The field of computational geometry is a relatively recent addition to the mathematical
landscape. Over the past ten years, a substantial number of papers and technical reports in …

Two points in a polygon are called if the straight line between them lies entirely inside the
polygon. The art gallery problem for a polygon P is to find a minimum set of points G in P …

Abstract In 1973, Victor Klee posed the following question: How many guards are necessary,
and how many are sufficient to patrol the paintings and works of art in an art gallery with n …

In this paper we consider the problem of finding shortest routes from which every point in a
given space is visible (watchman routes). We show that the problem is NP-hard when 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 devise a polynomial-time algorithm for partitioning a simple polygon P into a minimum
number of star-shaped polygons. The question of whether such an algorithm exists has …

Abstract The Rotating Calipers is a paradigm used to solve a number of problems in the field
of Computational Geometry. The original algorithm was presented by Shamos in 1978 in …

The following graph-coloring result is proved: let G be a 2-connected, bipartite, and plane
graph. Then one can triangulate G in such a way that the resulting graph is 3-colorable …

A bibliography of 370 references of books, papers in serial journals, and conference papers,
on convexity in relation to computer science is presented. The subject is divided into five …

We study the problem of converting triangulated domains to quadrangulations, under a
variety of constraints. We obtain a variety of characterizations for when a triangulation (of …