Distributed algorithms for edge dominating sets

An edge dominating set for a graph G is a set D of edges such that each edge of G is in D or adjacent to at least one edge in D. This work studies deterministic distributed approximation algorithms for finding minimum-size edge dominating sets. The focus is on anonymous port-numbered networks: there are no unique identifiers, but a node of degree d can refer to its neighbours by integers 1, 2, . . . , d. The present work shows that in the port-numbering model, edge dominating sets can be approximated as follows: in d-regular graphs, to within 4 − 6/(d + 1) for an odd d and to within 4−2/d for an even d; and in graphs with maximum degree ∆, to within 4 − 2/(∆ − 1) for an odd ∆ and to within 4 − 2/∆ for an even ∆. These approximation ratios are tight for all values of d and ∆: there are matching lower bounds. Categories and Subject Descriptors C.2.4 [Computer-Communication Networks]: Distributed Systems; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonn...

• Type: Conference
• Year: 2010
• Where: PODC
• Authors: Jukka Suomela
• Keywords: Deterministic Distributed Approximation, Distributed And Parallel Computing, Edge Dominating Sets, Minimum-size Edge, PODC 2010