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Algorithms for [formula omitted]-dispersion for points in convex position in the plane.

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Title: Algorithms for [formula omitted]-dispersion for points in convex position in the plane.
Authors: Singireddy, Vishwanath R.1 (AUTHOR) vishwanath.s@suh.edu.in, Basappa, Manjanna1,2 (AUTHOR) manjanna@nitk.edu.in, Mitchell, Joseph S.B.3 (AUTHOR) joseph.mitchell@stonybrook.edu
Source: Discrete Applied Mathematics. Jun2026, Vol. 386, p205-216. 12p.
Subjects: Computational geometry, Convex sets, Polynomial time algorithms, Combinatorial optimization, Deterministic algorithms, Algorithms, Approximation algorithms
Abstract: In this paper, we consider the following k -dispersion problem. Given a set S of n points placed in the plane in convex position and an integer k (0 < k < n), the objective is to compute a subset S ′ ⊂ S such that | S ′ | = k and the minimum distance between a pair of points in S ′ is maximized. Based on the bounded search tree method, we propose an exact fixed-parameter algorithm in O (2 k n 2 log 2 n) time for this problem, where k is the parameter. The proposed exact algorithm improves on the algorithm of Akagi et al. (2018), which requires time n O (k) , whenever k < c log 2 n for some constant c. We then give an exact polynomial-time (O (n 4 k 2)) algorithm, for any k > 0 , thus answering the open question about the complexity of this restricted dispersion problem. For k = 3 , there is an O (n 2) -time algorithm by Kobayashi et al. (2021). We then present an O (log n) -time 1 2 2 -approximation algorithm for the problem when k = 3 if the points are given in convex position order. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 192967408
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Algorithms for [formula omitted]-dispersion for points in convex position in the plane.
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  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Discrete+Applied+Mathematics%22&quot;&gt;Discrete Applied Mathematics&lt;/searchLink&gt;. Jun2026, Vol. 386, p205-216. 12p.
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  Data: In this paper, we consider the following k -dispersion problem. Given a set S of n points placed in the plane in convex position and an integer k (0 &lt; k &lt; n), the objective is to compute a subset S ′ ⊂ S such that | S ′ | = k and the minimum distance between a pair of points in S ′ is maximized. Based on the bounded search tree method, we propose an exact fixed-parameter algorithm in O (2 k n 2 log 2 n) time for this problem, where k is the parameter. The proposed exact algorithm improves on the algorithm of Akagi et al. (2018), which requires time n O (k) , whenever k &lt; c log 2 n for some constant c. We then give an exact polynomial-time (O (n 4 k 2)) algorithm, for any k &gt; 0 , thus answering the open question about the complexity of this restricted dispersion problem. For k = 3 , there is an O (n 2) -time algorithm by Kobayashi et al. (2021). We then present an O (log n) -time 1 2 2 -approximation algorithm for the problem when k = 3 if the points are given in convex position order. [ABSTRACT FROM AUTHOR]
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  Data: &lt;i&gt;Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.dam.2026.02.008
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 12
        StartPage: 205
    Subjects:
      – SubjectFull: Computational geometry
        Type: general
      – SubjectFull: Convex sets
        Type: general
      – SubjectFull: Polynomial time algorithms
        Type: general
      – SubjectFull: Combinatorial optimization
        Type: general
      – SubjectFull: Deterministic algorithms
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Approximation algorithms
        Type: general
    Titles:
      – TitleFull: Algorithms for [formula omitted]-dispersion for points in convex position in the plane.
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            NameFull: Singireddy, Vishwanath R.
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            NameFull: Basappa, Manjanna
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            NameFull: Mitchell, Joseph S.B.
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            – D: 15
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 386
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            – TitleFull: Discrete Applied Mathematics
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