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On Embedding Hamiltonian Cycles in Crossed Cubes

机译：关于交叉立方体中的哈密顿环的嵌入

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摘要

We study the embedding of Hamiltonian cycle in the Crossed Cube, a prominent variant of the classical hypercube, which is obtained by crossing some straight links of a hypercube, and has been attracting much research interest in literatures since its proposal. We will show that due to the loss of link-topology regularity, generating Hamiltonian cycles in a crossed cube is a more complicated procedure than in its original counterpart. The paper studies how the crossed links affect an otherwise succinct process to generate a host of well-structured Hamiltonian cycles traversing all nodes. The condition for generating these Hamiltonian cycles in a crossed cube is proposed. An algorithm is presented that works out a Hamiltonian cycle for a given link permutation. The useful properties revealed and algorithm proposed in this paper can find their way when system designers evaluate a candidate network'' s competence and suitability, balancing regularity and other performance criteria, in choosing an interconnection network.
机译：我们研究了哈密顿循环在交叉立方体中的嵌入，交叉立方体是经典超立方体的一个显着变体，它是通过交叉超立方体的一些直链而获得的，并且自提出以来就引起了文学界的很多研究兴趣。我们将显示由于链接拓扑规则性的损失，在交叉立方体中生成哈密顿循环比在其原始对应物中更为复杂。本文研究了交叉链接如何影响否则简洁的过程，以生成遍及所有节点的大量结构良好的哈密顿循环。提出了在交叉立方体中生成这些哈密顿循环的条件。提出了一种算法，该算法针对给定的链路置换计算出哈密顿循环。当系统设计人员评估候选网络的能力和适用性，平衡规则性和其他性能标准时，在选择互连网络时，本文揭示的有用特性和提出的算法可以找到解决方法。

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