Given a collection S of subsets of some set U, and M⊂ U, the set cover problem is to find the
smallest subcollection C⊂ S such that M is a subset of the union of the sets in C. While the …

In this paper, we present approximation algorithms for minimum vertex and edge guard
problems for polygons with or without holes with a total of n vertices. For simple polygons …

We introduce the notion of delineation. A graph class $\mathcal C $ is said delineated if for
every hereditary closure $\mathcal D $ of a subclass of $\mathcal C $, it holds that $\mathcal …

There has been much progress on geometric set cover problems, but most known
techniques only apply to the unweighted setting. For the weighted setting, very few results …

We propose heuristics for visibility coverage of a polygon with the fewest point guards. This
optimal coverage problem, often called the" art gallery problem", is known to be NP-hard, so …

A set G of points on a terrain, also known as an x-monotone polygonal chain, is said to
guard the terrain if every point on the terrain is seen by a point in G. Two points on the terrain …

Given an arbitrary viewpoint v and a terrain, the visibility map or viewshed of v is the set of
points in the terrain that are visible from v. In this article we consider the problem of …

We prove that guarding the vertices of a rectilinear polygon P, whether by guards lying at
vertices of P, or by guards lying on the boundary of P, or by guards lying anywhere in P, is …

We obtain a polynomial time approximation scheme for the terrain guarding problem
improving upon several recent constant factor approximations. Our algorithm is a local …

We present a number of positive and negative results for variants of the matroid secretary
problem. Most notably, we design a constant-factor competitive algorithm for the “random …