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Constructing dual-CISTs of folded divide-and-swap cubes
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-12-17 , DOI: 10.1016/j.tcs.2020.12.023
Yu-Huei Chang , Kung-Jui Pai , Chiun-Chieh Hsu , Jinn-Shyong Yang , Jou-Ming Chang

Spanning trees T1,T2,,Tk (k2) in a network are called completely independent spanning trees (CISTs for short) if they are pairwise edge-disjoint and inner-node-disjoint. Particularly, if k=2, the two CISTs are called a dual-CIST. Hasunuma (2002) [8] proved that the problem of determining whether there exists a dual-CIST in a network is NP-complete. Tapolcai (2013) [20] showed that a dual-CIST has an application on configuring a protection routing in intra-domain IP networks. The adoption of protection routing guarantees that there is a loop-free alternate path for packet forwarding when a single link or node failure occurs. Pai et al. (2020) [17] demonstrated that protection routing is also suitable for relatively large (static) network topologies with scalability, such as interconnection networks with recursive structure and data center networks (DCNs). Recently, Kim et al. (2019) [10] newly proposed a hypercube-variant network called folded divide-and-swap cube, denoted as FDSC(n), which is obtained from the divide-and-swap cube DSC(n) by adding an extra edge to each node. They also showed that DSC(n) and FDSC(n) have a better network performance than that of hypercubes, where the performance is measured by the product of degree and diameter. In this paper, we first point out that FDSC(n) is suitable as a candidate topology for DCNs. Then, we investigate the construction of a dual-CIST {T1,T2} in FDSC(n). In particular, the diameters of Ti for i=1,2 we constructed arediam(Ti)={9if n=4;478n1523(4d421)(dmod2+1)if n=2d for d3.



中文翻译:

构造折叠式立方体的双重CIST

生成树 Ť1个Ť2Ťķķ2如果网络中的)是成对的边不相交和内部节点不相交的,则称为完全独立的生成树(简称CIST)。特别是如果ķ=2,这两个CIST称为双重CIST。Hasunuma(2002)[8]证明确定网络中是否存在双重CIST的问题是NP完全的。Tapolcai(2013)[20]显示,双重CIST在域内IP网络中配置保护路由方面具有应用。采用保护路由可确保在发生单个链路或节点故障时,存在用于分组转发的无环路备用路径。排等。(2020)[17]证明保护路由也适用于具有可伸缩性的相对较大的(静态)网络拓扑,例如具有递归结构的互连网络和数据中心网络(DCN)。最近,金等。(2019)[10]新提出了一种称为折叠除法和交换立方的超立方变体网络,表示为FDSC(n),它是通过在每个节点上添加额外的边沿从交换矩阵DSC(n)获得的。他们还表明,DSC(n)和FDSC(n)具有比超立方体更好的网络性能,超立方体的性能由度和直径的乘积来衡量。在本文中,我们首先指出FDSC(n)适合作为DCN的候选拓扑。然后,我们研究双重CIST的构建{Ť1个Ť2}在FDSC(n)中。特别是直径Ť一世 对于 一世=1个2 我们建造的是直径Ť一世={9如果 ñ=4;478ñ-15-234d-42-1个d2+1个如果 ñ=2d 对于 d3

更新日期:2021-01-16
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