Gossip algorithms: design, analysis and applications

Abstract— Motivated by applications to sensor, peer-topeer and ad hoc networks, we study distributed asynchronous algorithms, also known as gossip algorithms, for computation and information exchange in an arbitrarily connected network of nodes. Nodes in such networks operate under limited computational, communication and energy resources. These constraints naturally give rise to “gossip” algorithms: schemes which distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for arbitrary network, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Using recent results of Boyd, Diaconis and Xiao (2003), we show that minimizing this quantity to design the fastest averaging algorithm on the network is a semidefinite program(SDP). In general, SDPs cannot be solved distributedly; ...

• Type: Conference
• Year: 2005
• Where: INFOCOM
• Authors: Stephen P. Boyd, Arpita Ghosh, Balaji Prabhakar, Devavrat Shah
• Keywords: Communications, Fastest Averaging Algorithm, Gossip Algorithm, INFOCOM 2005, Largest Eigenvalue