A partition (C1,C2,...,Cq) of G = (V,E) into clusters of strong (respectively, weak) diameter d, such that the supergraph obtained by contracting each Ci is ℓ-colorable is called a strong (resp., weak) (d, ℓ)-network-decomposition. Network-decompositions were introduced in a seminal paper by Awerbuch, Goldberg, Luby and Plotkin in 1989. Awerbuch et al. showed that strong network-decompositions can be computed in distributed deterministic time. Even more importantly, they demonstrated that network-decompositions can be used for a great variety of applications in the message-passing model of distributed computing. Much more recently Barenboim (2012) devised a distributed randomized constant-time algorithm for computing strong network decompositions with d = O(1). However, the parameter ℓ in his result is O(n1/2 + ε). In this paper we drastically improve the result of Barenboim and devise a distributed randomized constant-time algorithm for computing strong (O(1), O(nε))-network-decompositions. As a corollary we derive a constant-time randomized O(nε)-approximation algorithm for the distributed minimum coloring problem. This improves the best previously-known O(n1/2 + ε) approximation guarantee. We also derive other improved distributed algorithms for a variety of problems. Most notably, for the extremely well-studied distributed minimum dominating set problem currently there is no known deterministic polylogarithmic -time algorithm. We devise a deterministic polylogarithmic-time approximation algorithm for this problem, addressing an open problem of Lenzen and Wattenhofer (2010).
|Title of host publication||Structural Information and Communication Complexity - 22nd International Colloquium, SIROCCO 2015, Post-Proceedings|
|Number of pages||15|
|State||Published - 2015|
|Event||22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015 - Montserrat, Spain|
Duration: 14 Jul 2015 → 16 Jul 2015
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015|
|Period||14/07/15 → 16/07/15|
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© Springer International Publishing Switzerland 2015.