Algorithms for finding disjoint path covers in unit interval graphs

Park, Jung-Heum; Choi, Ji-Hyun; Lim, Hyeong-Seok

doi:10.1016/j.dam.2015.12.002

Cited by 6 publications

(2 citation statements)

References 35 publications

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“…There are, not closely related, problems, including [12][13][14], which consider di erent versions of nding disjoint paths inside a set of sources and a set of targets.…”

Section: Related Workmentioning

confidence: 99%

Time complexity of two disjoint simple paths

Razzazi

Sepahvand

2017

Scientia Iranica

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Abstract. Finding two disjoint simple paths on two given sets of points is a geometric problem introduced by Je Erickson. This problem has various applications in computational geometry, e.g. robot motion planning, generating polygon, etc. We will present a reduction from planar Hamiltonian path to this problem, and prove that it is NPcomplete. To the best of our knowledge, no study has considered its complexity up until now. We also present a reduction from planar Hamiltonian path problem to the problem of \ nding a path on given points in the presence of arbitrary obstacles" and prove that it is also NP-complete. Also, we present a heuristic algorithm with time complexity of O(n 4 ) to solve this problem. The proposed algorithm rst calculates the convex hull for each of the entry points and then produces two simple paths on the two entry point sets.

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“…There are, not closely related, problems, including [12][13][14], which consider di erent versions of nding disjoint paths inside a set of sources and a set of targets.…”

Section: Related Workmentioning

confidence: 99%

Time complexity of two disjoint simple paths

Razzazi

Sepahvand

2017

Scientia Iranica

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“…In addition, the problem is concerned with applications where full utilization of network nodes is important [3]. The problems have been studied for various classes of graphs, such as interval graphs [4,5], hypercubes [6,7,8], torus networks [9,10,11,12], dense graphs [13], and cubes of connected graphs [14,15].…”

Section: Introductionmentioning

confidence: 99%

Paired Many-to-Many 3-Disjoint Path Covers in Bipartite Toroidal Grids

Park¹

2018

JCSE

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Given two disjoint vertex-sets, S = {s1,. .. , s k } and T = {t1,. .. , t k } in a graph, a paired many-to-many k-disjoint path cover joining S and T is a set of pairwise vertex-disjoint paths {P1,. .. , P k } that altogether cover every vertex of the graph, in which each path Pi runs from si to ti. In this paper, we first study the disjoint-path-cover properties of a bipartite cylindrical grid. Based on the findings, we prove that every bipartite toroidal grid, excluding the smallest one, has a paired many-to-many 3-disjoint path cover joining S = {s1, s2, s3} and T = {t1, t2, t3} if and only if the set S ∪ T contains the equal numbers of vertices from different parts of the bipartition.

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A sufficient condition for the unpaired k-disjoint path coverability of interval graphs

Park

2021

J Supercomput

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Algorithms for finding disjoint path covers in unit interval graphs

Cited by 6 publications

References 35 publications

Time complexity of two disjoint simple paths

Time complexity of two disjoint simple paths

Paired Many-to-Many 3-Disjoint Path Covers in Bipartite Toroidal Grids

A sufficient condition for the unpaired k-disjoint path coverability of interval graphs

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