Distributed averaging in dynamic networks

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 39-40).The question of computing average of numbers present at nodes in a network in a distributed manner using gossip or message-passing algorithms has been of great recent interest across disciplines -- algorithms, control and robotics, estimation, social networks, etc. It has served as a non-trivial, representative model for an important class of questions arising in these disciplines and thus guiding intellectual progress over the past few decades. In most of these applications, there is inherent dynamics present, such as changes in the network topology in terms of communication links, changes in the values of numbers present at nodes, and nodes joining or leaving. The effect of dynamics in terms of communication links on the design and analysis of algorithms for averaging is reasonably well understood, e.g. [14][2][8][4]. However, little is known about the effect of other forms of dynamics. In this thesis, we study the effect of such types of dynamics in the context of maintaining average in the network. Specifically, we design dynamics-aware message-passing or gossip algorithm that maintains good estimate of average in presence of continuous change in numbers at nodes. Clearly, in presence of such dynamics the best one can hope for is a tradeoff between the accuracy of each node's estimate of the average at each time instant and the rate of dynamics. For our algorithm, we characterize this tradeoff and establish it to be near optimal. The dependence of the accuracy of the algorithm on the rate of dynamics as well as on the underlying graph structure is quantified.by Shreevatsa Rajagopalan.S.M

Empirical Centroid Fictitious Play: An Approach For Distributed Learning In Multi-Agent Games

The paper is concerned with distributed learning in large-scale games. The well-known fictitious play (FP) algorithm is addressed, which, despite theoretical convergence results, might be impractical to implement in large-scale settings due to intense computation and communication requirements. An adaptation of the FP algorithm, designated as the empirical centroid fictitious play (ECFP), is presented. In ECFP players respond to the centroid of all players' actions rather than track and respond to the individual actions of every player. Convergence of the ECFP algorithm in terms of average empirical frequency (a notion made precise in the paper) to a subset of the Nash equilibria is proven under the assumption that the game is a potential game with permutation invariant potential function. A more general formulation of ECFP is then given (which subsumes FP as a special case) and convergence results are given for the class of potential games. Furthermore, a distributed formulation of the ECFP algorithm is presented, in which, players endowed with a (possibly sparse) preassigned communication graph, engage in local, non-strategic information exchange to eventually agree on a common equilibrium. Convergence results are proven for the distributed ECFP algorithm.Comment: Submitted to the IEEE Transactions on Signal Processin

EDDA: An Efficient Distributed Data Replication Algorithm in VANETs

Efficient data dissemination in vehicular ad hoc networks (VANETs) is a challenging issue due to the dynamic nature of the network. To improve the performance of data dissemination, we study distributed data replication algorithms in VANETs for exchanging information and computing in an arbitrarily-connected network of vehicle nodes. To achieve low dissemination delay and improve the network performance, we control the number of message copies that can be disseminated in the network and then propose an efficient distributed data replication algorithm (EDDA). The key idea is to let the data carrier distribute the data dissemination tasks to multiple nodes to speed up the dissemination process. We calculate the number of communication stages for the network to enter into a balanced status and show that the proposed distributed algorithm can converge to a consensus in a small number of communication stages. Most of the theoretical results described in this paper are to study the complexity of network convergence. The lower bound and upper bound are also provided in the analysis of the algorithm. Simulation results show that the proposed EDDA can efficiently disseminate messages to vehicles in a specific area with low dissemination delay and system overhead