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

Several routing schemes in ad hoc networks first establish a virtual backbone and then route messages via back-bone nodes. One common way of constructing such a backbone is based on the construction of a minimum connected dominating set (CDS). In this paper 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. [INFOCOM'02], 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.

[1]  Deying Li,et al.  A polynomial‐time approximation scheme for the minimum‐connected dominating set in ad hoc wireless networks , 2003, Networks.

[2]  Charles J. Colbourn,et al.  Unit disk graphs , 1991, Discret. Math..

[3]  Khaled M. Alzoubi.  Connected dominating set and its induced position-less sparse spanner for mobile ad hoc networks , 2003, Proceedings of the Eighth IEEE Symposium on Computers and Communications. ISCC 2003.

[4]  Peng-Jun Wan,et al.  Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[5]  Peng-Jun Wan,et al.  Weakly-connected dominating sets and sparse spanners in wireless ad hoc networks , 2003, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings..

[6]  L. Fejes.  Über die dichteste Kugellagerung , 1942 .

[7]  Harry B. Hunt,et al.  Simple heuristics for unit disk graphs , 1995, Networks.

[8]  Michael Luby.  Removing randomness in parallel computation without a processor penalty , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[9]  Michael Luby,et al.  A simple parallel algorithm for the maximal independent set problem , 1985, STOC '85.

[10]  Srinivasan Parthasarathy,et al.  Fast Distributed Well Connected Dominating Sets for Ad Hoc Networks , 2004 .