Embedding Hamiltonian Paths with Prescribed Linear Forests into k-ary n-Cube Networks

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

JOURNAL OF INTERCONNECTION NETWORKS Pub Date : 2024-03-07 DOI:10.1142/s0219265924500038

Kaiyue Meng, Yuxing Yang

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引用次数: 0

Abstract

Graph embedding is a fundamental problem in computer science. Let [Formula: see text] (resp., [Formula: see text]) be the interconnection network for a parallel computer system [Formula: see text] (resp., [Formula: see text]). If [Formula: see text] could be embedded into [Formula: see text], then [Formula: see text] can simulate [Formula: see text]’s behavior. The [Formula: see text]-ary [Formula: see text]-cube [Formula: see text] is a node-symmetric and link-symmetric recursive interconnection network for parallel computer systems. Let [Formula: see text] be a prescribed linear forest of [Formula: see text], and let [Formula: see text] and [Formula: see text] be any two distinct nodes in [Formula: see text] such that [Formula: see text] has no path with [Formula: see text] or [Formula: see text] as internal nodes, or both as end-nodes. This paper shows that there is a Hamiltonian path passing through [Formula: see text] between [Formula: see text] and [Formula: see text] in [Formula: see text] with [Formula: see text] and odd [Formula: see text] even if the number of links in [Formula: see text] is up to [Formula: see text].

查看原文本刊更多论文

将带有规定线性森林的哈密顿路径嵌入 kary n 立方网络

图嵌入是计算机科学中的一个基本问题。设[公式：见正文]（或者，[公式：见正文]）是并行计算机系统[公式：见正文]（或者，[公式：见正文]）的互连网络。如果[公式：见文本]可以嵌入[公式：见文本]，那么[公式：见文本]就可以模拟[公式：见文本]的行为。公式：见文本]的[公式：见文本]立方体[公式：见文本]是并行计算机系统的节点对称和链路对称递归互连网络。设[式：见文本]是[式：见文本]的规定线性森林，设[式：见文本]和[式：见文本]是[式：见文本]中任意两个不同的节点，使得[式：见文本]没有以[式：见文本]或[式：见文本]为内部节点或两者都为端节点的路径。本文表明，即使[公式：见文本]中的链接数最多为[公式：见文本]，在[公式：见文本]中的[公式：见文本]与[公式：见文本]之间也存在一条经过[公式：见文本]的哈密顿路径，且[公式：见文本]为奇数。

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 INTERCONNECTION NETWORKS COMPUTER SCIENCE, THEORY & METHODS-

自引率

14.30%

发文量

121

期刊介绍： The Journal of Interconnection Networks (JOIN) is an international scientific journal dedicated to advancing the state-of-the-art of interconnection networks. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks. Interconnection problems occur at different levels in the hardware and software design of communicating entities in integrated circuits, multiprocessors, multicomputers, and communication networks as diverse as telephone systems, cable network systems, computer networks, mobile communication networks, satellite network systems, the Internet and biological systems.