当前位置: X-MOL 学术J. Parallel Distrib. Comput. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Packing internally disjoint Steiner trees to compute the κ3-connectivity in augmented cubes
Journal of Parallel and Distributed Computing ( IF 3.4 ) Pub Date : 2021-04-19 , DOI: 10.1016/j.jpdc.2021.04.004
Chao Wei , Rong-Xia Hao , Jou-Ming Chang

Given a connected graph G and SV(G) with |S|2, a tree T in G is called an S-Steiner tree (or S-tree for short) if SV(T). Two S-trees T1 and T2 are internally disjoint if E(T1)E(T2)= and V(T1)V(T2)=S. The packing number of internally disjoint S-trees, denoted as κG(S), is the maximum size of a set of internally disjoint S-trees in G. For an integer k2, the generalized k-connectivity (abbr. κk-connectivity) of a graph G is defined as κk(G)=min{κG(S)|SV(G) and |S|=k}. The n-dimensional augmented cube, denoted as AQn, is an important variant of the hypercube that possesses several desired topology properties such as diverse embedding schemes in applications of parallel computing. In this paper, we focus on the study of constructing internally disjoint S-trees with |S|=3 in AQn. As a result, we completely determine the κ3-connectivity of AQn as follows: κ3(AQ4)=5 and κ3(AQn)=2n2 for n=3 or n5.



中文翻译:

包装内部不相交斯坦纳树来计算κ 3在增强立方体-connectivity

给定一个连通图G小号伏特G|小号|2个,树Ťģ称为小号-Steiner树(或小号-tree的简称)如果小号伏特Ť。两个小号-树Ť1个Ť2个 在内部不相交,如果 EŤ1个EŤ2个=伏特Ť1个伏特Ť2个=小号。内部不相交的S树的包装数,表示为κG小号G中一组内部不相交S树的最大大小。对于整数ķ2个,广义k连通性(缩写κķG的-连通性定义为κķG={κG小号|小号伏特G|小号|=ķ}。在ñ维增强立方体,表示为一种ñ是超多维数据集的重要变体,它具有几个所需的拓扑属性,例如并行计算应用程序中的各种嵌入方案。在本文中,我们专注于构造内部不相交的S-树的研究。|小号|=3一种ñ。结果,我们完全确定了κ3的连接性 一种ñ 如下: κ3一种4=5κ3一种ñ=2个ñ-2个 为了 ñ=3 或者 ñ5

更新日期:2021-04-27
down
wechat
bug