Approximation algorithms for maximum independent set of pseudo-disks
Timothy M. Chan, Sariel Har-Peled · 2009
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, that 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.