Parallel techniques for paths, visibility, and related problems

Ziyi Danny Chen, Purdue University

Abstract

This dissertation presents several deterministic techniques for efficiently solving shortest paths, visibility, and other related geometric problems in parallel. Specifically, we give techniques for designing efficient deterministic parallel algorithms for solving the following problems: computing rectilinear shortest paths that avoid rectangular obstacles in the plane, computing the visible portions of a simple polygonal chain from a point, and detecting the weak visibility of a simple polygon. These parallel techniques further enable us to solve many related geometric problems that include: computing the convex hull of a set of planar points sorted by the x-coordinates, computing the convex hull of a simple polygon, finding the kernel of a simple polygon, triangulating a set of planar points sorted by the x-coordinates, triangulating monotone polygons and star-shaped polygons, solving the all dominating neighbors problem, computing shortest paths inside a weakly visible polygon, triangulating a weakly visible polygon, checking the weak external visibility of a simple polygon, and solving the one-cruising-guard problem. Most of the parallel algorithms we obtain for these problems are optimal in the complexities of the total running time and the total amount of operations performed. Our results improve the previously known parallel algorithms for these problems in either the time complexity, or the processor complexity, or the parallel computational model required by the algorithms (in the sense of using a weaker parallel model). The parallel computational models used by our algorithms are the CREW PRAM or the EREW PRAM.

Degree

Ph.D.

Advisors

Atallah, Purdue University.

Subject Area

Computer science

COinS