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DOI: 10.4230/LIPIcs.ISAAC.2021.62
URN: urn:nbn:de:0030-drops-154950
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15495/
Bacic, Joyce ; Mehrabi, Saeed ; Smid, Michiel
Shortest Beer Path Queries in Outerplanar Graphs
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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 | |
| Seminar: | 32nd International Symposium on Algorithms and Computation (ISAAC 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 30.11.2021 |
