MAXIMUM AREA INDEPENDENT SETS IN DISK INTERSECTION GRAPHS-Reference-Cited by-同舟云学术

MAXIMUM AREA INDEPENDENT SETS IN DISK INTERSECTION GRAPHS

Published:2010-04 Issue:02 Volume:20 Page:105-118
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

BEREG SERGEY¹,DUMITRESCU ADRIAN²,JIANG MINGHUI³

Affiliation:

1. Department of Computer Science, University of Texas at Dallas, Richardson, Texas 75083, USA

2. Department of Computer Science, University of Wisconsin – Milwaukee, Wisconsin 53201-0784, USA

3. Department of Computer Science, Utah State University, Logan, Utah 84322-4205, USA

Abstract

Maximum Independent Set (MIS) and its relative Maximum Weight Independent Set (MWIS) are well-known problems in combinatorial optimization; they are NP-hard even in the geometric setting of unit disk graphs. In this paper, we study the Maximum Area Independent Set (MAIS) problem, a natural restricted version of MWIS in disk intersection graphs where the weight equals the disk area. We obtain: (i) Quantitative bounds on the maximum total area of an independent set relative to the union area; (ii) Practical constant-ratio approximation algorithms for finding an independent set with a large total area relative to the union area.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195910003220

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1. Local ratio

2. Polynomial-time approximation schemes for packing and piercing fat objects

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