Identification, location-domination and metric dimension on interval and permutation graphs. I. Bounds

5 GOAL - Graphes, AlgOrithmes et AppLications
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : We consider the problems of finding optimal identifying codes, (open) locating–dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a solution set, using which all vertices of the graph are distinguished. The identification can be done by considering the neighborhood within the solution set, or by employing the distances to the solution vertices. Normally the goal is to minimize the size of the solution set then. Here we study the case of interval graphs, unit interval graphs, (bipartite) permutation graphs and cographs. For these classes of graphs we give tight lower bounds for the size of such solution sets depending on the order of the input graph. While such lower bounds for the general class of graphs are in logarithmic order, the improved bounds in these special classes are of the order of either quadratic root or linear in terms of number of vertices. Moreover, the results for cographs lead to linear-time algorithms to solve the considered problems on inputs that are cographs.
Type de document :
Article dans une revue
Theoretical Computer Science, Elsevier, 2017, 〈10.1016/j.tcs.2017.01.006〉

https://hal.archives-ouvertes.fr/hal-01198783
Contributeur : Petru Valicov <>
Soumis le : lundi 14 septembre 2015 - 13:42:57
Dernière modification le : jeudi 19 juillet 2018 - 16:58:09

Citation

Florent Foucaud, George B. Mertzios, Reza Naserasr, Aline Parreau, Petru Valicov. Identification, location-domination and metric dimension on interval and permutation graphs. I. Bounds. Theoretical Computer Science, Elsevier, 2017, 〈10.1016/j.tcs.2017.01.006〉. 〈hal-01198783〉

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