Geometric Optimization Revisited

Abstract

Many combinatorial optimization problems such as set cover, clustering, and graph matching have been formulated in geometric settings. We review the progress made in recent years on a number of such geometric optimization problems, with an emphasis on how geometry has been exploited to develop better algorithms. Instead of discussing many problems, we focus on a few problems, namely, set cover, hitting set, independent set, and computing maps between point sets.

Computation and Complexity

“…The chapter "Geometric Optimization Revisited" by Agarwal et al [1] deals with the area of computational geometry. Computational geometry is devoted to the study of algorithms that deal with points, lines, circles, triangles, polytopes, spheres, and other geometric objects.…”