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We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process is driven by an ergodic Markov chain and is reflected on the boundary of the d-dimensional cube. In the large resource limit, we prove Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi equation with a Neumann boundary condition. We give a complete analysis of the colliding 2-stacks problem and show an example where the system has a stable attractor which is a limit cycle.

In this paper, we determine the optimal convergence rates for strongly convex and smooth distributed optimization in two settings: centralized and decentralized communications over a network. For centralized (i.e. master/slave) algorithms, we show that distributing Nesterov's accelerated gradient descent is optimal and achieves a precision $\varepsilon > 0$ in time $O(\sqrt{\kappa_g}(1+\Delta\tau)\ln(1/\varepsilon))$, where $\kappa_g$ is the condition number of the (global) function to optimize, $\Delta$ is the diameter of the network, and $\tau$ (resp. $1$) is the time needed to communicate values between two neighbors (resp. perform local computations). For decentralized algorithms based on gossip, we provide the first optimal algorithm, called the multi-step dual accelerated (MSDA) method, that achieves a precision $\varepsilon > 0$ in time $O(\sqrt{\kappa_l}(1+\frac{\tau}{\sqrt{\gamma}})\ln(1/\varepsilon))$, where $\kappa_l$ is the condition number of the local functions and $\gamma$ is the (normalized) eigengap of the gossip matrix used for communication between nodes. We then verify the efficiency of MSDA against state-of-the-art methods for two problems: least-squares regression and classification by logistic regression.

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithm's correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results.

In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning tree after dynamic changes like edge weight changes, rather than having to recompute it from scatch each time. The first part of the paper surveys various algorithms available today both in sequential and distributed environments to solve static MST problem. We also present some of the efficient sequential algorithms for computing dynamic MST like the Frederickson's algorithm and Eppstein's sparsification technique. Lastly we present our new sequential and distributed algorithms for dynamic MST problem. To our knowledge, this is the first of the distributed algorithms for computing dynamic MSTs.

We consider distributed optimization over orthogonal collision channels in spatial random access networks. Users are spatially distributed and each user is in the interference range of a few other users. Each user is allowed to transmit over a subset of the shared channels with a certain attempt probability. We study both the non-cooperative and cooperative settings. In the former, the goal of each user is to maximize its own rate irrespective of the utilities of other users. In the latter, the goal is to achieve proportionally fair rates among users. Simple distributed learning algorithms are developed to solve these problems. The efficiencies of the proposed algorithms are demonstrated via both theoretical analysis and simulation results.

A new method for enhancing the convergence rate of iterative algorithms for the numerical integration of systems of partial differential equations was developed. It is termed the Distributed Minimal Residual (DMR) method and it is based on general Krylov subspace methods. The DMR method differs from the Krylov subspace methods by the fact that the iterative acceleration factors are different from equation to equation in the system. At the same time, the DMR method can be viewed as an incomplete Newton iteration method. The DMR method was applied to Euler equations of gas dynamics and incompressible Navier-Stokes equations. All numerical test cases were obtained using either explicit four stage Runge-Kutta or Euler implicit time integration. The formulation for the DMR method is general in nature and can be applied to explicit and implicit iterative algorithms for arbitrary systems of partial differential equations.

The purpose of this research is to explore methods used to parallelize NP-complete problems and the degree of improvement that can be realized using different methods of load balancing. A serial and four parallel A* branch and bound algorithms were implemented and executed on an Intel iPSC/2 hypercube computer. One parallel algorithm used a global, or centralized, list to store unfinished work and the other three parallel algorithms used a distributed list to store unfinished work locally on each processor. the three distributed list algorithms are: without load balancing, with load balancing, and with load balancing and work distribution. The difference between load balancing and work distribution is load balancing only occurs when a processor becomes idle and work distribution attempts to emulate the global list of unfinished work by sharing work throughout the algorithm, not just at the end. Factors which effect when and how often to load balance are also investigated. which algorithm performed best depended on how many processors were used to solve the problem. For a small number of processors, 16 or less, the centralized list algorithm easily outperformed all others. However, after 16 processors, the overhead of all processors trying to communicate and request work from the same centralized list began to outweigh any benefits of having a global list. Now the distributed list algorithms began to perform best. When using 32 processors, the distributed list with load balancing and work distribution out performed the other algorithms. Search, Hypercube, Parallel, NP-complete.

The goal of this project was to develop algorithms which will process the information collected by networks of large numbers of low power, low bandwidth sensors. We have analyzed failure modes for simple cases of hierarchical networks, developed foundational results in logic programming and hybrid control, and constructed a simulation package. We would like to continue with this project which, despite a slow start, is now-after 3 quarters-showing results.

Multisensor data fusion combines data from multiple sensor systems to achieve improved performance and provide more inferences than could be achieved using a single sensor system. One of the most important aspects of data fusion is data association. This dissertation develops new algorithms for data association, including measurement to track association, track to track association and track fusion, in distributed multisensor multitarget environment with overlapping sensor coverage. The performance of the proposed algorithms is compared to that of existing techniques. Computational complexity analysis is also presented. Numerical results based on Monte Carlo simulations and real data collected from the United States Coast Guard Vessel Traffic Services system are presented. The results show that the proposed algorithms reduce the computational complexity and achieve considerable performance improvement over those previously reported in the literature.

In this thesis we study the performance of update algorithms for replicated data in a distributed database. In doing so, we also investigate several other related issues. We start by presenting a simple model of a distributed database which is suitable for studying updates and concurrency control. We also develop a performance model and a set of parameters which represent the most important performance features of a distributed database. The distributed database models are used to study the performance of update algorithms for replicated data. This is done in two steps. First the algorithms are analyzed in the case of completely replicated databases in a no failure, update only environment. Then, the restrictions that we made are eliminated one at a time, and the impact on the system performance of doing this is evaluated. For the first step, we develop a new technique for analyzing the performance of update algorithms. This iterative technique is based on queueing theory. Several well known update algorithms are analyzed using this technique. The performance results are verified through detailed simulations of the algorithms. The results show that centralized control algorithms nearly always perform better than the more popular distributed control algorithms.

The authors use the paradigm of diffusing computation, introduced by Dijkstra and Scholten, to solve a class of graph problems. They present a detailed solution to the problem of computing shortest paths from a single vertex to all other vertices, in the presence of negative cycles. (Author)

The last years have seen a thriving research activity on cooperative control and motion coordination. This interest is motivated by the growing possibilities enabled by robotic networks in the monitoring of natural phenomena and the enhancement of human capabilities in hazardous and unknown environments. Our first objective with this book is to present a coherent introduction to basic distributed algorithms for robotic networks. This emerging discipline sits at the intersection of different areas such as distributed algorithms, parallel processing, control, and estimation. Our second objective is to provide a self-contained, broad exposition of the notions and tools from these areas that are relevant in cooperative control problems. These concepts include graph-theoretic notions (connectivity, adjacency and Laplacian matrices), distributed algorithms from computer science (leader election, basic tree computations) and from parallel processing (averaging algorithms, convergence rates), and geometric models and optimization (Voronoi partitions, proximity graphs). Our third objective is to put forth a model for robotic networks that helps to rigorously formalize coordination algorithms running on them. We illustrate how computational geometry plays an important role in modeling the interconnection topology of robotic networks. We draw on classical notions from distributed algorithms to provide complexity measures that characterize the execution of coordination algorithms. Such measures allow us to quantify the algorithm performance and implementation costs. Our fourth and last objective is to present various algorithms for coordination tasks such as connectivity maintenance, rendezvous, and deployment. We put special emphasis on analyzing the correctness of the algorithms and providing measures of their complexity.

Presented is a short tutorial survey of algorithms for locating and identifying spatially distributed sources and receivers. The emphasis is on methods that are either considered to be very basic or lend themselves potentially to distributed computations, the main objective of this work.

We consider the distributed version of the Multiple Knapsack Problem (MKP), where $m$ items are to be distributed amongst $n$ processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff between time and message complexities. The algorithms are based on the greedy approach of assigning the best item to the knapsack with the largest capacity. These algorithms obtain a solution with a bound of $\frac{1}{n+1}$ times the optimum solution, with either $\mathcal{O}\left(m\log n\right)$ time and $\mathcal{O}\left(m n\right)$ messages, or $\mathcal{O}\left(m\right)$ time and $\mathcal{O}\left(mn^{2}\right)$ messages.

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a different node, and a limited number of gradient oracle calls is allowed at each node. In this framework, we introduce a convex optimization algorithm based on the stochastic gradient descent (SGD) updates. Particularly, we use a carefully designed time-dependent weighted averaging of the SGD iterates, which yields a convergence rate of $O\left(\frac{N\sqrt{N}}{T}\right)$ after $T$ gradient updates for each node on a network of $N$ nodes. We then show that after $T$ gradient oracle calls, the average SGD iterate achieves a mean square deviation (MSD) of $O\left(\frac{\sqrt{N}}{T}\right)$. This rate of convergence is optimal as it matches the performance lower bound up to constant terms. Similar to the SGD algorithm, the computational complexity of the proposed algorithm also scales linearly with the dimensionality of the data. Furthermore, the communication load of the proposed method is the same as the communication load of the SGD algorithm. Thus, the proposed algorithm is highly efficient in terms of complexity and communication load. We illustrate the merits of the algorithm with respect to the state-of-art methods over benchmark real life data sets and widely studied network topologies.

Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting transitions to be nondeterministic or deterministic, we also obtain two strictly weaker variants of our automata for which the emptiness problem is decidable. As an application, we suggest how suitable graph automata might be useful in formal verification of distributed algorithms, using Floyd-Hoare logic.

Distributed Computing Principles, Algorithms, and Systems

Distributed Computing Principles, Algorithms, and Systems

We study the stability properties of linear time-varying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibrium set contains all states with identical state components. We present sufficient conditions guaranteeing uniform exponential stability of this equilibrium set, implying that all state components converge to a common value as time grows unbounded. Furthermore it is shown that this convergence result is robust with respect to an arbitrary delay, provided that the delay affects only the off-diagonal terms in the differential equation.

We study the stability properties of linear time-varying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibrium set contains all states with identical state components. We present sufficient conditions guaranteeing uniform exponential stability of this equilibrium set, implying that all state components converge to a common value as time grows unbounded. Furthermore it is shown that this convergence result is robust with respect to an arbitrary delay, provided that the delay affects only the off-diagonal terms in the differential equation.

Distributed systems deadlock is similar to single-processor system deadlock, but is worse. It is harder to avoid, prevent or detect and is harder to cure, when it is tracked down because all the relevant information is scattered over many machines. In some systems, such as distributed database systems, it can be extremely serious, so it is important to understand how it differs from ordinary deadlock and what can be done about it. Two important deadlock prevention algorithms in distributed systems are wait-die and wound-wait. Their problem is that they just attend to the time stamp of processes, but not priority of them. In a real operating system, attending to priority of processes is very important. The proposed improved algorithms are attending to both priority and time stamp of processes.

Typical desktop workstations can be a severe bottleneck in the viewing and enhancement of imagery data. Due to the nature of many image processing algorithms, an effective method for alleviating this problem is through parallelism. Parallel hardware can come in many forms, from small clusters of workstations and workstations with many processors to dedicated hardware containing 10's, 100's and 1000's of processing nodes. One of the challenges is developing a portable parallel image processing library in such a potentially diverse environment. These issues led to the development of a Parallel Image Processing Toolkit (PIPT). The toolkit hides the detail of parallelization from the users of the PIPT and provides a uniform programming interface. In developing the toolkit the issues of advanced data handling, load, balancing and parallel visualization were addressed. In addition a specific computationally expensive High Resolution Video Stills algorithm was implemented within the PIPT. The important contributions that resulted from this work transcend the individual tasks that were undertaken. First, the general approach that was taken to implement the PIPT illustrates several important principles for the design and implementation of general purpose parallel libraries. in this regard, the PIPT design can serve as a design pattern for an extensible parallel library. Second, the design pattern of the current implementation of the PIPT contains some notable attempts at programming image processing tasks in a generic fashion.

The research described in this report is presented in six parts: (1) On Interprocess Communication studies interprocess communication without assuming any lower-level communication primitives. A formalism is developed for reasoning about concurrent systems that does not assume an atomic grain of action, (2) The Intersecting Broadcast Machine is a novel array processor architecture, capable of processing efficiently programs whose arbitrary or complex structure would make them difficult to map onto conventional array processors. The architecture also supports fault-tolerant operation, (3) Broadcast Protocols for Distributed Systems considers how the broadcast character of coummications media such as Ethernet and packet radio can be exploited to yield reliable communication witt very little overhead, (4) Extending Interval Logic to Real Time Systems presents a technique for the formal expression of the real-time constraints that are critical to the specification of fault-tolerant distributed systems, (5) Consistency of Replicated Information in Multichannel Fault Tolerant Systems considers the possibility of using similar, but not identical, processing in the replicas of a fault-tolerant system. Conventional fault-tolerant systems using replicated processing require the replicas to be identical, so that they can be compared by exact match algorithms. This exact replication increases the risk that a common fault will affect all replicas and cause system failure, and (6) Experimental Implementation and Evaluation of the TRANS Broadcast Protocol describes an Implementation and evaluation of the broadcast protocol outlined in Part III.

This report describes the research activities in the Information Systems Laboratory at Stanford University on Distributed Sensor Networks (DSN). The objectives are to develop new and innovative signal processing and computer network techniques with applications to systems employing multiple sensors for target surveillance and tracking. Such systems would be composed of sensors, processors, and data bases distributed throughout an area, interconnected by a suitable communication system. The system will serve a user-community that is also distributed and connected to the same communication system. A basic premise of our approach is that most of the currently available signal processing algorithms are not well suited to the DSN problem because of their highly centralized structure. The straightforward application of standard techniques in the context of distributed networks leads to ad hoc, suboptimal designs. We feel that it is essential to have a more careful look at the basic requirements for developing and implementing distributed algorithms. Our preliminary conclusions were that improved system performance and a more natural system structure will result if innovative signal processing modules will be used; new analytical and computational techniques have to be developed and used in the DSN design, rather than trying to adapt this problem to standard solutions. Accordingly, the major emphasis of our research effort to date has been the development of novel signal processing algorithms which are especially suited to the DSN.

One routing strategy frequently used in computer networks assigns traffic dependent distances to the links of the network and then increases the traffic flow on shortest paths. If a central facility monitors all network traffic, classical algorithms can be readily employed to compute shortest paths. If traffic is only locally monitored, we wish to have distributed procedures in which the nodes begin with only local information and compute shortest paths by communicating with one another. We present several such distributed shortest path algorithms and analyze their communication cost. Since the transmission of control information required for network operation reduces the bandwidth available to users, we concentrate on finding algorithms that use a minimum of information exchange.

This paper presents two distributed algorithms for finding shortest paths from a source node to all other nodes in an N-node network. These algorithms are executed at individual nodes using only local information. Algorithm 1 works in networks where there are no topological changes such as link failures, link recoveries or changes of link lengths. Algorithm 2 is a mofification of Algorithm 1 for networks where there are topological changes. Algorithm 1 determines the optimal shortest paths in at most N3/4 steps, which is only one-half of the computational upper bounds of Abram and Rhodes' and Segall, Merlin and Gallager's algorithms. After the last topological change, Algorithm 2 determines the optimal shortest paths in the same number of steps as Algorithm 1. There are many situations where the present algorithms will work up to N/2 times faster than the algorithms proposed by these authors. (Author)

This paper describes a new fast and implicitly parallel approach to neighbour-finding in multi-resolution Smoothed Particle Hydrodynamics (SPH) simulations. This new approach is based on hierarchical cell decompositions and sorted interactions, within a task-based formulation. It is shown to be faster than traditional tree-based codes, and to scale better than domain decomposition-based approaches on hybrid shared/distributed-memory parallel architectures, e.g. clusters of multi-cores, achieving a $40\times$ speedup over the Gadget-2 simulation code.

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not often exploited in previously published mesh-related algorithms. This is because the branches are not explicitly stored, and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work we combine hierarchical and topological relationships between octree branches to design efficient recursive algorithms. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a domain partition, as well as every interface (face, edge and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order $C^0$ nodal basis functions. We analyze the complexity of the new recursive algorithms theoretically, and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458k cores of the JUQUEEN supercomputer.

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not often exploited in previously published mesh-related algorithms. This is because the branches are not explicitly stored, and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work we combine hierarchical and topological relationships between octree branches to design efficient recursive algorithms. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a domain partition, as well as every interface (face, edge and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order $C^0$ nodal basis functions. We analyze the complexity of the new recursive algorithms theoretically, and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458k cores of the JUQUEEN supercomputer.

Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of $U$-statistics, relying on more expensive averaging over pairs of observations, is a less investigated area. Yet, such data functionals are essential to describe global properties of a statistical population, with important examples including Area Under the Curve, empirical variance, Gini mean difference and within-cluster point scatter. This paper proposes new synchronous and asynchronous randomized gossip algorithms which simultaneously propagate data across the network and maintain local estimates of the $U$-statistic of interest. We establish convergence rate bounds of $O(1/t)$ and $O(\log t / t)$ for the synchronous and asynchronous cases respectively, where $t$ is the number of iterations, with explicit data and network dependent terms. Beyond favorable comparisons in terms of rate analysis, numerical experiments provide empirical evidence the proposed algorithms surpasses the previously introduced approach.

This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.) time-series consisting of a nonlinear function of the true but unknown parameter corrupted by noise. A distributed recursive estimator of the \emph{consensus} + \emph{innovations} type, namely $\mathcal{CIWNLS}$, is proposed, in which the agents update their parameter estimates at each observation sampling epoch in a collaborative way by simultaneously processing the latest locally sensed information~(\emph{innovations}) and the parameter estimates from other agents~(\emph{consensus}) in the local neighborhood conforming to a pre-specified inter-agent communication topology. Under rather weak conditions on the connectivity of the inter-agent communication and a \emph{global observability} criterion, it is shown that at every network agent, the proposed algorithm leads to consistent parameter estimates. Furthermore, under standard smoothness assumptions on the local observation functions, the distributed estimator is shown to yield order-optimal convergence rates, i.e., as far as the order of pathwise convergence is concerned, the local parameter estimates at each agent are as good as the optimal centralized nonlinear least squares estimator which would require access to all the observations across all the agents at all times. In order to benchmark the performance of the proposed distributed $\mathcal{CIWNLS}$ estimator with that of the centralized nonlinear least squares estimator, the asymptotic normality of the estimate sequence is established and the asymptotic covariance of the distributed estimator is evaluated. Finally, simulation results are presented which illustrate and verify the analytical findings.

We initiate a thorough study of \emph{distributed property testing} -- producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called \emph{dense} testing model we emulate sequential tests for nearly all graph properties having $1$-sided tests, while in the \emph{sparse} and \emph{general} models we obtain faster tests for triangle-freeness and bipartiteness respectively. In most cases, aided by parallelism, the distributed algorithms have a much shorter running time as compared to their counterparts from the sequential querying model of traditional property testing. The simplest property testing algorithms allow a relatively smooth transitioning to the distributed model. For the more complex tasks we develop new machinery that is of independent interest. This includes a method for distributed maintenance of multiple random walks.

We study the problem of source localization as a multiple hypothesis testing, where each hypothesis corresponds to the event that the source belongs to a particular region. We use sequential hypothesis tests based on posterior computations to solve for the correct hypothesis. Measurements corrupted with noise are used to calculate conditional posteriors. We prove that the regional localization problem has geometric properties that allow correct detection almost surely in the limit of infinite measurements. We present the Sense, Transmit & Test algorithm that allows sequential sensing communication and testing and we analyze the accuracy of this distributed algorithm and show that the test ends in a finite time. We also present numerical results illustrating properties of the suggested algorithm.

Role allocation has emerged as one of the key issue in teamwork involving communication. While direct point-to-point communication is expensive and uncertain, access to neighbors is reliable and efficient in scale-free networks such as those found in open environments and social networks. This suggests decentralized approaches to role allocation based on communication between neighbors. This paper adapts and evaluates some of the basic types of algorithms in distributed role allocation in open environments using a novel coordination measure in the prey/predator domain.

This report summarizes the progress and results of the second of a three-year study whose goal is the use of fault-tolerant distributed and parallel processing techniques to decrease the cost and improve the performance and reliability of large, disposable sonar arrays. In this second phase, tasks have concentrated on the design, development, analysis and evaluation of conventional and basic split-aperture beamforming algorithms. A broad assortment of parallel algorithms and programs for FFT beamformers have been completed, and their performance evaluated via a cluster testbed and via rapid virtual prototyping capabilities derived from new network architecture models. These models include a wide variety of network protocols centered around unidirectional, ring, and bidirectional topologies. In addition, new emphasis has begun with split-aperture conventional beamforming and initial results indicate a significant potential for performance improvement through parallel processing. Finally, the architecture for the hardware prototype has been developed, and work has begun on its construction and that of its software system.

This document considers algorithms for flow control in computer networks with fixed routing. The goal is to establish input rates, for each source-destination pair, that satisfy a particular fairness criterion. Described are several algorithms in which the input rates are calculated based on controls established by the links of the network. These controls are updated iteratively, using feedback information from the network. It is shown that the rates thus calculated converge to the desired values when the links are assumed to update synchronously, and without feedback delay. A model for asynchronous operation with delay is given, and we demonstrate for this model that the input rates calculated by the synchronous algorithms may fail to converge. We show how to modify the algorithms, by the introduction of an update protocol and by using more of the available feedback information, so that convergence of the rates is guaranteed. The author extends the model for asynchronous computation developed by Bertsekas to get some results relating to general asynchronous distributed algorithms with update protocols. These results are used to give an alternate proof of the correct operation of one of the flow control algorithms. A computer program is developed to simulate the flow control algorithms for a voice packet network. The simulation results indicate that the algorithms behave as expected for a network with static loads. However, when input loads change in imitation of real conversations, the control algorithms do not adapt fast enough to control the flows effectively. (Author)

Distributed decision problems arise when two or more sensors viewing the same phenomenon must work cooperatively to draw inferences about the observed situation. Typical examples are in target detection and target classification. Such problems are characterized by distributed processing of information and communication between processors over a limited bandwidth data link. This thesis presents some statistical distributed decision algorithms and describes the implementation of one of them on a set of loosely coupled multiprocessor clusters which simulate the distributed environment characterizing multisensor decision problems. Keywords include: Distributed Decision Processing; Computer Network; Microcomputer Clusters; Process Synchronization; and Network Communication. (Theses)

The asymptotic properties of extensions of the type of distributed or decentralized stochastic approximation proposed are developed. Such algorithms have numerous potential applications in decentralized estimation, detection and adaptive control, or in decentralized Monte Carlo simulation for system optimization (where they can exploit th possibilities of parallel processing). The structure involves several isolated processors (recursive algorithms) who communicate to each other asyhnchronously and at random intervals. The asymptotic (small gain) properties are derived. The communication intervals need not be strictly bounded and they and the system noise can depend on the (communicating) system state. State space constraints are also handled. In many applications, the dynamical terms are merely indicator functions, or have other types of discontinuities. The typical such case is also treated, as is the case where there is noise in the communication. The linear stochastic differential equation satisfied by the (interpolated) asymptotic normalized error sequence is derived, and issued to compare alternative algorithms and communication strategies. Weak convergence methods provide the basic tools.

Data collection in a distributed embedded system requires dealing with failures: data corruptions by malicious devices and arbitrary message delay/loss in the network. Replication of data collection devices deals with such failures by voting among the replica devices to move a correct data to the end-user. Here, a data voted upon can be large-sized and/or take a long time to be compiled. The goal of this paper is to engineer the voting protocols for good performance while meeting the reliability requirements of data delivery in a high assurance setting. Two metric quantify the effectiveness of voting protocols: Data Transfer Efficiency (DTE) and Time-to-Complete (TTC) data delivery. DTE captures the network bandwidth wasted and/or the energy drain in wireless-connected devices; whereas, TTC captures the degradation in user-level Quality of Service (QoS) due to delayed/missed data deliveries. Given the distributed nature of voting, the protocol-level optimizations to improve DTE and TTC reduce the movement of user-level data over the network, the number of control messages generated, and the latency in effecting a data delivery. The paper describes these optimizations, and reports experimental results from a prototype voting system.

In this paper we present adaptive and distributed algorithms for motion coordination of a group of m vehicles. The vehicles must service demands whose time of arrival, spatial location and service requirement are stochastic; the objective is to minimize the average time demands spend in the system. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized task assignment and are not robust against changes in the environment. In this paper, we first devise new control policies for the 1-DTRP that: (i) are provably optimal both in light-load conditions (i.e., when the arrival rate for the demands is small) and in heavy-load conditions (i.e., when the arrival rate for the demands is large), and (ii) are adaptive, in particular, they are robust against changes in load conditions. Then, we show that specific partitioning policies whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules within its own region, are optimal in heavy-load conditions. Building upon the previous results, we finally design control policies for the m-DTRP that (i) are adaptive and distributed, and (ii) have strong performance guarantees in heavy-load conditions and stabilize the system in any load condition.

We address four problems related to multi-agent optimization, filtering and agreement. First, we investigate collaborative optimization of an objective function expressed as a sum of local convex functions, when the agents make decisions in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, assumed independent and identically distributed. Specifically, we study the performance of the consensusbased multi-agent distributed subgradient method and show how it depends on the probability distribution of the random graph. For the case of a constant stepsize, we first give an upper bound on the difference between the objective function, evaluated at the agents--estimates of the optimal decision vector, and the optimal value. In addition, for a particular class of convex functions, we give an upper bound on the distances between the agents-- estimates of the optimal decision vector and the minimizer and we provide the rate of convergence to zero of the time varying component of the aforementioned upper bound. The addressed metrics are evaluated via their expected values. As an application we show how the distributed optimization algorithm can be used to perform collaborative system identification and provide numerical experiments under the randomized and broadcast gossip protocols. Second, we generalize the asymptotic consensus problem to convex metric spaces. Under minimal connectivity assumptions, we show that if at each iteration an agent updates its state by choosing a point from a particular subset of the generalized convex hull generated by the agents current state and the states of its neighbors, then agreement is achieved asymptotically. In addition, we give bounds on the distance between the consensus point(s) and the initial values of the agents.

We consider optimizations that are required for efficient execution of code segments that consists of loops over distributed data structures. The PARTI (Parallel Automated Runtime Toolkit at ICASE) execution time primitives are designed to carry out these optimizations and can be used to implement a wide range of scientific algorithms on distributed memory machines. These primitives allow the user to control array mappings in a way that gives an appearance of shared memory. Computations can be based on a global index set. Primitives are used to carry out gather and scatter operations on distributed arrays. Communications patterns are derived at runtime, and the appropriate send and receive messages are automatically generated. (kr)

We develop distributed algorithms to allocate resources in multi-hop wireless networks with the aim of minimizing total cost. In order to observe the fundamental duplexing constraint that co-located transmitters and receivers cannot operate simultaneously on the same frequency band, we first devise a spectrum allocation scheme that divides the whole spectrum into multiple sub-bands and activates conflict-free links on each sub-band. We show that the minimum number of required sub-bands grows asymptotically at a logarithmic rate with the chromatic number of network connectivity graph. A simple distributed and asynchronous algorithm is developed to feasibly activate links on the available sub-bands. Given a feasible spectrum allocation, we then design node-based distributed algorithms for optimally controlling the transmission powers on active links for each sub-band, jointly with traffic routes and user input rates in response to channel states and traffic demands. We show that under specified conditions, the algorithms asymptotically converge to the optimal operating point.

In distributed target tracking for wireless sensor networks, agreement on the target state can be achieved by the construction and maintenance of a communication path, in order to exchange information regarding local likelihood functions. Such an approach lacks robustness to failures and is not easily applicable to ad-hoc networks. To address this, several methods have been proposed that allow agreement on the global likelihood through fully distributed belief consensus (BC) algorithms, operating on local likelihoods in distributed particle filtering (DPF). However, a unified comparison of the convergence speed and communication cost has not been performed. In this paper, we provide such a comparison and propose a novel BC algorithm based on belief propagation (BP). According to our study, DPF based on metropolis belief consensus (MBC) is the fastest in loopy graphs, while DPF based on BP consensus is the fastest in tree graphs. Moreover, we found that BC-based DPF methods have lower communication overhead than data flooding when the network is sufficiently sparse.

We introduce an automated parameterized verification method for fault-tolerant distributed algorithms (FTDA). FTDAs are parameterized by both the number of processes and the assumed maximum number of Byzantine faulty processes. At the center of our technique is a parametric interval abstraction (PIA) where the interval boundaries are arithmetic expressions over parameters. Using PIA for both data abstraction and a new form of counter abstraction, we reduce the parameterized problem to finite-state model checking. We demonstrate the practical feasibility of our method by verifying several variants of the well-known distributed algorithm by Srikanth and Toueg. Our semi-decision procedures are complemented and motivated by an undecidability proof for FTDA verification which holds even in the absence of interprocess communication. To the best of our knowledge, this is the first paper to achieve parameterized automated verification of Byzantine FTDA.

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets incremented over time, and the goal is to track an $\eps$-approximation of their sum $n=\sum_i n_i$ continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is $\Theta(k/\eps \cdot \log N)$, where $N$ is the final value of $n$ when the tracking finishes, we show that with randomization, the communication cost can be reduced to $\Theta(\sqrt{k}/\eps \cdot \log N)$. Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: {\em frequency-tracking} and {\em rank-tracking}, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets incremented over time, and the goal is to track an $\eps$-approximation of their sum $n=\sum_i n_i$ continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is $\Theta(k/\eps \cdot \log N)$, where $N$ is the final value of $n$ when the tracking finishes, we show that with randomization, the communication cost can be reduced to $\Theta(\sqrt{k}/\eps \cdot \log N)$. Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: {\em frequency-tracking} and {\em rank-tracking}, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets incremented over time, and the goal is to track an $\eps$-approximation of their sum $n=\sum_i n_i$ continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is $\Theta(k/\eps \cdot \log N)$, where $N$ is the final value of $n$ when the tracking finishes, we show that with randomization, the communication cost can be reduced to $\Theta(\sqrt{k}/\eps \cdot \log N)$. Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: {\em frequency-tracking} and {\em rank-tracking}, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets incremented over time, and the goal is to track an $\eps$-approximation of their sum $n=\sum_i n_i$ continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is $\Theta(k/\eps \cdot \log N)$, where $N$ is the final value of $n$ when the tracking finishes, we show that with randomization, the communication cost can be reduced to $\Theta(\sqrt{k}/\eps \cdot \log N)$. Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: {\em frequency-tracking} and {\em rank-tracking}, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets incremented over time, and the goal is to track an $\eps$-approximation of their sum $n=\sum_i n_i$ continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is $\Theta(k/\eps \cdot \log N)$, where $N$ is the final value of $n$ when the tracking finishes, we show that with randomization, the communication cost can be reduced to $\Theta(\sqrt{k}/\eps \cdot \log N)$. Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: {\em frequency-tracking} and {\em rank-tracking}, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.