Fast linear iterations for distributed averaging

We consider the problem of finding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of finding the fastest converging linear iteration can be cast as a semidefinite program, and therefore efficiently and globally solved. These optimal linear iterations are often substantially faster than several common heuristics that are based on the Laplacian of the associated graph.We show how problem structure can be exploited to speed up interior-point methods for solving the fastest distributed linear iteration problem, for networks with up to a thousand or so edges. We also describe a simple subgradient method that handles far larger problems, with up to 100 000 edges. We give several extensions and variations on the basic problem.     

Optimal distributed linear averaging

A new optimal distributed linear averaging (ODLA) problem is presented in this paper. This problem is motivated by the distributed averaging problem which arises in the context of distributed algorithms in computer science and coordination of groups of autonomous agents in engineering. The aim of the ODLA problem is to compute the average of the initial values at nodes of a graph through an optimal distributed algorithm in which the nodes in the graph can only communicate with their neighbors. Optimality is given by a minimization problem of a quadratic cost functional under infinite horizon. We show that this problem has a very close relationship with the notion of semistability. By developing new necessary and sufficient conditions for semistability of linear discrete-time systems, we convert the proposed ODLA problem into an equivalent, constrained optimization problem and then derive a solvable, fixed-structure convex optimization problem.     

A multiplicative multisplitting method for solving the linear complementarity problem

The convergence of the multiplicative multisplitting-type method for solving the linear complementarity problem with an H-matrix is discussed using classical and new results from the theory of splitting. This directly results in a sufficient condition for guaranteeing the convergence of the multiplicative multisplitting method. Moreover, the multiplicative multisplitting method is applied to the H-compatible splitting and the multiplicative Schwarz method, separately. Finally, we establish the monotone convergence of the multiplicative multisplitting method under appropriate conditions.     

Decentralized observers with consensus filters for distributed discrete-time linear systems

This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors’ estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtained a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of graphs with self-loops.     

Global and robust formation-shape stabilization of relative sensing networks

This paper proposes a simple, distributed algorithm that achieves global stabilization of formations for relative sensing networks in arbitrary dimensions with fixed topology. Assuming the network runs an initialization procedure to equally orient all agent reference frames, convergence to the desired formation shape is guaranteed even in partially asynchronous settings. We characterize the algorithm robustness against several sources of errors: link failures, measurement errors, and frame initialization errors. The technical approach combines algebraic graph theory, multidimensional scaling, and distributed linear iterations.     

Asynchronous multisplitting relaxation methods for linear complementarity problems

To solve the linear complementarity problems efficiently on the high-speed multiprocessor systems, we set up a class of asynchronous parallel matrix multisplitting accelerated over-relaxation (AOR) method by technical combination of the matrix multisplitting and the accelerated overrelaxation techniques. The convergence theory of this new method is thoroughly established under the condition that the system matrix of the linear complementarity problem is an H-matrix with positive diagonal elements. At last, we also make multi-parameter extension for this new asynchronous multisplitting AOR method, and investigate the convergence property of the resulted asynchronous multisplitting unsymmetric AOR method. Thereby, an extensive sequence of asynchronous parallel relaxed iteration methods in the sense of multisplitting is presented for solving the large scale linear complementarity problems in the asynchronous parallel computing environments. This not only affords various choices, but also presents systematic convergence theories about the asynchronous parallel relaxation methods for solving the linear complementarity problems.     

Stochastic sensor activation for distributed state estimation over a sensor network

We consider distributed state estimation over a resource-limited wireless sensor network. A stochastic sensor activation scheme is introduced to reduce the sensor energy consumption in communications, under which each sensor is activated with a certain probability. When the sensor is activated, it observes the target state and exchanges its estimate of the target state with its neighbors; otherwise, it only receives the estimates from its neighbors. An optimal estimator is designed for each sensor by minimizing its mean-squared estimation error. An upper and a lower bound of the limiting estimation error covariance are obtained. A method of selecting the consensus gain and a lower bound of the activating probability is also provided.     

Two-stage iterations based on composite splittings for rectangular linear systems

In this paper, we introduce a two-stage method to solve rectangular linear systems that exhibits faster convergence than typical stationary iterative methods. Under suitable conditions, we prove convergence of the new method. The number of outer iterations can be reduced by using a few significant number of inner iterations for efficient computations. Further, we perform a comparison analysis, and establish that a higher number of inner iterations ensures a smaller spectral radius of the global iteration matrix. We also discuss the uniqueness of a proper splitting, and illustrate different comparison theorems for different subclasses of proper splittings.     

Lower bounds for asynchronous consensus

Impossibility results and best-case lower bounds are proved for the number of message delays and the number of processes required to reach agreement in an asynchronous consensus algorithm that tolerates non-Byzantine failures. General algorithms exist that achieve these lower bounds in the normal case, when the response time of non-faulty processes and the transmission delay of messages they send to one another are bounded. Our theorems allow algorithms to do better in certain exceptional cases, and such algorithms are presented. Two of these exceptional algorithms may be of practical interest.     

Fast and simple distributed consensus

Summary The problem of fault-tolerant agreement is fundamental to distributed computing. When agreement is to be reached in spite of arbitrary behavior by faulty processors, this problem is calledDistributed Consensus. By requiring that the number of faulty processors be , wheren is the number of processors in the system, we are able to derive two new protocols forDistributed Consensus. Both are simple and use messages that are only one bit in length, and both provide forearly stopping: the fewer failures there are, the fewer rounds of communication are required. One protocol is optimal with respect to the number of rounds of communication required, and the other is asymptotically optimal with respect to the total number of message bits exchanged. James E. Burns received the B.S. degree in mathematics from the California Institute of Technology, the M.B.I.S. degree from Georgia State University, and the M.S. and Ph.D. degrees in information and computer science from the Georgia Institute of Technology. He served on the faculty of Computer Science at Indiana University and the College of Computing at the Georgia Institute of Technology before joining Bellcore in 1993. He is currently a Member of Technical Staff in the Network Control Research Department, where he is studying the telephone control network with special interest in behavior when faults occur. He also has research interests in theoretical issues of distributed and parallel computing, especially relating to problems of synchronization and fault tolerance. Gil Neiger was born on February 19, 1957 in New York, New York. In June 1979, he received an A.B. in Mathematics and Psycholinguistics from Brown University in Proidence, Rhode Island. In February 1985, he spent two weeks picking cotton in Nicaragua in a brigade of international volunteers. In January 1986, he received an M.S. in Computer Science from Cornell University in Ithaca, New York and, in August 1988, he received a Ph.D. in Computer Science, also from Cornell University. On August 20, 1988, Dr. Neiger married Hilary Lombard in Lansing, New York. Since August 1988, he has been an Assistant Professor in the College of Computing (formely School of Information and Computer Science) at the Georgia Institute of Technology in Atlanta, Georgia. Dr. Neiger is a member of the editorial board of theChicago Journal of Theoretical Computer Science and theJournal of Parallel and Distributed Computing.This author was supported in part by the National Science Foundation under grants CCR-8909663, CCR-9106627, and CCR-9301454.     

An efficient distributed algorithm for finding all hinge vertices in networks

Let G=(V, E) be a graph with vertex set V of size n and edge set E of size m. A vertex v∈V is called a hinge vertex if there exist two vertices in V\{v} such that their distance becomes longer when v is removed. In this paper, we present a distributed algorithm that finds all hinge vertices on an arbitrary graph. The proposed algorithm works for named static asynchronous networks and achieves O(n ²) time complexity and O(m) message complexity. In particular, the total messages exchanged during the algorithm are at most 2m(log n+nlog n+1) bits.     

A framework for the collective movement of mobile robots based on distributed decisions

A novel framework for the control of the collective movement of mobile robots is presented and analyzed in this article. It allows a group of robots to move as a unique entity performing the following functions: obstacle avoidance at group level, speed control and modification of the inter-robot distance. Its flocking controller is distributed among the robots, allowing them to move in the desired common direction and maintain a desired inter-robot distance. The framework is made up of different modules that modify the behavior of the group thus allowing different functions. They are based on consensus algorithms that allow the robots to agree on different parameters, taking into account which robot has more relevant information. New modules can be easily designed and incorporated into the framework in order to augment its capabilities. It can be easily implemented on any mobile robot capable of measuring the relative positions of neighboring robots and communicating with them. It has been successfully tested using 8 real robots and in simulation with up to 40 robots, demonstrating experimentally its scalability with an increasing number of robots.     

Competitive distributed decision-making

We study several natural problems in distributed decision-making from the standpoint of competitive analysis; in these problems incomplete information is a result of the distributed nature of the problem, as opposed to the on-line mode of decision making that was heretofore prevalent in this area. In several simple situations of distributed scheduling, the competitive ratio can be computed exactly, and the different ratios can be used as a measure of the value of information and communication between decision-makers. In a more general distributed scheduling situation, we give tight upper and lower bounds on the competitive ratio achievable in the deterministic case, and give an optimal randomized algorithm with a much better competitive ratio.The research of Xiaotie Deng was supported by an NSERC grant and that of C. H. Papadimitriou was supported by an NSF grant.     

Accelerated low rank matrix approximate algorithms for matrix completion

In this paper, we propose two accelerated algorithms for the low-rank approximate method in Wang et al. (0000) for matrix completion. The main idea is to use the successive over-relaxation technique. Based on the successive over-relaxation method for the feasible matrices or projection matrices, the low-rank matrix approximate method is modified and accelerated. Meanwhile, we discuss the convergence of the over-relaxation algorithm for the feasible matrix. Finally, the numerical experiments show them to be effective.     

An efficient distributed algorithm for maximum matching in general graphs

We present a distributed algorithm for maximum cardinality matching in general graphs. On a general graph withn vertices, our algorithm requiresO(n ^5/2) messages in the worst case. On trees, our algorithm computes a maximum matching usingO(n) messages after the election of a leader.Work on this paper has been supported by the Office of Naval Research under Contract N00014-85-K-0570.     

An algorithm for privacy-preserving distributed user statistics

In this paper, we propose a privacy-preserving method to determine the number of distinct users who connected to one or more entry points of a distributed Internet service with multiple service operators. The problem is motivated by the anonymization network Tor, and the difficulties that arise when aiming to estimate the number of Tor users. We present a way to perform distributed user counting with accurate estimates and a high level of privacy protection, based on a probabilistic data structure. We start from a relatively naive approach, and analyze the level of privacy protection that it provides. Subsequently, we improve on this baseline mechanism, building upon the gained insights. In order to assess the privacy properties of the discussed techniques, we use a novel probabilistic analysis approach which compares an attacker’s a priori and a posteriori knowledge.     

Practical uses of synchronized clocks in distributed systems

Summary Synchronized clocks are interesting because they can be used to improve performance of a distributed system by reducing communications. Since they have only recently become a reality in distributed systems, their use in distributed algorithms has received relatively little attention. This paper discusses a number of distributed algorithms that make use of synchronized clocks and analyzes how clocks are used in these algorithms Barbara Liskov received her B.A. in mathematics from the University of California at Berkeley and her M.S. and Ph.D. in computer science from Stanford University. She is currently a member of the faculty at the Massachusetts Institute of Technology, where she is NEC Professor of Software Science and Engineering. Her research and teaching interests include programming languages, programming methodology, distributed computing, and parallel computing. Her work on data abstraction led to the development of the CLU programming language and to a programming methodology based on data abstraction and specifications. This work is described in her book Abstraction and Specification in Program Development. Her subsequent research in distributed computing resulted in the Argus programming language, which supports robust distributed programs that survive hardware failures, and the Mercury communications mechanism, which supports efficient communication in a heterogeneous distributed system. At present Prof. Liskov is continuing her work in distributed computing, including development of replication algorithms for implementing highly-available systems. She is working on Harp, a replicated Unix file system for use via NFS, and on the design and implementation of Thor, a highly available object repository for use in a heterogeneous distributed environment. She is a member of ACM, IEEE, the National Academy of Engineering, and is a fellow of the American Academy of Arts and Sciences.This research was supported in part by the Advanced Research Projects Agency of the Department of Defense, monitored by the Office of Naval Research under contract N00014-89-J-1988, and in part by the National Science Foundation under grant CCR-8822158.     

Reconfigurable distributed storage for dynamic networks

This paper presents a new algorithm for implementing a reconfigurable distributed shared memory in an asynchronous dynamic network. The algorithm guarantees atomic consistency (linearizability) in all executions in the presence of arbitrary crash failures of the processing nodes, message delays, and message loss. The algorithm incorporates a classic quorum-based algorithm for read/write operations, and an optimized consensus protocol, based on Fast Paxos for reconfiguration, and achieves the design goals of: (i) allowing read and write operations to complete rapidly and (ii) providing long-term fault-tolerance through reconfiguration, a process that evolves the quorum configurations used by the read and write operations. The resulting algorithm tolerates dynamism. We formally prove our algorithm to be correct, we present its performance and compare it to existing reconfigurable memories, and we evaluate experimentally the cost of its reconfiguration mechanism.