research-article

Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs

Author:

Sergio CabelloAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 15, Issue 2

Article No.: 21, Pages 1 - 38

https://doi.org/10.1145/3218821

Published: 07 December 2018 Publication History

Abstract

In this article, we show how to compute for n-vertex planar graphs in O(n^11/6 polylog(n)) expected time the diameter and the sum of the pairwise distances. The algorithms work for directed graphs with real weights and no negative cycles. In O(n^15/8 polylog(n)) expected time, we can also compute the number of pairs of vertices at distances smaller than a given threshold. These are the first algorithms for these problems using time O(n^c) for some constant c< 2, even when restricted to undirected, unweighted planar graphs.

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Charalampopoulos PGawrychowski PLong YMozes SPettie SWeimann OWulff-Nilsen C(2023)Almost Optimal Exact Distance Oracles for Planar GraphsJournal of the ACM10.1145/358047470:2(1-50)Online publication date: 25-Mar-2023
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Index Terms

Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs
1. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Shortest paths
  2. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 15, Issue 2

Special Issue on Soda'17 and Regular Papers

April 2019

407 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3292530

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2018 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Publication History

Published: 07 December 2018

Accepted: 01 May 2018

Revised: 01 November 2017

Received: 01 February 2017

Published in TALG Volume 15, Issue 2

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https://dl.acm.org/doi/10.1007/s00453-024-01246-z
Charalampopoulos PGawrychowski PLong YMozes SPettie SWeimann OWulff-Nilsen C(2023)Almost Optimal Exact Distance Oracles for Planar GraphsJournal of the ACM10.1145/358047470:2(1-50)Online publication date: 25-Mar-2023
https://dl.acm.org/doi/10.1145/3580474
Chang HConroy JLe HMilenkovic LSolomon SThan C(2023)Covering Planar Metrics (and Beyond): O(1) Trees Suffice2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00139(2231-2261)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00139
Ducoffe G(2023)Distance problems within Helly graphs and k-Helly graphsTheoretical Computer Science10.1016/j.tcs.2023.113690946(113690)Online publication date: Feb-2023
https://doi.org/10.1016/j.tcs.2023.113690
Gawrychowski PUznański P(2023)Better Distance Labeling for Unweighted Planar GraphsAlgorithmica10.1007/s00453-023-01133-z85:6(1805-1823)Online publication date: 15-May-2023
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Dumitrescu ATóth C(2023)Maximal Distortion of Geodesic Diameters in Polygonal DomainsCombinatorial Algorithms10.1007/978-3-031-34347-6_17(197-208)Online publication date: 7-Jun-2023
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Jin CXu YLeonardi SGupta A(2022)Tight dynamic problem lower bounds from generalized BMM and OMvProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520036(1515-1528)Online publication date: 9-Jun-2022
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Cabello S(2022)Computing the Inverse Geodesic Length in Planar Graphs and Graphs of Bounded TreewidthACM Transactions on Algorithms10.1145/350130318:2(1-26)Online publication date: 4-Mar-2022
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