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SIAM Journal on Computing
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ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
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IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
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Theoretical Computer Science
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We consider the problem of deterministic distributed coloring of an n-vertex graph with maximum degree &Dgr;, assuming that every vertex knows a priori only its own label and parameters n and &Dgr;. The aim is to get a fast algorithm using few colors. Linial [17] showed a vertex-coloring algorithm working in time &Ogr;(log* n) and using &Ogr;(&Dgr;2 colors. We improve both the time and the number of colors simultaneously by showing an algorithm working in time &Ogr;(log*(n/&Dgr;)) and using &Ogr;(&Dgr;) colors. This is the first known &Ogr;(&Dgr;)-vertex-coloring distributed algorithm which can work faster than in polylogarithmic time.Our method also gives an edge-coloring algorithm with the number of colors and time as above. On the other hand, it follows from Linial [17] that our time of &Ogr;(&Dgr;)-coloring cannot be improved in general. In addition we show how our method gives fast coloring algorithms in communication models weaker than Linial's.