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.2021.62
URN: urn:nbn:de:0030-drops-154950
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15495/
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Bacic, Joyce ; Mehrabi, Saeed ; Smid, Michiel

Shortest Beer Path Queries in Outerplanar Graphs

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LIPIcs-ISAAC-2021-62.pdf (0.9 MB)

Abstract

A beer graph is an undirected graph G, in which each edge has a positive weight and some vertices have a beer store. A beer path between two vertices u and v in G is any path in G between u and v that visits at least one beer store.
We show that any outerplanar beer graph G with n vertices can be preprocessed in O(n) time into a data structure of size O(n), such that for any two query vertices u and v, (i) the weight of the shortest beer path between u and v can be reported in O(α(n)) time (where α(n) is the inverse Ackermann function), and (ii) the shortest beer path between u and v can be reported in O(L) time, where L is the number of vertices on this path. Both results are optimal, even when G is a beer tree (i.e., a beer graph whose underlying graph is a tree).

BibTeX - Entry

@InProceedings{bacic_et_al:LIPIcs.ISAAC.2021.62,
  author =	{Bacic, Joyce and Mehrabi, Saeed and Smid, Michiel},
  title =	{{Shortest Beer Path Queries in Outerplanar Graphs}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{62:1--62:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15495},
  URN =		{urn:nbn:de:0030-drops-154950},
  doi =		{10.4230/LIPIcs.ISAAC.2021.62},
  annote =	{Keywords: shortest paths, outerplanar graph}
}

Keywords: shortest paths, outerplanar graph
Collection: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue Date: 2021
Date of publication: 30.11.2021

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