Length-bounded disjoint paths in planar graphs

H. Holst, van der; J.C. Pina, de

doi:10.1016/S0166-218X(01)00294-3

Length-bounded disjoint paths in planar graphs

H. Holst, van der, J.C. Pina, de

Research output: Contribution to journal › Article › Academic › peer-review

16 Citations (Scopus)

Abstract

The following problem is considered: given: an undirected planar graph G=(V,E) embedded in , distinct pairs of vertices {r1,s1},…,{rk,sk} of G adjacent to the unbounded face, positive integers b1,…,bk and a function ; find: pairwise vertex-disjoint paths P1,…,Pk such that for each i=1,…,k, Pi is a ri-si-path and the sum of the l-length of all edges in Pi is at most bi. It is shown that the problem is NP-hard in the strong sense. A pseudo-polynomial-time algorithm is given for the case of k=2.

Original language	English
Pages (from-to)	251-261
Journal	Discrete Applied Mathematics
Volume	120
Issue number	1-3
DOIs	https://doi.org/10.1016/S0166-218X(01)00294-3
Publication status	Published - 2002

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title = "Length-bounded disjoint paths in planar graphs",

abstract = "The following problem is considered: given: an undirected planar graph G=(V,E) embedded in , distinct pairs of vertices {r1,s1},…,{rk,sk} of G adjacent to the unbounded face, positive integers b1,…,bk and a function ; find: pairwise vertex-disjoint paths P1,…,Pk such that for each i=1,…,k, Pi is a ri-si-path and the sum of the l-length of all edges in Pi is at most bi. It is shown that the problem is NP-hard in the strong sense. A pseudo-polynomial-time algorithm is given for the case of k=2.",

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AU - Pina, de, J.C.

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AB - The following problem is considered: given: an undirected planar graph G=(V,E) embedded in , distinct pairs of vertices {r1,s1},…,{rk,sk} of G adjacent to the unbounded face, positive integers b1,…,bk and a function ; find: pairwise vertex-disjoint paths P1,…,Pk such that for each i=1,…,k, Pi is a ri-si-path and the sum of the l-length of all edges in Pi is at most bi. It is shown that the problem is NP-hard in the strong sense. A pseudo-polynomial-time algorithm is given for the case of k=2.

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DO - 10.1016/S0166-218X(01)00294-3

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VL - 120

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EP - 261

JO - Discrete Applied Mathematics

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IS - 1-3

ER -

Length-bounded disjoint paths in planar graphs

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