Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks

We present a distributed algorithm that finds a maximal edge packing in O(∆ + log∗ W) synchronous communication rounds in a weighted graph, independent of the number of nodes in the network; here ∆ is the maximum degree of the graph and W is the maximum weight. As a direct application, we have a distributed 2-approximation algorithm for minimum-weight vertex cover, with the same running time. We also show how to find an f-approximation of minimumweight set cover in O(f2 k2 + fk log∗ W) rounds; here k is the maximum size of a subset in the set cover instance, f is the maximum frequency of an element, and W is the maximum weight of a subset. The algorithms are deterministic, and they can be applied in anonymous networks. Categories and Subject Descriptors C.2.4 [Computer-Communication Networks]: Distributed Systems; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems—computations on discrete structures General Terms Algorithms, Theory

• Type: Conference
• Year: 2010
• Where: SPAA
• Authors: Matti Åstrand, Jukka Suomela
• Keywords: Algorithms, Distributed And Parallel Computing, Log∗ W, Maximum Weight, SPAA 2010