Approximation Algorithms for Unit Disk Graphs
We consider several graph theoretic problems on unit disk graphs (Maximum Independent Set, Minimum Vertex Cover, and Minimum (Connected) Dominating Set) relevant to mobile ad hoc networks. We propose two new notions: thickness and density. If the thickness of a unit disk graph is bounded, then the m...
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Published in | Graph-Theoretic Concepts in Computer Science pp. 351 - 361 |
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Main Author | |
Format | Book Chapter Conference Proceeding |
Language | English |
Published |
Berlin, Heidelberg
Springer Berlin Heidelberg
2005
Springer |
Series | Lecture Notes in Computer Science |
Subjects | |
Online Access | Get full text |
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Summary: | We consider several graph theoretic problems on unit disk graphs (Maximum Independent Set, Minimum Vertex Cover, and Minimum (Connected) Dominating Set) relevant to mobile ad hoc networks. We propose two new notions: thickness and density. If the thickness of a unit disk graph is bounded, then the mentioned problems can be solved in polynomial time. For unit disk graphs of bounded density, we present a new asymptotic fully-polynomial approximation scheme for the considered problems. The scheme for Minimum Connected Dominating Set is the first Baker-like asymptotic FPTAS for this problem. By adapting the proof, it implies e.g. an asymptotic FPTAS for Minimum Connected Dominating Set on planar graphs. |
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Bibliography: | This research was supported by the Netherlands Organisation for Scientific Research NWO (project Treewidth and Combinatorial Optimisation) and by the Bsik project BRICKS). |
ISBN: | 3540310002 9783540310006 |
ISSN: | 0302-9743 1611-3349 |
DOI: | 10.1007/11604686_31 |