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On Contention Resolution Protocols and Associated Probabilistic Phenomena
 IN PROCEEDINGS OF THE 26TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1994
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Fast Distributed Graph Coloring With ... Colors
"... We consider the problem of deterministic distributed coloring of an nvertex graph with maximum degree \Delta, assuming that every vertex knows a priori only its own label and parameters n and \Delta. The aim is to get a fast algorithm using few colors. Linial [9] showed a vertexcoloring algorit ..."
Abstract

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We consider the problem of deterministic distributed coloring of an nvertex graph with maximum degree \Delta, assuming that every vertex knows a priori only its own label and parameters n and \Delta. The aim is to get a fast algorithm using few colors. Linial [9] showed a vertexcoloring algorithm working in time O(log n) and using O(\Delta 2 ) colors. We improve both the time and the number of colors simultaneously by showing an algorithm working in time O(log (n=\Delta)) and using O(\Delta) colors. This is the first known O(\Delta)vertexcoloring distributed algorithm which can work faster than in polylogarithmic time. Our method also gives an edgecoloring algorithm with the number of colors and time as above. On the other hand, it follows from Linial [9] that our time of O(\Delta)coloring cannot be improved in general. 1