Shortest Noncrossing Paths in Plane Graphs

Jun Ya Takahashi, Hitoshi Suzuki, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


Let G be an undirected plane graph with nonnegative edge length, and let k terminal pairs lie on two specified face boundaries. This paper presents an algorithm for finding k "noncrossing paths" in G, each connecting a terminal pair, and whose total length is minimum. Noncrossing paths may share common vertices or edges but do not cross each other in the plane. The algorithm runs in time O(n log n) where n is the number of vertices in G and k is an arbitrary integer.

Original languageEnglish
Pages (from-to)339-357
Number of pages19
Issue number3
Publication statusPublished - 1996 Sept


  • Noncrossing paths
  • Plane graphs
  • Shortest path
  • Single-layer routing
  • VLSI


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