Distance- k knowledge in self-stabilizing algorithms

  • Authors:
  • Wayne Goddard;Stephen T. Hedetniemi;David P. Jacobs;Vilmar Trevisan

  • Affiliations:
  • School of Computing, Clemson University, SC 29634, USA;School of Computing, Clemson University, SC 29634, USA;School of Computing, Clemson University, SC 29634, USA;Instituto de Matemática, UFRGS, Porto Alegre, Brazil

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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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 n^O^(^l^o^g^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.