Homotopic C-oriented routing

Abstract

We study the problem of finding non-crossing minimum-link C-oriented paths that are homotopic to a set of input paths in an environment with C-oriented obstacles. We introduce a special type of C-oriented paths-smooth paths-and present a 2-approximation algorithm that runs in O(n2 (n + log κ) + kin log n) time, where n is the total number of paths and obstacle vertices, kin is the total number of links in the input, and κ = |C|. The algorithm also computes an O(κ)-approximation for general C-oriented paths. As a related result we show that, given a set of C-oriented paths with L links in total, non-crossing C-oriented paths homotopic to the input paths can require a total of Ω(L log κ) links. © 2013 Springer-Verlag.