Complexity of Recognizing Multidistance Graphs in $$\mathbb{R}^d$$

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s000143462405016x

G. M. Sokolov

引用次数: 0

Abstract

We study the complexity of recognizing $A$-distance graphs in $\mathbb{R}^d$ and prove that for all finite sets $A$ such that any two elements of the set differ by a factor $\ge2$, the recognition problem for $A$-distance graphs is $\mathrm{NP}$-hard for any $d \geq 3$.

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识别$$\mathbb{R}^d$$中多距图的复杂性

摘要我们研究了在$\mathbb{R}^d$中识别$A$-距离图的复杂性，并证明对于所有有限集合$A$，使得集合中的任意两个元素相差一个因子$\ge2$，对于任意$d \geq 3$ ，$A$-距离图的识别问题是$\mathrm{NP}$-困难的。

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

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.