Linear time algorithms for disjoint two-face paths problems in planar graphs

Abstract

In this paper we present a linear time algorithm for the vertexdisjoint Two-Face Paths Problem in planar graphs, i.e., the problem of finding k vertex-disjoint paths between pairs of terminals which lie on two face boundaries. The algorithm is based on the idea of findingrightmost paths with a certain property in planar graphs. Using this method, a linear time algorithm for finding vertex-disjoint paths of a certain homotopy is derived. Moreover, the algorithm can be modified to solve the more general linkage problem in linear time as well.