Fast Distributed Computation in Dynamic Networks via Random Walks

Abstract

The paper investigates efficient distributed computation in dynamic networks in which the network topology changes (arbitrarily) from round to round. Random walks are a fundamental primitive in a wide variety of network applications; the local and lightweight nature of random walks is especially useful for providing uniform and efficient solutions to distributed control of dynamic networks. Given their applicability in dynamic networks, we focus on developing fast distributed algorithms for performing random walks in such networks.

Our first contribution is a rigorous framework for design and analysis of distributed random walk algorithms in dynamic networks. We then develop a fast distributed random walk based algorithm that runs in $\tilde{O}(\sqrt{\tau \Phi})$ rounds (with high probability), where τ is the dynamic mixing time and Φ is the dynamic diameter of the network respectively, and returns a sample close to a suitably defined stationary distribution of the dynamic network.

Our next contribution is a fast distributed algorithm for the fundamental problem of information dissemination (also called as gossip) in a dynamic network. In gossip, or more generally, k-gossip, there are k pieces of information (or tokens) that are initially present in some nodes and the problem is to disseminate the k tokens to all nodes. We present a random-walk based algorithm that runs in $\tilde{O}(\min\{n^{1/3}k^{2/3}(\tau \Phi)^{1/3}, nk\})$ rounds (with high probability). To the best of our knowledge, this is the first o(nk)-time fully-distributed token forwarding algorithm that improves over the previous-best O(nk) round distributed algorithm [Kuhn et al., STOC 2010], although in an oblivious adversary model.

Supported in part by the following research grants: Nanyang Technological University grant M58110000, Singapore Ministry of Education Academic Research Fund Tier 2 grant MOE2010-T2-2-082, and a grant from the US-Israel Binational Science Foundation.