Shortest Paths and Networks

Abstract

We survey various forms of the problem, primarily in two and three dimensions, for motion of a single point, since most results have focused on these cases. We discuss shortest paths in a simple polygon (Section 31.1), shortest paths among obstacles (Section 31.2), and other metrics for length (Section 31.3). We also survey other related geometric network optimization problems (Section 31.4). Higher dimensions are discussed in Section 31.5.