Self-stabilizing algorithm for maximal graph decomposition into disjoint paths of fixed length

Authors:
Brahim Neggazi;Mohammed Haddad;Hammamache Kheddouci
Affiliations:
Université de Lyon, France;Université de Lyon, France;Université de Lyon, France
Venue:
Proceedings of the 4th International Workshop on Theoretical Aspects of Dynamic Distributed Systems
Year:
2012

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Abstract

The graph decomposition problem consists of dividing a graph into components, patterns or partitions which satisfy some specifications. In this paper, we give interest to graph decomposition into particular patterns: disjoint paths of length two. We present the first Self-stabilizing algorithm for finding a Maximal Decomposition of an arbitrary graph into disjoint Paths of length two (SMDP). Then, we give the correctness proof and we show that SMDP converges in O(Δm) moves where m is the number of edges and Δ the maximum degree in the graph G.