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
Optimal bounds for decision problems on the CRCW PRAM
Journal of the ACM (JACM)
Fast algorithms for the dominating set problem on permutation graphs
SIGAL '90 Proceedings of the international symposium on Algorithms
Parallel computation of longest-common-subsequence
ICCI'90 Proceedings of the international conference on Advances in computing and information
An introduction to parallel algorithms
An introduction to parallel algorithms
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
On the performance of the First-Fit coloring algorithm on permutation graphs
Information Processing Letters
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
NC coloring algorithms for permutation graphs
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
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Parallel algorithms for P4-comparability graphs
Journal of Algorithms
An O(n)-time algorithm for the paired domination problem on permutation graphs
European Journal of Combinatorics
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A coloring of a graph G is an assignment of colors to its vertices so that no two adjacent vertices have the same color. We study the problem of coloring permutation graphs using certain properties of the lattice representation of a permutation and relationships between permutations, directed acyclic graphs and rooted trees having specific key properties. We propose an efficient parallel algorithm which colors an n-node permutation graph in O(log2 n) time using O(n2/log n) processors on the CREW PRAM model. Specifically, given a permutation π we construct a tree T*[π], which we call coloring-permutation tree, using certain combinatorial properties of π. We show that the problem of coloring a permutation graph is equivalent to finding vertex levels in the coloring-permutation tree.