Algorithms for finding optimal disjoint paths around a rectangle

Abstract

We give algorithms to find the optimal disjoint paths around a rectangle. The set of disjoint paths connects a set of sources to a set of sinks (no fixed pairing between the sources and sinks) on the boundary of a rectangle where either the longest path length or the total path length is minimized. One algorithm finds the set of disjoint paths with the longest path length minimized in O(n log n) time and the other finds the set of disjoint paths with the total path length minimized in O(n 2) time. In particular, if the sets of sources and sinks lie on a straight line, the set of disjoint paths with the minimum longest path length or minimum total path length can be found in O(n) or O(n 2) time respectively.