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A Simple and Fast Parallel Coloring Algorithm for Distance-Hereditary Graphs
December 2003 (vol. 14 no. 12)
pp. 1201-1208

Abstract—In the literature, there are quite a few sequential and parallel algorithms to solve problems on distance-hereditary graphs. Two well-known classes of graphs, which contain trees and cographs, belong to distance-hereditary graphs. In this paper, we consider the vertex-coloring problem on distance-hereditary graphs. Let T_{d}(|V|,|E|) and P_{d}(|V|,|E|) denote the time and processor complexities, respectively, required to construct a decomposition tree representation of a distance-hereditary graph G=(V,E) on a PRAM model M_{d}. Our algorithm runs in O(T_{d}(|V|,|E|)+\log |V|) time using O(P_{d}(|V|,|E|)+|V|/\log |V|) processors on M_{d}. The best known result for constructing a decomposition tree needs O(\log^{2}|V|) time using O(|V|+|E|) processors on a CREW PRAM. If a decomposition tree is provided as input, we solve the problem in O(\log |V|) time using O(|V|/\log |V|) processors on an EREW PRAM. To the best of our knowledge, there is no parallel algorithm for this problem on distance-hereditary graphs.

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Index Terms:
Algorithms, distance-hereditary graphs, the vertex-coloring problem, PRAM.
Sun-Yuan Hsieh, "A Simple and Fast Parallel Coloring Algorithm for Distance-Hereditary Graphs," IEEE Transactions on Parallel and Distributed Systems, vol. 14, no. 12, pp. 1201-1208, Dec. 2003, doi:10.1109/TPDS.2003.1255633
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