Dynamic Reconfiguration of Complete Binary Trees in Faulty Locally Twisted Cubes

Zhao Liu, Jianxi Fan, Cheng-Kuan Lin, B. Cheng, Jingya Zhou
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引用次数: 1

Abstract

The complete binary tree is an important network structure for parallel and distributed computing, which has many nice properties and is often used to be embedded into other interconnection architectures. The locally twisted cube LTQn is an important variant of the hypercube Qn. It has many better properties than Qn with the same number of edges and vertices. In this paper, we prove that the complete binary tree CBTn can be embedded with dilation 2 and congestion 1 into LTQn. Furthermore, it is proven that if there exists an arbitrary faulty node in LTQn, then both the dilation and congestion values will become 2 after reconfiguring CBTn, while if there are two arbitrary faulty nodes in LTQn, then both the dilation and congestion values will become 3 after reconfiguration.
故障局部扭曲立方体中完全二叉树的动态重构
完全二叉树是并行和分布式计算的重要网络结构,它具有许多优良的特性,经常被嵌入到其他互连体系结构中。局部扭曲立方体LTQn是超立方体Qn的一个重要变体。它比具有相同数量边和顶点的Qn有许多更好的性质。在本文中,我们证明了完全二叉树CBTn可以嵌入膨胀2和拥塞1到LTQn中。进一步证明,如果LTQn中存在任意故障节点,则重新配置CBTn后,其膨胀值和拥塞值都变为2,如果LTQn中存在两个任意故障节点,则重新配置后,其膨胀值和拥塞值都变为3。
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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