to do so (with the permission of the Aix police, of course), and goes to work. Will he be up to the job? And will Harry Wethermill ultimately be glad that he called in the great man? We can only wait to find out. But surely Hanaud will exercise his powerful little grey cells – one of several characteristics he shares with a famous Belgian detective of later decades, and indeed some scholars of mystery stories suggest that Agatha Christie, in her invention of Hercule Poirot, owes a debt to Mason and his invention of Inspector Hanaud. And indeed Julius Ricardo has than a passing resemblance to Arthur Hastings, Poirot's sidekick, who is invariably a few confused steps behind the detective.<br>(Introduction by Nicholas Clifford)

5Watchers

By A. E. W. Mason

A dark tale of adventure, piracy, murder, and revenge set on a rugged Cornish island in the mid-1700s. Told with the literary excellence to be expected from the author of The Four Feathers, the tale begins with a dangerous youth who sat in the stocks, and a girl named Helen, and a gang of men watching a granite house at the edge of the sea. NOTE: Contains some language that would be considered offensive to the modern ear. (Christine Dufour)

6Life of Isaac Mason as a Slave

By Isaac Mason

Isaac Mason was born into slavery. As a young man, he escaped to freedom and made a life for himself. An intelligent man, he gave lectures on his experiences and was later encouraged to publish them in book form. - Summary by Lynne Thompson

7Astounding Stories 14, February 1931

By Harry Bates, Charles Willard Diffin, Anthony Gilmore, Desmond Winter Hall, F. V. W. Mason and Captain S. P. Meek

This issue includes "Werewolves of War" by D. W. Hall, "The Tentacles from Below" by Anthony Gilmore, "The Black Lamp" by Captain S. P. Meek, "Phalanxes of Atlans" by F. V. W. Mason, and continues with "The Pirate Planet" by Charles W. Diffin, - Summary by Bill Boerst

8Astounding Stories 15, March 1931

By Ray Cummings, Charles Willard Diffin, F. V. W. Mason, Harl Vincent and Jack Williamson

This issue includes "When the Mountain Came to Miramar" by Charles W. Diffin, "Beyond the Vanishing Point" by Ray Cummings, "Terrors Unseen" by Harl Vincent, the conclusion of "Phalanxes of Atlans" by F. V. W. Mason, and "The Meteor Girl" by Jack Williamson. - Summary by Bill Boerst

This is the first volume in the Home Education Series detailing Charlotte Mason's method of education. This volume is subtitled: The Education of Children under Nine Years of Age. The series is used today by many homeschoolers around the globe and is considered a classic reference by the founder of the homeschooling movement. Volume 1 of 6. - Summary by rachelrw

10Witness for the Defence

By A. E. W. Mason

Part romance, part mystery, part courtroom and quasi-courtroom drama. Young love reignites itself after a hiatus of some years. Or does it? Much can change in that time -- both to the people themselves, and to the events that shape their lives. The action moves from England to India, and back again, confronting the protagonists with problems they never dreamed they’d have to face. ( Nicholas Clifford)

11Clementina

By A. E. W. Mason

This well-written novel is a fictional account of a true historical rescue mission. In 1719, at the age of 17, when she was on her way across Europe to marry James Stuart, the Catholic pretender to the British throne, Princess Maria Clementina Sobieska was kidnapped and held prisoner by Holy Roman Emperor Charles VI, with the approval of his ally, the Protestant king of England. The king feared that the marriage would produce heirs who might raise a rebellion against the Crown, though Stuart’s own rebellion had failed four years earlier. But Irish soldier of fortune and Stuart's ablest spy, hatches a daring plot to rescue the princess. Filled with spies, romance, palace intrigue and uncertain loyalties, this is the story of how Charles Wogan, once indicted for High Treason in Protestant England, set out to play his part on the international stage. Failure would mean certain death at the hands of Wogan's powerful enemies. But would success bring the result he expects? (Jacquerie)<br><br>Prooflisteners: <a href="https://librivox.org/reader/3220">Betty M.</a> and <a href="https://librivox.org/reader/5796">Linette Geisel</a>

Volume two of the Home Education Series by Charlotte Mason talks about parents and children. Charlotte breaks down a couple of different topics about home education, like the family, the parent's role as the teacher, and much more. - Summary by Elijah Fisher

A compendium of Oscar Wilde's wit, including some of his most famous epigrams as well as unpublished quotations supplied by his friends. The book is formatted as a calendar, with one saying for each day of the year, and was edited by Wildean scholar, Stuart Mason (born Christopher Sclater Millard). - Summary by Rob Marland

14Affair at the Semiramis Hotel

By A. E. W. Mason

Inspector Hanaud is a member of the French Sûreté. He is said to have been the model for Agatha Christie’s Hercule Poirot, as well as the opposite of Conan Doyle’s Sherlock Holmes. The Affair At The Semiramis Hotel (1917), a novella, is the second Hanaud mystery. Did the robbery/murder really happen or was it the mescal-induced hallucination of the witness? The first novel is At The Villa Rose (1910). The third is The House Of The Arrow (1924) (there are seven through 1949, available at project gutenberg Australia). In 1910, Mason undertook to create a fictional detective as different as possible from Sherlock Holmes, who had recently been resuscitated after his supposed death by Arthur Conan Doyle in 1903. Inspector Gabriel Hanaud was stout, not gaunt like Holmes; a professional policeman, not a gentleman amateur; from the French Sûreté, not Victorian England; and relying on psychological insights rather than physical evidence. His "Watson" is a retired London banker named Mr. Julius Ricardo. - Summary by David Wales

15House Of The Arrow

By A. E. W. Mason

A young English girl is accused in Dijon of murdering her French aunt. Hanaud to the rescue! Inspector Hanaud is a member of the French Sûreté. He is said to have been the model for Agatha Christie’s Hercule Poirot, as well as the opposite of Conan Doyle’s Sherlock Holmes. In 1910, Mason undertook to create a fictional detective as different as possible from Sherlock Holmes, who had recently been resuscitated after his supposed death by Arthur Conan Doyle in 1903. Inspector Gabriel Hanaud was stout, not gaunt like Holmes; a professional policeman, not a gentleman amateur; from the French Sûreté, not Victorian England; and relying on psychological insights rather than physical evidence. His "Watson" is a retired London banker named Mr. Julius Ricardo, though he appears only briefly in this novel. (David Wales )

This is third volume in the Home Education Series detailing Charlotte Mason's method of education. This volume is subtitled: School Education. The series is used today by many homeschoolers around the globe and is considered a classic reference by the founder of the homeschooling movement. Volume 3 of 6. - Summary by rachelrw / linny

17Woman Of Yesterday

By Caroline Atwater Mason

Anna is the daughter of a clergyman in a small town in Vermont. She is very happy with her lot. But when she goes to nurse a woman in the big city, she starts to discover the world. She sees new places, meets new people, and falls in love. This will test all the resolutions she once held dear. - Summary by Stav Nisser.

This is Book I of the forth volume in the Home Education Series detailing Charlotte Mason's method of education. This volume is subtitled Ourselves and Book I is titled Self-Knowledge. The series is used today by many home-schoolers around the globe and is considered a classic reference by the founder of the homeschooling movement. - Summary by rachelrw / linny

The sixth volume in the Home Education Series detailing Charlotte Mason's method of education. This volume is subtitled A Liberal Education for All. The series is used today by many home-schoolers around the globe and is considered a classic reference by the founder of the homeschooling movement. - Summary by InTheDesert

This is the fifth volume in the Home Education Series detailing Charlotte Mason's method of education. This volume is subtitled "Some Studies in the Formation of Character," although the author explains in the preface why she considers this to be somewhat of a misnomer. The series is used today by many home-schoolers around the globe and is considered a classic reference by the founder of the homeschooling movement. - Summary by Devorah Allen

This is Book II of the fourth volume in the Home Education Series detailing Charlotte Mason's method of education. This volume is subtitled Ourselves and Book II is titled Self Knowledge. The series is used today by many home - schoolers around the globe and is considered a classic reference by the founder of the home - schooling movement. - Summary by L Andrus

In proposing these lectures, my original notion was to popularize and amplify the valuable educational hints contained in some two or three chapters of Dr. Carpenter's "Mental Physiology;" but the subject is a wide one, and I have found it necessary to cover much ground untouched in that work. A complete or worthy treatment of "Home Education" within the limits of a single small volume is out of the question. My attempt is, to suggest a method of education resting upon a basis of natural law: and to touch, in this connection, upon the mother's duties to her children in the three stages of life during which they fall under her personal training, childhood, school-life, and young maidenhood. - Summary by Introductory