Abstract
In this paper, parallel algorithms are presented for solving some problems on permutation graphs. The coloring problem is solved inO(log2 n) time usingO(n 3/logn) processors on the CREW PRAM, orO(logn) time usingO(n 3) processors on the CRCW PRAM. The weighted clique problem, the weighted independent set problem, the cliques cover problem, and the maximal layers problem are all solved with the same complexities. We can also show that the longest common subsequence problem belongs to the class NC.
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Yu, CW., Chen, GH. Parallel algorithms for permutation graphs. BIT 33, 413–419 (1993). https://doi.org/10.1007/BF01990525
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DOI: https://doi.org/10.1007/BF01990525