Reprint of: Memory-constrained algorithms for simple polygons

Memory-constrained algorithms for simple polygons

A constant-work-space algorithm has read-only access to an input array and may use only O(1) additional words of O(log n) bits, where n is the input size. We show how to triangulate a plane straight-line graph with n vertices in O(n) time and constant workspace. We also consider the problem of preprocessing a simple n-gon P for shortest path queries, where P is given by the ordered sequence of ...

Optimal Mesh Computer Algorithms for Simple Polygons

We present optimal parallel algorithms that run in O(p n) time on a p n p n mesh-connected computer for a number of fundamental problems concerning visibility and distance properties inside a simple polygon. These include computing shortest paths, shortest path trees, shortest path partitions, all-farthest neighbors (both internal and external), the visibility polygon of a point, the weak visib...

Optimal Algorithms for Two-Guard Walkability of Simple Polygons

An Overview of Triangulation Algorithms for Simple Polygons

Decomposing simple polygon into simpler components is one of the basic tasks in computational geometry and its applications. The most important simple polygon decomposition is triangulation. Different techniques for triangulating simple polygon were designed. The first part of the paper is an overview of triangulation algorithms based on diagonal inserting. In the second part we present algorit...

A Contribution to Triangulation Algorithms for Simple Polygons

Decomposing simple polygon into simpler components is one of the basic tasks in computational geometry and its applications. The most important simple polygon decomposition is triangulation. The known algorithms for polygon triangulation can be classified into three groups: algorithms based on diagonal inserting, algorithms based on Delaunay triangulation, and the algorithms using Steiner point...