A fast parallel algorithm to color graph with &Dgr; colors
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A log-star distributed maximal independent set algorithm for growth-bounded graphs
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Distributed (δ+1)-coloring in linear (in δ) time
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A new technique for distributed symmetry breaking
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Deterministic distributed vertex coloring in polylogarithmic time
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DISC'11 Proceedings of the 25th international conference on Distributed computing
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ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Stone age distributed computing
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Symmetry breaking depending on the chromatic number or the neighborhood growth
Theoretical Computer Science
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We deterministically compute a Δ + 1 coloring in time O(Δ5c+2 ċ (Δ5)2/c/(Δ1)ε + (Δ1)ε + log* n) and O(Δ5c+2 ċ (Δ5)1/c/Δε + Δε + (Δ5)d log Δ5 log n) for arbitrary constants d, ε and arbitrary constant integer c, where Δi is defined as the maximal number of nodes within distance i for a node and Δ := Δ1. Our greedy algorithm improves the state-of-the-art Δ + 1 coloring algorithms for a large class of graphs, e.g. graphs of moderate neighborhood growth. We also state and analyze a randomized coloring algorithm in terms of the chromatic number, the run time and the used colors. If Δ ∈ Ω(log1+1/log* n n) and χ ∈ O(Δ/ log1+1/log* n n) then our algorithm executes in time O(log χ + log* n) with high probability. For graphs of polylogarithmic chromatic number the analysis reveals an exponential gap compared to the fastest Δ + 1 coloring algorithm running in time O(log Δ + √log n). The algorithm works without knowledge of χ and uses less than Δ colors, i.e., (1 - 1/O(χ))Δ with high probability. To the best of our knowledge this is the first distributed algorithm for (such) general graphs taking the chromatic number χ into account.