A Local Constant Factor MDS Approximation for Bounded Genus Graphs

A Local Constant Factor MDS Approximation for Bounded Genus Graphs

Abstract

The Minimum Dominating Set (MDS) problem is not only one of the most fundamental problems in distributed computing, it is also one of the most challenging ones. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last years, several breakthroughs have been made on computing local approximations on sparse graphs. This paper presents a deterministic and local constant factor approximation for minimum dominating sets on bounded genus graphs, a large family of sparse graphs. Our main technical contribution is a new analysis of a slightly modified variant of an existing algorithm by Lenzen et al. Interestingly, unlike existing proofs for planar graphs, our analysis does not rely on direct topological arguments. We believe that our techniques can be useful for the study of local problems on sparse graphs beyond the scope of this paper.

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Authors
  • Amiri, Saeed Akhoondian
  • Schmid, Stefan
  • Siebertz, Sebastian
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Supplemental Material
Shortfacts
Category
Paper in Conference Proceedings or in Workshop Proceedings (Paper)
Event Title
ACM Symposium on Principles of Distributed Computing (PODC)
Divisions
Communication Technologies
Subjects
Informatik Allgemeines
Event Location
Chicago, Illinois
Event Type
Conference
Event Dates
July 2016
Date
2016
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