Abstract. Given a simple n-sided polygon in the plane with a boundary partitioned into subchains some of which are convex and colored, we consider the following problem: Which is t...
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their ...
Julia Chuzhoy, Yury Makarychev, Anastasios Sidirop...
Abstract. We present an O(n log n)-time algorithm to solve the threedimensional layers-of-maxima problem, an improvement over the prior O(n log n log log n)-time solution. A previo...
A three-dimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line-segments representing the edges ...
Two long-open problems have been solved: (1) every sufficiently large planar point set in general position contains the vertices of an empty hexagon; (2) every finite collection o...