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<p><b>Abstract</b>—In the literature, there are quite a few sequential and parallel algorithms for solving problems on distance-hereditary graphs. With an <it>n</it>-vertex and <it>m</it>-edge distance-hereditary graph <it>G</it>, we show that the efficient domination problem on <it>G</it> can be solved in <tmath>\big. O(\log^{2} n)\bigr.</tmath> time using <tmath>\big. O(n+m)\bigr.</tmath> processors on a CREW PRAM. Moreover, if a binary tree representation of <it>G</it> is given, the problem can be optimally solved in <tmath>\big. O(\log n)\bigr.</tmath> time using <tmath>\big. O(n/\log n)\bigr.</tmath> procssors on an EREW PRAM.</p>
Parallel algorithm, PRAM, distance-hereditary graphs, the efficient domination problem, binary tree contraction technique.
Sun-yuan Hsieh, "An Efficient Parallel Algorithm for the Efficient Domination Problem on Distance-Hereditary Graphs", IEEE Transactions on Parallel & Distributed Systems, vol. 13, no. , pp. 985-993, September 2002, doi:10.1109/TPDS.2002.1036071
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