On domination problems for permutation and other graphs
Theoretical Computer Science
Finding a minimum independent dominating set in a permutation graph
Discrete Applied Mathematics
Fast algorithms for the dominating set problem on permutation graphs
SIGAL '90 Proceedings of the international symposium on Algorithms
An introduction to parallel algorithms
An introduction to parallel algorithms
Information Processing Letters
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
Optimal parallel algorithms for direct dominance problems
Nordic Journal of Computing
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
Coloring permutation graphs in parallel
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
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We show that the problem of coloring a permutation graph of size n can be solved in O(log n log k) time using O(kn2/log k log2 n) processors on the CREW PRAM model of computation, where 1 . We estimate the parameter k on random permutation graphs and show that the coloring problem can be solved in O(log n log log n) time in the average-case on the CREW PRAM model of computation with O(n2) processors. Our computational strategy goes as follows: Given a permutation pi; or its corresponding permutation graph G[π], we first construct a directed acyclic graph G*[π] using certain combinatorial properties of π, and then compute longest paths in the directed acyclic graph using divide-and-conquer techniques. We show that the problem of coloring a permutation graph G[π] is equivalent to finding longest paths in its acyclic digraph G*[π]. The best-known parallel algorithms for the same problem run in O(log2 n) time using O(n3/log n) processors on the CREW PRAM model of computation.