Algorithms for finding noncrossing paths with minimum total length in plane graphs

Jun‐Ya ‐Y Takahashi, Hitoshi Suzuki, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review


Assume that G is an undirected planar graph and the edge length of G is a nonnegative real number. When k terminal pairs are specified on two specified face boundaries, this paper gives an algorithm that derives the “noncrossing paths” with the minimum sum of lengths that connects the respective terminal pairs. By the noncrossing paths is meant the paths which do not cross on the plane, although the point or the edge may be shared. the computation time of the proposed algorithm is O(n log n), where n is the number of points on the planar graph G; k need not be a constant.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalElectronics and Communications in Japan (Part III: Fundamental Electronic Science)
Issue number4
Publication statusPublished - 1995 Apr


  • Planar graph
  • VLSI single‐layer routing
  • algorithm
  • noncrossing paths
  • shortest‐path problem

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this