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Conference on Algorithms and Discrete Applied Mathematics

CALDAM 2023: Algorithms and Discrete Applied Mathematics pp 89–100Cite as

Rectilinear Voronoi Games with a Simple Rectilinear Obstacle in Plane

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13947))

Abstract

We study two player single round rectilinear Voronoi games in the plane for a finite set of clients where service paths are obstructed by a rectilinear polygon. The players wish to maximize the net number of their clients where a client is served by the nearest facility of players in \(\mathbb {L}_1 \) metric. We prove the tight bounds for the payoffs of both the players for the class of games with simple, convex and orthogonal convex polygons. We also generalize the results for \(\mathbb {L}_\infty \) metric in the plane.

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Author information

Authors and Affiliations

  1. Indian Statistical Institute, Kolkata, India

    Arun Kumar Das & Sandip Das

  2. Carleton University, Ottawa, ON, Canada

    Anil Maheshwari

  3. Ramakrishna Mission Vivekananda Educational and Research Institute, Howrah, India

    Sarvottamananda

Authors
  1. Arun Kumar Das
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  2. Sandip Das
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  3. Anil Maheshwari
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  4. Sarvottamananda
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Corresponding author

Correspondence to Arun Kumar Das .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India

    Amitabha Bagchi

  2. Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, India

    Rahul Muthu

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Das, A.K., Das, S., Maheshwari, A., Sarvottamananda (2023). Rectilinear Voronoi Games with a Simple Rectilinear Obstacle in Plane. In: Bagchi, A., Muthu, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2023. Lecture Notes in Computer Science, vol 13947. Springer, Cham. https://doi.org/10.1007/978-3-031-25211-2_7

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  • DOI: https://doi.org/10.1007/978-3-031-25211-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-25210-5

  • Online ISBN: 978-3-031-25211-2

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