Article

Short path queries in planar graphs in constant time

Authors:

Lukasz Kowalik,

Maciej KurowskiAuthors Info & Claims

STOC '03: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing

Pages 143 - 148

https://doi.org/10.1145/780542.780565

Published: 09 June 2003 Publication History

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Abstract

We present a new algorithm for answering short path queries in planar graphs. For any fixed constant k and a given unweighted planar graph G=(V,E) one can build in O(|V|) time a data structure, which allows to check in O(1) time whether two given vertices are distant by at most k in G and if so a shortest path between them is returned. This significantly improves the previous result of D. Eppstein [5] where after a linear preprocessing the queries are answered in O(log |V|) time. Our approach can be applied to compute the girth of a planar graph and a corresponding shortest cycle in O(|V|) time provided that the constant bound on the girth is known.Our results can be easily generalized to other wide classes of graphs~--~for instance we can take graphs embeddable in a surface of bounded genus or graphs of bounded tree-width.

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D. A. Chen and J. Xu. Shortest path queries in planar graphs. In Proc. of the 32nd Annual ACM Symposium on Theory of Computing, pages 469--478, 2000.]]

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D. Eppstein. Subgraph isomorphism in planar graphs and related problems. J. Graph Algorithms & Applications, 3(3):1--27, 1999.]]

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Balzotti LFranciosa P(2024)How vulnerable is an undirected planar graph with respect to max flowNetworks10.1002/net.2220583:3(570-586)Online publication date: 3-Jan-2024
https://doi.org/10.1002/net.22205
Balzotti LFranciosa P(2023)How Vulnerable is an Undirected Planar Graph with Respect to Max FlowAlgorithms and Complexity10.1007/978-3-031-30448-4_7(82-96)Online publication date: 25-Apr-2023
https://doi.org/10.1007/978-3-031-30448-4_7
Le HWulff-Nilsen C(2022)Optimal Approximate Distance Oracle for Planar Graphs2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00044(363-374)Online publication date: Feb-2022
https://doi.org/10.1109/FOCS52979.2021.00044
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Index Terms

Short path queries in planar graphs in constant time
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Paths and connectivity problems

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STOC '03: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing

June 2003

740 pages

ISBN:1581136749

DOI:10.1145/780542

Conference Chair:
Lawrence L. Larmore
University of Nevada Las Vegas, Las Vegas, NV
,
Program Chair:
Michel X. Goemans
Massachusetts Institute of Technology, Cambridge, MA

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Published: 09 June 2003

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Balzotti LFranciosa P(2023)How Vulnerable is an Undirected Planar Graph with Respect to Max FlowAlgorithms and Complexity10.1007/978-3-031-30448-4_7(82-96)Online publication date: 25-Apr-2023
https://doi.org/10.1007/978-3-031-30448-4_7
Le HWulff-Nilsen C(2022)Optimal Approximate Distance Oracle for Planar Graphs2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00044(363-374)Online publication date: Feb-2022
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Balzotti LFranciosa P(2022)Non-crossing Shortest Paths in Undirected Unweighted Planar Graphs in Linear TimeComputer Science – Theory and Applications10.1007/978-3-031-09574-0_6(77-95)Online publication date: 24-Jun-2022
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Equitable colorings of planar graphs without short cycles

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Equitable colorings of planar graphs without short cycles

Improper colorability of planar graphs without prescribed short cycles

Acyclic edge colouring of planar graphs without short cycles

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