ABSTRACT
The spread of computer networks, from sensor networks to the Internet, creates an ever growing need for efficient distributed algorithms. In such scenarios, familiar combinatorial structures such as spanning trees and dominating sets are often useful for a variety of tasks. Others, like maximal independent sets, turn out to be a very useful primitive for computing other structures. This chapter studies the minimum dominating set (MDS) problem. The advent of wireless networks gives a new significance to the problem as (connected) dominating sets are the structure of choice to set up the routing infrastructure of such ad-hoc networks, the so-called backbone. It also develops an efficient distributed algorithm for computing “best possible” connected dominating sets. Maximum matching is probably one of the best studied problems in computer science: given a weighted undirected graph, compute a subset of pairwise nonincident edges (matching) of maximum cost.
