Discrete Applied Mathematics
On domination problems for permutation and other graphs
Theoretical Computer Science
Finding a minimum independent dominating set in a permutation graph
Discrete Applied Mathematics
An O(n2 log n) parallel max-flow algorithm
Journal of Algorithms
SIAM Journal on Computing
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Efficient parallel algorithms for some graph problems
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Fast Algorithms for the Dominating Set Problem on Permutation Graphs
SIGAL '90 Proceedings of the International Symposium on Algorithms
NC Algorithms for Comparability Graphs, Interval Gaphs, and Testing for Unique Perfect Matching
Proceedings of the Fifth Conference on Foundations of Software Technology and Theoretical Computer Science
Logarithmic Time NC Algorithms for Comparability Graphs and Circle Graphs
ICCI '91 Proceedings of the International Conference on Computing and Information: Advances in Computing and Information
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Interval Graphs: Canonical Representations in Logspace
SIAM Journal on Computing
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In this paper, we present a parallel recognition algorithm for bipartite-permutation graphs. The algorithm can be executed in O(log n) time on the CRCW PRAM if O(n3 /log n) processors are used, or O(log2n) time on the CREW PRAM if O(n3 /log2n) processors are used. Previously, Chen and Yesha have presented another CRCW PRAM algorithm that takes O(log2n) time if O(n3) processors are used. Compared with Chen and Yesha's algorithm, our algorithm requires either less time and fewer processors on the same machine model, or fewer processors on a weaker machine model. Besides, our algorithm can be applied to determine if two bipartite-permutation graphs are isomorphic.