Competitive Self-Stabilizing k-Clustering

Ajoy K. Datta, Lawrence L. Larmore, Stephane Devismes, Karel Heurtefeux, Yvan Rivierre
2012 2012 IEEE 32nd International Conference on Distributed Computing Systems  
In this paper, we propose a silent self-stabilizing asynchronous distributed algorithm for constructing a kclustering 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
more » ... st 7.2552k + 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 λ, then our algorithm is 7.2552λ 2 k + O(λ)-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 Θ(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.
doi:10.1109/icdcs.2012.72 dblp:conf/icdcs/DattaLDHR12 fatcat:x2ijwcajq5ckhcgjnzqrgvoc7m