Distributed Connected Dominating Sets in Unit Square and Disk Graphs

Abstract

The Minimum Dominating Set (MDS) and Minimum Connected Dominating set (MCDS) problems are well-studied problems in the distributed computing communities due to their numerous applications across the field. We study these problems in axis-parallel unit square and unit disk graphs. We exploit the underlying geometric structures of these graph classes and present constant round distributed algorithms in the $$\mathcal {LOCAL}$$ communication model. Our results are distributed constant factor approximation algorithms for the MCDS problem in unit square graphs that run in 18 rounds and in unit disk graphs that run in 44 rounds. The message complexity is linear for both the algorithms.