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 polynomial transformation for constructing self-stabilizing algorithms which utilize distance-shape k knowledge, with a slowdown of n O(log k). Our main application is a polynomial-time self-stabilizing algorithm for finding maximal irredundant sets, a problem which seems to require distance-4 information. We also show how to find maximal k-packings in polynomial-time. Our techniques extend results in a recent paper by Gairing et al. for achieving distance-two information.
Research supported by: NSF grant CCR-0222648; CNPq grant 453991/2005-0; and FAPERGS grant 05/2024.1.
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Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Trevisan, V. (2006). Distance-k Information in Self-stabilizing Algorithms. In: Flocchini, P., Gąsieniec, L. (eds) Structural Information and Communication Complexity. SIROCCO 2006. Lecture Notes in Computer Science, vol 4056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780823_27
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DOI: https://doi.org/10.1007/11780823_27
Publisher Name: Springer, Berlin, Heidelberg
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