License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2022.47
URN: urn:nbn:de:0030-drops-173322
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17332/
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Kobayashi, Yusuke ; Terao, Tatsuya

One-Face Shortest Disjoint Paths with a Deviation Terminal

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LIPIcs-ISAAC-2022-47.pdf (0.8 MB)

Abstract

For an undirected graph G and distinct vertices s₁, t₁, … , s_k, t_k called terminals, the shortest k-disjoint paths problem asks for k pairwise vertex-disjoint paths P₁, … , P_k such that P_i connects s_i and t_i for i = 1, … , k and the sum of their lengths is minimized. This problem is a natural optimization version of the well-known k-disjoint paths problem, and its polynomial solvability is widely open. One of the best results on the shortest k-disjoint paths problem is due to Datta et al. [Datta et al., 2018], who present a polynomial-time algorithm for the case when G is planar and all the terminals are on one face. In this paper, we extend this result by giving a polynomial-time randomized algorithm for the case when all the terminals except one are on some face of G. In our algorithm, we combine the arguments of Datta et al. with some results on the shortest disjoint (A + B)-paths problem shown by Hirai and Namba [Hirai and Namba, 2018]. To this end, we present a non-trivial bijection between k disjoint paths and disjoint (A + B)-paths, which is a key technical contribution of this paper.

BibTeX - Entry

@InProceedings{kobayashi_et_al:LIPIcs.ISAAC.2022.47,
  author =	{Kobayashi, Yusuke and Terao, Tatsuya},
  title =	{{One-Face Shortest Disjoint Paths with a Deviation Terminal}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{47:1--47:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17332},
  URN =		{urn:nbn:de:0030-drops-173322},
  doi =		{10.4230/LIPIcs.ISAAC.2022.47},
  annote =	{Keywords: shortest disjoint paths, polynomial time algorithm, planar graph}
}

Keywords: shortest disjoint paths, polynomial time algorithm, planar graph
Collection: 33rd International Symposium on Algorithms and Computation (ISAAC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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