Discrete & Computational Geometry

, Volume 48, Issue 2, pp 373–392

Approximation Algorithms for Maximum Independent Set of Pseudo-Disks

Article

DOI: 10.1007/s00454-012-9417-5

Cite this article as:
Chan, T.M. & Har-Peled, S. Discrete Comput Geom (2012) 48: 373. doi:10.1007/s00454-012-9417-5

Abstract

We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local-search algorithm yields a PTAS. For the weighted case, we suggest a novel rounding scheme based on an LP relaxation of the problem, which leads to a constant-factor approximation.

Most previous algorithms for maximum independent set (in geometric settings) relied on packing arguments that are not applicable in this case. As such, the analysis of both algorithms requires some new combinatorial ideas, which we believe to be of independent interest.

Keywords

Fréchet distanceApproximation algorithmsRealistic input models

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Department of Computer ScienceUniversity of IllinoisUrbanaUSA