Combinatorial Geometry and Approximation Algorithms

Abstract

In this talk, I will discuss some recent applications of combinatorial geometry to the analysis of approximation algorithms—specifically, approximation algorithms for geometric versions of set cover, hitting set, and independent set problems, for different types of objects such as disks and rectangles (both unweighted and weighted). These problems turn out to be related, via LP rounding, to a number of well-known combinatorial problems: ε-nets, union complexity, (≤ k)-levels, and conflict-free coloring. I will attempt to explain all these inter-relationships, survey some of the latest results, and mention open problems.