2016/02/09 by Saeed Akhoondian Amiri, Stefan Schmid, Amiri, Saeed Akhoondian +3
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #Distributed #FOS: Computer and information sciences #Parallel #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.1602.02991
openalex publication_date 2016/02/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 very large family of sparse graphs. Our main technical contribution is a new analysis of a slightly modified, first-order definable variant of an existing algorithm by Lenzen et al. Interestingly, unlike existing proofs for planar graphs, our analysis does not rely on any 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.