
Sariel Har-Peled and Kent Quanrud.
We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient $(1+\eps)$-approximation algorithms for these graphs, for \ProblemC{Independent Set}, Set Cover, and Dominating Set problems, among others. We also prove corresponding hardness of approximation for some of these optimization problems, providing a characterization of their intractability in terms of density.
PDF.
Slides: ESA 2015 talk (created and presented by Kent).