Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs

Abstract. Let G be a directed planar graph of complexity n, each arc having a nonnegative length. Let s and t be two distinct faces of G; let s1, . . . , sk be vertices incident with s; let t1, . . . , tk be vertices incident with t. We give an algorithm to compute k pairwise vertex-disjoint paths connecting the pairs (si, ti) in G, with minimal total length, in O(kn log n) time.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Éric Colin de Verdière, Alexander Schrijver
• Keywords: CORR 2008, Directed Planar Graph, Distinct Faces, Education, Nonnegative Length