A simple improved distributed algorithm for minimum CDS in unit disk graphs

Authors:
Stefan Funke;Alexander Kesselman;Ulrich Meyer;Michael Segal
Affiliations:
Stanford University, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Ben Gurion University, Beer-Sheva, Israel
Venue:
ACM Transactions on Sensor Networks (TOSN)
Year:
2006

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Abstract

Several routing schemes in ad hoc networks first establish a virtual backbone and then route messages via backbone nodes. One common way of constructing such a backbone is based on the construction of a connected dominating set (CDS). In this article we present a very simple distributed algorithm for computing a small CDS. Our algorithm has an approximation factor of at most 6.91, improving upon the previous best-known approximation factor of 8 due to Wan et al. [2002]. The improvement relies on a refined analysis of the relationship between the size of a maximal independent set and a minimum CDS in a unit disk graph. This subresult also implies improved approximation factors for many existing algorithm.