区间图的并行最大团算法及其应用

Proceedings of the International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN) Pub Date : 1994-12-14 DOI:10.1109/ISPAN.1994.367160

Chi-Su Wang, R. Chang

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引用次数: 5

摘要

本文提出了一种O(n log n)时间的求区间图中所有极大团的算法。该算法也可以使用O(n/sup 2/)个处理器在O(log n)时间内并行实现。区间图的极大团包含了重要的结构信息。区间图上的许多问题在已知最大团之后就可以解决了。结果表明，在已知最大团之后，切点、桥和顶点连通性都可以很容易地确定。最后，基于最大团之间的关系，求解了区间图的全对最短路径问题。全对最短路径算法也可以使用O(n/sup 2/)个处理器在O(log n)时间内并行化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Parallel maximal cliques algorithms for interval graphs with applications

In this paper, an O(n log n) time algorithm for finding all the maximal cliques of an interval graph is proposed. This algorithm can also be implemented in parallel in O(log n) time using O(n/sup 2/) processors. The maximal cliques of an interval graph contain important structural information. Many problems on interval graphs can be solved after all the maximal cliques are known. It is shown that cut vertices, bridges, and vertex connectivities can all be determined easily after the maximal cliques are known. Finally, the all-pair shortest path problem for interval graphs is solved based on the relationship between maximal cliques. The all-pair shortest path algorithm can also be parallelized in O(log n) time using O(n/sup 2/) processors.<>

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Proceedings of the International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN)

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