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This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs (QPs) and approximate projections arising from partially solving the QPs are sufficient for multiple-term superlinear convergence for nonsmooth problems. Second, we identify additional regularity, which we call the second order supporting hyperplane property (SOSH), that gives multiple-term quadratic convergence. Third, we show that these fast convergence results carry over for the convex inequality problem. Fourth, we show that infeasibility can be detected in finitely many operations. Lastly, we explain how we can use the dual active set QP algorithm of Goldfarb and Idnani to get useful iterates by solving the QPs partially, overcoming the problem of solving large QPs in our algorithms.

We study the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. The FIFO Stack-Up problem asks whether there is some processing of the sequences of bins such that at most p stack-up places are used. In this paper we strengthen the hardness of the FIFO Stack-Up by considering practical cases and the distribution of the pallets onto the sequences. We introduce a digraph model for this problem, the so called decision graph, which allows us to give a breadth first search solution. Further we apply methods to solve hard problems to the FIFO Stack-Up problem. In order to evaluate our algorithms, we introduce a method to generate random, but realistic instances for the FIFO Stack-Up problem. Our experimental study of running times shows that the breadth first search solution on the decision graph combined with a cutting technique can be used to solve practical instances on several thousands of bins of the FIFO Stack-Up problem. Further we analyze two integer programming approaches implemented in CPLEX and GLPK. As expected CPLEX can solve the instances much faster than GLPK and our pallet solution approach is much better than the bin solution approach.

We study the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. The FIFO Stack-Up problem asks whether there is some processing of the sequences of bins such that at most p stack-up places are used. In this paper we strengthen the hardness of the FIFO Stack-Up by considering practical cases and the distribution of the pallets onto the sequences. We introduce a digraph model for this problem, the so called decision graph, which allows us to give a breadth first search solution. Further we apply methods to solve hard problems to the FIFO Stack-Up problem. In order to evaluate our algorithms, we introduce a method to generate random, but realistic instances for the FIFO Stack-Up problem. Our experimental study of running times shows that the breadth first search solution on the decision graph combined with a cutting technique can be used to solve practical instances on several thousands of bins of the FIFO Stack-Up problem. Further we analyze two integer programming approaches implemented in CPLEX and GLPK. As expected CPLEX can solve the instances much faster than GLPK and our pallet solution approach is much better than the bin solution approach.

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

The investigators associated with the research reported herein have been supported by ARO almost continuously over the past 20 years, from the inception of their early development of penalty function and branch and bound methodology. This report covers results developed from 1 January 1974 to 31 May 1981 under two ARO contracts and one grant, results dealing mainly with nonconvex programming, second order algorithms and sensitivity and stability methodology. Technical details are omitted, the main intent being the provision of a concise chronicle of the major accomplishments.

The investigators associated with the research reported herein have been supported by ARO almost continuously over the past 20 years, from the inception of their early development of penalty function and branch and bound methodology. This report covers results developed from 1 January 1974 to 31 May 1981 under two ARO contracts and one grant, results dealing mainly with nonconvex programming, second order algorithms and sensitivity and stability methodology. Technical details are omitted, the main intent being the provision of a concise chronicle of the major accomplishments.

In this lecture, we will study various applications of the theory of Multiplicative Weights (MW). In this section, we brie�y review the general version of the MW algorithm that we studied in the previous lecture. The following sections then show how the theory can be applied to approximately solve zero-sum games and linear programs, and how it connects with the theory of boosting and approximation algorithms.

Donald Knuth is one of the greatest and most impactful computer scientists and mathematicians ever. He is the recipient in 1974 of the Turing Award, considered the Nobel Prize of computing. He is the author of the multi-volume work, the magnum opus, The Art of Computer Programming. He made several key contributions to the rigorous analysis of the computational complexity of algorithms. He popularized asymptotic notation, that we all affectionately know as the big-O notation. He also created the TeX typesetting which most computer scientists, physicists, mathematicians, and scientists and engineers use to write technical papers and make them look

The investigators associated with the research reported herein have been supported by ARO almost continuously over the past 20 years, from the inception of their early development of penalty function and branch and bound methodology. This report covers results developed from 1 January 1974 to 31 May 1981 under two ARO contracts and one grant, results dealing mainly with nonconvex programming, second order algorithms and sensitivity and stability methodology. Technical details are omitted, the main intent being the provision of a concise chronicle of the major accomplishments.

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)

A nonlinear 0-1 program can be restated as a multilinear 0-1 program, which in turn is known to be equivalent to a linear 0-1 program with generalized covering (g.c.) inequalities. In a companion paper 6 we have defined a family of linear inequalities that contains more compact (smaller cardinality) linearizations of a multilinear 0-1 program than the one based on the g.c. inequalities. In this paper we analyze the dominance relations between inequalities of the above family. In particular, we give a criterion that can be checked in linear time, for deciding whether a g.c. inequality can be strengthened by extending the cover from which it was derived. We then describe a class of algorithms based on these results and discuss our computational experience. We conclude that the g.c. inequalities can be strengthened most of the time an extent that increases with problem density. In particular, the algorithm using the strengthening procedure outperforms the one using only g.c. inequalities whenever the number of nonlinear terms per constraint exceeds about 12-15, and the difference in their performance grows with the number of such terms. (Author)

A nonlinear 0-1 program can be restated as a multilinear 0-1 program, which in turn is known to be equivalent to a linear 0-1 program with generalized covering (g.c.) inequalities. In a companion paper 6 we have defined a family of linear inequalities that contains more compact (smaller cardinality) linearizations of a multilinear 0-1 program than the one based on the g.c. inequalities. In this paper we analyze the dominance relations between inequalities of the above family. In particular, we give a criterion that can be checked in linear time, for deciding whether a g.c. inequality can be strengthened by extending the cover from which it was derived. We then describe a class of algorithms based on these results and discuss our computational experience. We conclude that the g.c. inequalities can be strengthened most of the time an extent that increases with problem density. In particular, the algorithm using the strengthening procedure outperforms the one using only g.c. inequalities whenever the number of nonlinear terms per constraint exceeds about 12-15, and the difference in their performance grows with the number of such terms. (Author)

A nonlinear 0-1 program can be restated as a multilinear 0-1 program, which in turn is known to be equivalent to a linear 0-1 program with generalized covering (g.c.) inequalities. In a companion paper 6 we have defined a family of linear inequalities that contains more compact (smaller cardinality) linearizations of a multilinear 0-1 program than the one based on the g.c. inequalities. In this paper we analyze the dominance relations between inequalities of the above family. In particular, we give a criterion that can be checked in linear time, for deciding whether a g.c. inequality can be strengthened by extending the cover from which it was derived. We then describe a class of algorithms based on these results and discuss our computational experience. We conclude that the g.c. inequalities can be strengthened most of the time an extent that increases with problem density. In particular, the algorithm using the strengthening procedure outperforms the one using only g.c. inequalities whenever the number of nonlinear terms per constraint exceeds about 12-15, and the difference in their performance grows with the number of such terms. (Author)

We present a new programming paradigm which can be useful, in particular, for implementing window interfaces and parallel algorithms. This paradigm allows a user to define operators which can contain nested operators. The new paradigm is called operator-oriented. One of the goals of this paradigm is to escape the complexity of objects definitions inherent in many object-oriented languages and to move to transparent algorithms definitions.

Bibliography: p. 20-22

Bibliography: p. 20-22

In this thesis we study several computer implementations of the thinning algorithm, a new method for generating non-homogeneous Poisson processes. The method, developed by Professor P.A.W. Lewis, Naval Postgraduate School, Monterey, California, and G.S. Shedler, IBM Research Laboratory, San Jose, California, is valid for Poisson processes with any given intensity function. The basic thinning algorithm is modified to exploit several refinements which reduce computer execution time by approximately one-third. The basic and modified thinning programs are compared with a previous algorithm of Lewis and Shedler, the Poisson decomposition and gap-statistics algorithm, which is easily implemented for Poisson processes with intensity functions of the form exp (aQ+a, t+a^t 2 ). The thinning programs are competitive in both execution time and computer memory requirements. One program implementation generates the events in a Poisson process one at a time; another program implements the algorithmic refinements which improve efficiency.

In this thesis we study several computer implementations of the thinning algorithm, a new method for generating non-homogeneous Poisson processes. The method, developed by Professor P.A.W. Lewis, Naval Postgraduate School, Monterey, California, and G.S. Shedler, IBM Research Laboratory, San Jose, California, is valid for Poisson processes with any given intensity function. The basic thinning algorithm is modified to exploit several refinements which reduce computer execution time by approximately one-third. The basic and modified thinning programs are compared with a previous algorithm of Lewis and Shedler, the Poisson decomposition and gap-statistics algorithm, which is easily implemented for Poisson processes with intensity functions of the form exp (aQ+a, t+a^t 2 ). The thinning programs are competitive in both execution time and computer memory requirements. One program implementation generates the events in a Poisson process one at a time; another program implements the algorithmic refinements which improve efficiency.

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)

Although large amounts of programming knowledge are available to human programmers in the form of books and articles, very little of this knowledge is available in a form suitable for use by a machine in performing programming tasks automatically. The principal goal of the research reported here is the explication of programming knowledge to a sufficient level of detail that it can be used effectively by a machine. The programming task considered in this experiment is that of constructing concrete implementations of abstract algorithms in the domain of symbolic programming. Knowledge about several aspects of symbolic programming has been expressed as a collection of four hundred refinement rules. The rules deal primarily with collections and mappings and ways of manipulating such structures, including several enumeration, sorting and searching techniques. The principal representation techniques covered include the representation of sets as linked lists and arrays (both ordered and unordered), and the representation of mappings as tables, sets of pairs, property list markings, and inverted mappings (indexed by range element). In addition to these general constructs, many low-level programming details are covered (such as the use of variables to store values).

Although large amounts of programming knowledge are available to human programmers in the form of books and articles, very little of this knowledge is available in a form suitable for use by a machine in performing programming tasks automatically. The principal goal of the research reported here is the explication of programming knowledge to a sufficient level of detail that it can be used effectively by a machine. The programming task considered in this experiment is that of constructing concrete implementations of abstract algorithms in the domain of symbolic programming. Knowledge about several aspects of symbolic programming has been expressed as a collection of four hundred refinement rules. The rules deal primarily with collections and mappings and ways of manipulating such structures, including several enumeration, sorting and searching techniques. The principal representation techniques covered include the representation of sets as linked lists and arrays (both ordered and unordered), and the representation of mappings as tables, sets of pairs, property list markings, and inverted mappings (indexed by range element). In addition to these general constructs, many low-level programming details are covered (such as the use of variables to store values).

The investigators associated with the research reported herein have been supported by ARO almost continuously over the past 20 years, from the inception of their early development of penalty function and branch and bound methodology. This report covers results developed from 1 January 1974 to 31 May 1981 under two ARO contracts and one grant, results dealing mainly with nonconvex programming, second order algorithms and sensitivity and stability methodology. Technical details are omitted, the main intent being the provision of a concise chronicle of the major accomplishments.

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)

A number of algorithms were developed for image warping and pyramid image filtering. Techniques were investigated for the parallel processing of a large number of independent irregular shaped regions on the MPP. In addition some utilities for dealing with very long vectors and for sorting were developed. Documentation pages for the algorithms which are available for distribution are given. The performance of the MPP for a number of basic data manipulations was determined. From these results it is possible to predict the efficiency of the MPP for a number of algorithms and applications. The Parallel Pascal development system, which is a portable programming environment for the MPP, was improved and better documentation including a tutorial was written. This environment allows programs for the MPP to be developed on any conventional computer system; it consists of a set of system programs and a library of general purpose Parallel Pascal functions. The algorithms were tested on the MPP and a presentation on the development system was made to the MPP users group. The UNIX version of the Parallel Pascal System was distributed to a number of new sites.

A number of algorithms were developed for image warping and pyramid image filtering. Techniques were investigated for the parallel processing of a large number of independent irregular shaped regions on the MPP. In addition some utilities for dealing with very long vectors and for sorting were developed. Documentation pages for the algorithms which are available for distribution are given. The performance of the MPP for a number of basic data manipulations was determined. From these results it is possible to predict the efficiency of the MPP for a number of algorithms and applications. The Parallel Pascal development system, which is a portable programming environment for the MPP, was improved and better documentation including a tutorial was written. This environment allows programs for the MPP to be developed on any conventional computer system; it consists of a set of system programs and a library of general purpose Parallel Pascal functions. The algorithms were tested on the MPP and a presentation on the development system was made to the MPP users group. The UNIX version of the Parallel Pascal System was distributed to a number of new sites.

Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague's use of lambda calculus formulas as meaning of words and phrases. With ASP as the target language the meaning of words and phrases are ASP-lambda formulas. In an earlier work we illustrated our approach by manually developing a dictionary of words and their ASP-lambda formulas. However such an approach is not scalable. In this paper our focus is on two algorithms that allow one to construct ASP-lambda formulas in an inverse manner. In particular the two algorithms take as input two lambda-calculus expressions G and H and compute a lambda-calculus expression F such that F with input as G, denoted by F@G, is equal to H; and similarly G@F = H. We present correctness and complexity results about these algorithms. To do that we develop the notion of typed ASP-lambda calculus theories and their orders and use it in developing the completeness results. (To appear in Theory and Practice of Logic Programming.)

ai how i fail

The investigators associated with the research reported herein have been supported by ARO almost continuously over the past 20 years, from the inception of their early development of penalty function and branch and bound methodology. This report covers results developed from 1 January 1974 to 31 May 1981 under two ARO contracts and one grant, results dealing mainly with nonconvex programming, second order algorithms and sensitivity and stability methodology. Technical details are omitted, the main intent being the provision of a concise chronicle of the major accomplishments.

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)

Outline: 1) Introduction * Optimal control * Dynamic programming (DP). 2) Path Planning * Discrete planning as optimal control * Dijkstra's algorithm & its problems * Continuous DP & the Hamilton-Jacobi (HJ) PDE * The fast marching method (FMM): Dijkstra's for continuous spaces. 3) Algorithms for Static HJ PDEs * Four alternatives * FMM pros & cons. 4) Generalizations * Alternative action norms * Multiple objective planning.

This paper investigates session programming and typing of benchmark examples to compare productivity, safety and performance with other communications programming languages. Parallel algorithms are used to examine the above aspects due to their extensive use of message passing for interaction, and their increasing prominence in algorithmic research with the rising availability of hardware resources such as multicore machines and clusters. We contribute new benchmark results for SJ, an extension of Java for type-safe, binary session programming, against MPJ Express, a Java messaging system based on the MPI standard. In conclusion, we observe that (1) despite rich libraries and functionality, MPI remains a low-level API, and can suffer from commonly perceived disadvantages of explicit message passing such as deadlocks and unexpected message types, and (2) the benefits of high-level session abstraction, which has significant impact on program structure to improve readability and reliability, and session type-safety can greatly facilitate the task of communications programming whilst retaining competitive performance.

We propose Chunks and Tasks, a parallel programming model built on abstractions for both data and work. The application programmer specifies how data and work can be split into smaller pieces, chunks and tasks, respectively. The Chunks and Tasks library maps the chunks and tasks to physical resources. In this way we seek to combine user friendliness with high performance. An application programmer can express a parallel algorithm using a few simple building blocks, defining data and work objects and their relationships. No explicit communication calls are needed; the distribution of both work and data is handled by the Chunks and Tasks library. This makes efficient implementation of complex applications that require dynamic distribution of work and data easier. At the same time, Chunks and Tasks imposes restrictions on data access and task dependencies that facilitates the development of high performance parallel back ends. We discuss the fundamental abstractions underlying the programming model, as well as performance and fault resilience considerations. We also present a pilot C++ library implementation for clusters of multicore machines and demonstrate its performance for sparse blocked matrix-matrix multiplication.

We propose Chunks and Tasks, a parallel programming model built on abstractions for both data and work. The application programmer specifies how data and work can be split into smaller pieces, chunks and tasks, respectively. The Chunks and Tasks library maps the chunks and tasks to physical resources. In this way we seek to combine user friendliness with high performance. An application programmer can express a parallel algorithm using a few simple building blocks, defining data and work objects and their relationships. No explicit communication calls are needed; the distribution of both work and data is handled by the Chunks and Tasks library. This makes efficient implementation of complex applications that require dynamic distribution of work and data easier. At the same time, Chunks and Tasks imposes restrictions on data access and task dependencies that facilitates the development of high performance parallel back ends. We discuss the fundamental abstractions underlying the programming model, as well as performance and fault resilience considerations. We also present a pilot C++ library implementation for clusters of multicore machines and demonstrate its performance for sparse blocked matrix-matrix multiplication.

We propose Chunks and Tasks, a parallel programming model built on abstractions for both data and work. The application programmer specifies how data and work can be split into smaller pieces, chunks and tasks, respectively. The Chunks and Tasks library maps the chunks and tasks to physical resources. In this way we seek to combine user friendliness with high performance. An application programmer can express a parallel algorithm using a few simple building blocks, defining data and work objects and their relationships. No explicit communication calls are needed; the distribution of both work and data is handled by the Chunks and Tasks library. This makes efficient implementation of complex applications that require dynamic distribution of work and data easier. At the same time, Chunks and Tasks imposes restrictions on data access and task dependencies that facilitates the development of high performance parallel back ends. We discuss the fundamental abstractions underlying the programming model, as well as performance and fault resilience considerations. We also present a pilot C++ library implementation for clusters of multicore machines and demonstrate its performance for sparse blocked matrix-matrix multiplication.

Motivated by Bland's linear-programming generalization of the renowned Edmonds-Karp efficient refinement of the Ford-Fulkerson maximum-flow algorithm, we discuss three closely-related natural augmentation rules for linear and integer-linear optimization. In several nice situations, we show that polynomially-many augmentation steps suffice to reach an optimum. In particular, when using "discrete steepest-descent augmentations" (i.e., directions with the best ratio of cost improvement per unit 1-norm length), we show that the number of augmentation steps is bounded by the number of elements in the Graver basis of the problem matrix, giving the first ever strongly polynomial-time algorithm for $N$-fold integer-linear optimization. Our results also improve on what is known for such algorithms in the context of linear optimization (e.g., generalizing the bounds of Kitahara and Mizuno for the number of steps in the simplex method) and are closely related to research on the diameters of polytopes and the search for a strongly polynomial-time simplex or augmentation algorithm.

Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which enables them to construct solutions in a dynamic programming fashion. We take a general approach and relate the construction of such algorithms to the development of algorithms using dynamic programming techniques. Thereby, we give general guidelines on how to develop evolutionary algorithms that have the additional ability of carrying out dynamic programming steps. Finally, we show that for a wide class of the so-called DP-benevolent problems (which are known to admit FPTAS) there exists a fully polynomial-time randomized approximation scheme based on an evolutionary algorithm.

Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which enables them to construct solutions in a dynamic programming fashion. We take a general approach and relate the construction of such algorithms to the development of algorithms using dynamic programming techniques. Thereby, we give general guidelines on how to develop evolutionary algorithms that have the additional ability of carrying out dynamic programming steps. Finally, we show that for a wide class of the so-called DP-benevolent problems (which are known to admit FPTAS) there exists a fully polynomial-time randomized approximation scheme based on an evolutionary algorithm.

Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications discusses algorithmic developments in the context of genetic algorithms (GAs) and genetic programming (GP). It applies the algorithms to significant combinatorial optimization problems and describes structure identification using HeuristicLab as a platform for al

The class $(r,2)$-CSP, or simply Max 2-CSP, consists of constraint satisfaction problems with at most two $r$-valued variables per clause. For instances with $n$ variables and $m$ binary clauses, we present an $O(n r^{5+19m/100})$-time algorithm which is the fastest polynomial-space algorithm for many problems in the class, including Max Cut. The method also proves a treewidth bound $\tw(G) \leq (13/75+o(1))m$, which gives a faster Max 2-CSP algorithm that uses exponential space: running in time $\Ostar{2^{(13/75+o(1))m}}$, this is fastest for most problems in Max 2-CSP. Parametrizing in terms of $n$ rather than $m$, for graphs of average degree $d$ we show a simple algorithm running time $\Ostar{2^{(1-\frac{2}{d+1})n}}$, the fastest polynomial-space algorithm known. In combination with ``Polynomial CSPs'' introduced in a companion paper, these algorithms also allow (with an additional polynomial-factor overhead in space and time) counting and sampling, and the solution of problems like Max Bisection that escape the usual CSP framework. Linear programming is key to the design as well as the analysis of the algorithms.

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)

This is the third and final report on the work done for NASA Grant 5-403 on Algorithms and Programming Tools for Image Processing on the MPP:3. All the work done for this grant is summarized in the introduction. Work done since August 1986 is reported in detail. Research for this grant falls under the following headings: (1) fundamental algorithms for the MPP; (2) programming utilities for the MPP; (3) the Parallel Pascal Development System; and (4) performance analysis. In this report, the results of two efforts are reported: region growing, and performance analysis of important characteristic algorithms. In each case, timing results from MPP implementations are included. A paper is included in which parallel algorithms for region growing on the MPP is discussed. These algorithms permit different sized regions to be merged in parallel. Details on the implementation and peformance of several important MPP algorithms are given. These include a number of standard permutations, the FFT, convolution, arbitrary data mappings, image warping, and pyramid operations, all of which have been implemented on the MPP. The permutation and image warping functions have been included in the standard development system library.

This is CMPE 130 Course's Sylabus

We present a new parallel algorithm for computing a least-squares solution to a sparse overdetermined system of linear equations Ax=b such that mXn matrix A is sparse and the graph, G = (V,E), of the matrix H. Our algorithm uses O(log(m+n) log squared s(m+n)) steps and or = s cubed (m+n) processors; it relies on our recent parallel algorithm for solving sparse linear systems. The objective of this paper is to reexamine the time-complexity of the l.l.s.p. and to indicate the possibility of speeding up its solution using the parallel algorithms of PR in brackets. As a major consequence, (which may become decisive for determining the best algorithm for the linear programming problem (l.p.p) at least over some important classes of instances of that problem), we will substantially speed up Karmarkar's algorithm, K, for the l.p.p. because solving the l.l.s.p. constitutes the most costly part of every iteration of that algorithm. A very wide range of applications leads to in particular the acceleration of the simplex algorithms, see C,M, for sparse l.p. problems. Further applications may include several combinatorial computations. In the next section we recall two known representations of the l.l.s.p. using normal equations. In sect. 3 we reexamine the computational cost of sequential algorithms for l.l.s.p. In sect. 4 we estimate the cost of performing our parallel algorithm for the same problem. In sect. 5 we consider one of the major applications of our results, that is, to the acceleration of Karmarkar's algorithm. In Appendix we will briefly comment on the current estimates for the computational cost of solving the l.p.p. Keywords: Nested dissection; Linear programming; Karmarkar's algorithm.

In course design, topic outline organization encompasses the structuring and sequencing of topics to be delivered in a learning environment. Recent studies in topic outline optimization revolve around massive open online courses (MOOCs) due to their abundance but not much has been studied on the traditional courses. This study investigates the organization of topic outlines in traditional introductory programming courses across Philippine higher education institutions (HEIs) and evaluates the viability of the synthesized alternative topic outlines. Course syllabi were collected from 16 HEIs. A topic precedence graph (TPG) model that provides a structured overview of the introductory programming was created via a semi-supervised pairwise constrained k-means (PCK-Means) clustering to structure the topics which produced 20 topic clusters with strong topic cohesion within the clusters. The TPG showed that HEIs tend to start the outline similarly, followed by core programming topics with varied sequences, and divergent ways of ending the outline. Two anomaly clusters were identified as having topic titles grouped that do not seem to have a unifying topic. Limitations of the clustering algorithm are identified where it cannot identify semantic meaning between words which may affect its applicability in situations where topic titles are named inconsistently. From the TPG, alternative optimal and comprehensive topic outlines were synthesized via greedy and DFS graph traversal algorithms. However, these alternative outlines performed very poorly when compared with the evaluators' (n=19) arrangement of topic outlines due to some prerequisite topics being discussed in the latter part already. Overall, this study introduces a method to incorporate computer science technologies in structuring topics across HEIs and aiding educators in topic outline design but more research is needed before it can be implemented in a real classroom setting.

In course design, topic outline organization encompasses the structuring and sequencing of topics to be delivered in a learning environment. Recent studies in topic outline optimization revolve around massive open online courses (MOOCs) due to their abundance but not much has been studied on the traditional courses. This study investigates the organization of topic outlines in traditional introductory programming courses across Philippine higher education institutions (HEIs) and evaluates the viability of the synthesized alternative topic outlines. Course syllabi were collected from 16 HEIs. A topic precedence graph (TPG) model that provides a structured overview of the introductory programming was created via a semi-supervised pairwise constrained k-means (PCK-Means) clustering to structure the topics which produced 20 topic clusters with strong topic cohesion within the clusters. The TPG showed that HEIs tend to start the outline similarly, followed by core programming topics with varied sequences, and divergent ways of ending the outline. Two anomaly clusters were identified as having topic titles grouped that do not seem to have a unifying topic. Limitations of the clustering algorithm are identified where it cannot identify semantic meaning between words which may affect its applicability in situations where topic titles are named inconsistently. From the TPG, alternative optimal and comprehensive topic outlines were synthesized via greedy and DFS graph traversal algorithms. However, these alternative outlines performed very poorly when compared with the evaluators' (n=19) arrangement of topic outlines due to some prerequisite topics being discussed in the latter part already. Overall, this study introduces a method to incorporate computer science technologies in structuring topics across HEIs and aiding educators in topic outline design but more research is needed before it can be implemented in a real classroom setting.

The main purpose of this work is to give explicit sparsity-preserving SOR(Successive Overrelaxation) algorithms for the solution of separable quadratic and linear programming problems. The principal and computationally distinguishing feature of the present SOR algorithms is that they preserve the sparsity structure of the problem and do not require the computation of the product of the constraint matrix by its transpose as is the case in earlier SOR algorithms for linear and quadratic programming. (Author)