On domination problems for permutation and other graphs
Theoretical Computer Science
Finding a minimum independent dominating set in a permutation graph
Discrete Applied Mathematics
Edge domination on bipartite permutation graphs and cotriangulated graphs
Information Processing Letters
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
An optimal algorithm for finding the minimum cardinality dominating set on permutation graphs
Discrete Applied Mathematics
On the performance of the First-Fit coloring algorithm on permutation graphs
Information Processing Letters
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
An $O(N + M)$-Time Algorithm for Finding a Minimum-WeightDominating Set in a Permutation Graph
SIAM Journal on Computing
Journal of Global Optimization
Coloring permutation graphs in parallel
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Perfect edge domination and efficient edge domination in graphs
Discrete Applied Mathematics
Paired-domination in inflated graphs
Theoretical Computer Science
Paired-Domination in Claw-Free Cubic Graphs
Graphs and Combinatorics
Paired domination on interval and circular-arc graphs
Discrete Applied Mathematics
A polynomial-time algorithm for the paired-domination problem on permutation graphs
Discrete Applied Mathematics
Discrete Applied Mathematics
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A vertex subset D of a graph G is a dominating set if every vertex of G is either in D or is adjacent to a vertex in D. The paired domination problem on G asks for a minimum-cardinality dominating set S of G such that the subgraph induced by S contains a perfect matching; motivation for this problem comes from the interest in finding a small number of locations to place pairs of mutually visible guards so that the entire set of guards monitors a given area. The paired domination problem on general graphs is known to be NP-complete. In this paper, we consider the paired domination problem on permutation graphs. We define an embedding of permutation graphs in the plane which enables us to obtain an equivalent version of the problem involving points in the plane, and we describe a sweeping algorithm for this problem; if the permutation over the set N"n={1,2,...,n} defining a permutation graph G on n vertices is given, our algorithm computes a paired dominating set of G in O(n) time, and is therefore optimal.