Abstract
We improve here the expected performance of parallel algorithms for graph coloring. This is achieved through new adaptive techniques that may be useful for the average-case analysis of many graph algorithms. We apply our techniques to:
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(a)
the class G n,p of random graphs. We present a parallel algorithm which colors the graph with a number of colors at most twice its chromatic number and runs in time O(log4 n/ log log n) almost surely, for p = Ω((log(3) n)2/ log(2) n). The number of processors used is O(m) where m is the number of edges of the graph.
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(b)
the class of all k-colorable graphs, uniformly chosen. We present a parallel algorithm which actually constructs the coloring in expected parallel time O(log2 n), for constant k, by using O(m) processors on the average. This problem is not known to have a polynomial time algorithm in the worst case.
This work was partially supported by the EEC ESPRIT Basic Research Action No. 3075 (ALCOM), by the Ministry of Industry, Energy and Technology of Greece and by the NSF grant CCR-89-6949.
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© 1992 Springer-Verlag Berlin Heidelberg
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Kedem, Z.M., Palem, K.V., Pantziou, G.E., Spirakis, P.G., Zaroliagis, C.D. (1992). Fast parallel algorithms for coloring random graphs. In: Schmidt, G., Berghammer, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 1991. Lecture Notes in Computer Science, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55121-2_13
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DOI: https://doi.org/10.1007/3-540-55121-2_13
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