Modules in Robinson Spaces

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-01-08 DOI:10.1137/22m1494348

Mikhael Carmona, Victor Chepoi, Guyslain Naves, Pascal Préa

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 190-224, March 2024.
Abstract. A Robinson space is a dissimilarity space [math] (i.e., a set [math] of size [math] and a dissimilarity [math] on [math]) for which there exists a total order [math] on [math] such that [math] implies that [math]. Recognizing if a dissimilarity space is Robinson has numerous applications in seriation and classification. An mmodule of [math] (generalizing the notion of a module in graph theory) is a subset [math] of [math] which is not distinguishable from the outside of [math]; i.e., the distance from any point of [math] to all points of [math] is the same. If [math] is any point of [math], then [math], and the maximal-by-inclusion mmodules of [math] not containing [math] define a partition of [math], called the copoint partition. In this paper, we investigate the structure of mmodules in Robinson spaces and use it and the copoint partition to design a simple and practical divide-and-conquer algorithm for recognition of Robinson spaces in optimal [math] time.

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罗宾逊空间中的模块

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 190-224 页，2024 年 3 月。摘要。罗宾逊空间是一个相似性空间[math]（即大小为[math]的集合[math]和[math]上的相似性[math]），对于它，[math]上存在一个总阶[math]，使得[math]意味着[math]。识别异或空间是否为鲁滨逊空间在序列化和分类中有着广泛的应用。[math]的模块（概括图论中模块的概念）是[math]的子集[math]，它与[math]的外部无法区分；也就是说，从[math]的任意一点到[math]的所有点的距离是相同的。如果[math]是[math]的任意一点，那么[math]和不包含[math]的[math]最大包含模块定义了[math]的一个分区，称为共点分区。在本文中，我们研究了罗宾逊空间中的模块结构，并利用它和共点分割设计了一种简单实用的分而治之算法，用于在最优[math]时间内识别罗宾逊空间。

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

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.