Constrained many-to-many point matching in two dimensions

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2024-01-26 DOI:10.1007/s11590-023-02089-3

L. E. Caraballo, R. A. Castro, J. M. Díaz-Báñez, M. A. Heredia, J. Urrutia, I. Ventura, F. J. Zaragoza

引用次数: 0

Abstract

In the minimum-weight many-to-many point matching problem, we are given a set R of red points and a set B of blue points in the plane, of total size N, and we want to pair up each point in R to one or more points in B and vice versa so that the sum of distances between the paired points is minimized. This problem can be solved in \(O(N^3)\) time by using a reduction to the minimum-weight perfect matching problem, and thus, it is not fast enough to be used for on-line systems where a large number of tunes need to be compared. Motivated by similarity problems in music theory, in this paper we study several constrained minimum-weight many-to-many point matching problems in which the allowed pairings are given by geometric restrictions, i.e., a bichromatic pair can be matched if and only if the corresponding points satisfy a specific condition of closeness. We provide algorithms to solve these constrained versions in O(N) time when the sets R and B are given ordered by abscissa.

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二维受限多对多点匹配

在最小权重多对多点匹配问题中，我们给定了平面上总大小为 N 的红色点集合 R 和蓝色点集合 B，我们希望将 R 中的每个点与 B 中的一个或多个点配对，反之亦然，从而使配对点之间的距离之和最小。通过对最小权重完全匹配问题的还原，这个问题可以在（O(N^3)\)时间内解决，因此，对于需要比较大量曲调的在线系统来说，它的速度还不够快。受音乐理论中相似性问题的启发，我们在本文中研究了几种受限的最小权重多对多点匹配问题，其中允许的配对是由几何限制给出的，即只有当且仅当对应点满足特定的接近条件时，才能匹配一对双色点。当 R 集和 B 集按横座标排序时，我们提供了在 O(N) 时间内求解这些受限版本的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.