Embedding hypercubes into torus and Cartesian product of paths and/or cycles for minimizing wirelength

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2024-11-13 DOI:10.1016/j.jcss.2024.103603

Zhiyi Tang

引用次数: 0

Abstract

Though embedding problems have been considered for several regular graphs [1], [2], [3], it is still an open problem for hypercube into torus [4], [2]. In the paper, we prove the conjecture mathematically and obtain the minimum wirelength of embedding for hypercube into Cartesian product of paths and/or cycles. In addition, we explain that Gray code embedding is an optimal strategy in such embedding problems.

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将超立方体嵌入环面和路径及/或循环的笛卡尔乘积，以尽量减少线长

虽然人们已经考虑了几种规则图的嵌入问题 [1]、[2]、[3]，但对于超立方体嵌入环 [4]、[2]，这仍然是一个未决问题。在本文中，我们用数学方法证明了这一猜想，并得到了超立方体嵌入路径和/或循环的笛卡尔积的最小线长。此外，我们还解释了灰色代码嵌入是此类嵌入问题的最优策略。

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

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.