Distance- k knowledge in self-stabilizing algorithms

Abstract. Many graph problems seem to require knowledge that extends beyond the immediate neighbors of a node. The usual self-stabilizing model only allows for nodes to make decisions based on the states of their immediate neighbors. We provide a general transformation for constructing self-stabilizing algorithms which utilize distance-k knowledge. Our transformation has both a slowdown and space overhead in nO(log k) , and might be thought of as a distance-k resource allocation algorithm. Our main application is a polynomial-time self-stabilizing algorithm for finding maximal irredundant sets, a problem which seems to require distance-4 information. These results can be generalized to efficiently find maximal P-sets, for properties P which we call local monotonic. Our techniques extend results in a recent paper by Gairing et al. for achieving distance-two information.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Wayne Goddard, Stephen T. Hedetniemi, David Pokrass Jacobs, Vilmar Trevisan
• Keywords: Immediate Neighbors, Self-stabilizing Algorithm, TCS 2008, Theoretical Computer Science, Usual Self-stabilizing Model