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An Efficient Parallel Algorithm for the Efficient Domination Problem on Distance-Hereditary Graphs
September 2002 (vol. 13 no. 9)
pp. 985-993

Abstract—In the literature, there are quite a few sequential and parallel algorithms for solving problems on distance-hereditary graphs. With an n-vertex and m-edge distance-hereditary graph G, we show that the efficient domination problem on G can be solved in \big. O(\log^{2} n)\bigr. time using \big. O(n+m)\bigr. processors on a CREW PRAM. Moreover, if a binary tree representation of G is given, the problem can be optimally solved in \big. O(\log n)\bigr. time using \big. O(n/\log n)\bigr. procssors on an EREW PRAM.

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Index Terms:
Parallel algorithm, PRAM, distance-hereditary graphs, the efficient domination problem, binary tree contraction technique.
Citation:
Sun-yuan Hsieh, "An Efficient Parallel Algorithm for the Efficient Domination Problem on Distance-Hereditary Graphs," IEEE Transactions on Parallel and Distributed Systems, vol. 13, no. 9, pp. 985-993, Sept. 2002, doi:10.1109/TPDS.2002.1036071
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