TY - JOUR

T1 - Algorithms for finding noncrossing paths with minimum total length in plane graphs

AU - Takahashi, Jun‐Ya ‐Y

AU - Suzuki, Hitoshi

AU - Nishizeki, Takao

PY - 1995/4

Y1 - 1995/4

N2 - 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.

AB - 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.

KW - algorithm

KW - noncrossing paths

KW - Planar graph

KW - shortest‐path problem

KW - VLSI single‐layer routing

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U2 - 10.1002/ecjc.4430780401

DO - 10.1002/ecjc.4430780401

M3 - Article

AN - SCOPUS:0029282483

SN - 1042-0967

VL - 78

SP - 1

EP - 15

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

IS - 4

ER -