2012 IEEE 32nd International Conference on Distributed Computing Systems (2012)

Macau, China China

June 18, 2012 to June 21, 2012

ISSN: 1063-6927

ISBN: 978-1-4577-0295-2

pp: 476-485

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ICDCS.2012.72

ABSTRACT

In this paper, we propose a silent self-stabilizing asynchronous distributed algorithm for constructing a k-clustering of any connected network with unique IDs. Our algorithm stabilizes in O (n) rounds, using O (log n) space per process, where n is the number of processes. In the general case, our algorithm constructs O (n/k) k-clusters. If the network is a Unit Disk Graph (UDG), then our algorithm is 7.2552k+O (1) -competitive, that is, the number of k-clusters constructed by the algorithm is at most 7.2552*k + O (1) times the minimum possible number of k-clusters in any k-clustering of the same network. More generally, if the network is an Approximate Disk Graph (ADG) with approximation ratio ?, then our algorithm is 7.2552* (?^2k) +O (*?) -competitive. Our solution is based on the self-stabilizing construction of a data structure called the MIS Tree, a spanning tree of the network whose processes at even levels form a maximal independent set of the network. The MIS tree construction is the time bottleneck of our k-clustering algorithm, as it takes T (n) rounds in the worst case, while the rest of the algorithm takes O (D) rounds, where D is the diameter of the network. We would like to improve that time to be O (D), but we show that our distributed MIS tree construction is a P-complete problem.

INDEX TERMS

Vegetation, Clustering algorithms, Algorithm design and analysis, Approximation algorithms, Data structures, Complexity theory, Encoding, competitiveness, self-stabilization, maximal independent set, MIS tree, k-clustering

CITATION

K. Heurtefeux, S. Devismes, L. L. Larmore, A. K. Datta and Y. Rivierre, "Competitive Self-Stabilizing k-Clustering,"

*2012 IEEE 32nd International Conference on Distributed Computing Systems(ICDCS)*, Macau, China China, 2012, pp. 476-485.

doi:10.1109/ICDCS.2012.72