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Bounds for the Oriented Diameter of Planar Triangulations

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Frontiers of Algorithmic Wisdom (IJTCS-FAW 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13461))

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Abstract

The diameter of an undirected or a directed graph is defined to be the maximum shortest path distance over all pairs of vertices in the graph. Given an undirected graph G, we examine the problem of assigning directions to each edge of G such that the diameter of the resulting oriented graph is minimized. The minimum diameter over all strongly connected orientations is called the oriented diameter of G. The problem of determining the oriented diameter of a graph is known to be NP-hard, but the time-complexity question is open for planar graphs. In this paper we compute the exact value of the oriented diameter for triangular grid graphs. We then prove an n/3 lower bound and an \(n/2+O(\sqrt{n})\) upper bound on the oriented diameter of planar triangulations. It is known that given a planar graph G with bounded treewidth and a fixed positive integer k, one can determine in linear time whether the oriented diameter of G is at most k. In contrast, we consider a weighted version of the oriented diameter problem and show it to be weakly NP-complete for planar graphs with bounded pathwidth.

The work of D. Mondal is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Saskatchewan, Saskatoon, Canada

    Debajyoti Mondal

  2. Department of Data Science and Business Systems, School of Computing, SRM Institute of Science and Technology, Kattankulathur, India

    N. Parthiban

  3. Division of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, India

    Indra Rajasingh

Authors
  1. Debajyoti Mondal
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  2. N. Parthiban
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  3. Indra Rajasingh
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Corresponding author

Correspondence to N. Parthiban .

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Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Hong Kong, China

    Minming Li

  2. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

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Mondal, D., Parthiban, N., Rajasingh, I. (2022). Bounds for the Oriented Diameter of Planar Triangulations. In: Li, M., Sun, X. (eds) Frontiers of Algorithmic Wisdom. IJTCS-FAW 2022. Lecture Notes in Computer Science, vol 13461. Springer, Cham. https://doi.org/10.1007/978-3-031-20796-9_14

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  • DOI: https://doi.org/10.1007/978-3-031-20796-9_14

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-20796-9

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