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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]
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Database: Engineering Source
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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]
ISSN:0166218X
DOI:10.1016/j.dam.2026.02.008