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The Conditional Covering Problem on Unweighted Interval Graphs with Nonuniform Coverage Radius

The Conditional Covering Problem on Unweighted Interval Graphs with Nonuniform Coverage Radius Let G = (V, E) be an interval graph with n vertices and m edges. A positive integer R(x) is associated with every vertex $${x\in V}$$ . In the conditional covering problem, a vertex $${x \in V}$$ covers a vertex $${y \in V}$$ (x ≠ y) if d(x, y) ≤ R(x) where d(x, y) is the shortest distance between the vertices x and y. The conditional covering problem (CCP) finds a minimum cardinality vertex set $${C\subseteq V}$$ so as to cover all the vertices of the graph and every vertex in C is also covered by another vertex of C. This problem is NP-complete for general graphs. In this paper, we propose an efficient algorithm to solve the CCP with nonuniform coverage radius in O(n 2) time, when G is an interval graph containing n vertices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics in Computer Science Springer Journals

The Conditional Covering Problem on Unweighted Interval Graphs with Nonuniform Coverage Radius

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Basel AG
Subject
Mathematics; Computer Science, general; Mathematics, general
ISSN
1661-8270
eISSN
1661-8289
DOI
10.1007/s11786-011-0106-1
Publisher site
See Article on Publisher Site

Abstract

Let G = (V, E) be an interval graph with n vertices and m edges. A positive integer R(x) is associated with every vertex $${x\in V}$$ . In the conditional covering problem, a vertex $${x \in V}$$ covers a vertex $${y \in V}$$ (x ≠ y) if d(x, y) ≤ R(x) where d(x, y) is the shortest distance between the vertices x and y. The conditional covering problem (CCP) finds a minimum cardinality vertex set $${C\subseteq V}$$ so as to cover all the vertices of the graph and every vertex in C is also covered by another vertex of C. This problem is NP-complete for general graphs. In this paper, we propose an efficient algorithm to solve the CCP with nonuniform coverage radius in O(n 2) time, when G is an interval graph containing n vertices.

Journal

Mathematics in Computer Science – Springer Journals

Published: Nov 27, 2011

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