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Constructing dual-CISTs of pancake graphs and performance assessment of protection routings on some Cayley networks
The Journal of Supercomputing ( IF 2.5 ) Pub Date : 2020-05-04 , DOI: 10.1007/s11227-020-03297-9
Kung-Jui Pai , Ruay-Shiung Chang , Jou-Ming Chang

For a connected graph $$G=(V,E)$$ G = ( V , E ) , two spanning trees $$T_1$$ T 1 and $$T_2$$ T 2 of G are said to be a pair of completely independent spanning trees (or a dual-CIST for short) if for any two vertices $$u,v\in V$$ u , v ∈ V , the paths joining u and v in the two trees have no common vertex except for u and v . Although the existence of a dual-CIST in the underlying graph of a network has the practical application of protection routing on fault-tolerance, it has been proved that determining whether a graph G admits a dual-CIST is NP-complete. As we know that Cayley graphs are a large family of graphs, some of its subclasses have been attracted and thus graphs in these subclasses have been adopted as the topologies of interconnection networks, such as the n -dimensional star graphs $$S_n$$ S n , bubble sort graphs $$BS_n$$ B S n , pancake graph $$P_n$$ P n , alternating group networks $$AGN_n$$ A G N n and so on. Pai and Chang (IEEE/ACM Trans Netw 27(3): 1112–1123, 2019) recently showed that there exist dual-CISTs in $$S_n$$ S n , $$BS_n$$ B S n , $$AGN_n$$ A G N n for $$n\geqslant 5$$ n ⩾ 5 and provided their corresponding protection routings. So far, the problem of constructing dual-CISTs on $$P_n$$ P n has not been dealt with yet. In this sequel, we continue the investigation of the construction of dual-CISTs in pancake graphs as a complementary result. Since $$P_n$$ P n , $$S_n$$ S n , and $$BS_n$$ B S n are with the same scale, we experimentally assess the performance of protection routing through simulation results for comparing them when $$n=5,6,7$$ n = 5 , 6 , 7 .

中文翻译:

在某些 Cayley 网络上构建煎饼图的双 CIST 和保护路由的性能评估

对于连通图 $$G=(V,E)$$ G = ( V , E ) ,G 的两棵生成树 $$T_1$$ T 1 和 $$T_2$$ T 2 被称为一对完全独立的生成树(或简称为双 CIST)如果对于任意两个顶点 $$u,v\in V$$ u , v ∈ V ,两棵树中连接 u 和 v 的路径没有公共顶点,除了你和 v。虽然网络底层图中双CIST的存在在容错保护路由方面具有实际应用,但已经证明确定图G是否承认双CIST是NP完全的。众所周知,凯莱图是一个很大的图族,它的一些子类被吸引,因此这些子类中的图被用作互连网络的拓扑,例如n维星形图$$S_n$$S n ,冒泡排序图 $$BS_n$$ BS n ,煎饼图 $$P_n$$ P n ,交替组网络 $$AGN_n$$ AGN n 等等。Pai 和 Chang (IEEE/ACM Trans Netw 27(3): 1112–1123, 2019) 最近表明 $$S_n$$ S n , $$BS_n$$ BS n , $$AGN_n$$ 中存在双 CIST AGN n 为 $$n\geqslant 5$$ n ⩾ 5 并提供了它们相应的保护路由。到目前为止,在 $$P_n$$P n 上构建双 CIST 的问题还没有得到解决。在本续集中,我们继续研究在煎饼图中构建双 CIST 作为补充结果。由于$$P_n$$ P n 、$$S_n$$ S n 和$$BS_n$$ BS n 具有相同的规模,我们通过模拟结果实验性地评估保护路由的性能,以便在$$n= 5,6,7$$ n = 5 , 6 , 7 。Pai 和 Chang (IEEE/ACM Trans Netw 27(3): 1112–1123, 2019) 最近表明 $$S_n$$ S n , $$BS_n$$ BS n , $$AGN_n$$ 中存在双 CIST AGN n 为 $$n\geqslant 5$$ n ⩾ 5 并提供了它们相应的保护路由。到目前为止,在 $$P_n$$P n 上构建双 CIST 的问题还没有得到解决。在本续集中,我们继续研究在煎饼图中构建双 CIST 作为补充结果。由于$$P_n$$ P n 、$$S_n$$ S n 和$$BS_n$$ BS n 具有相同的规模,我们通过模拟结果实验性地评估保护路由的性能,以便在$$n= 5,6,7$$ n = 5 , 6 , 7 。Pai 和 Chang (IEEE/ACM Trans Netw 27(3): 1112–1123, 2019) 最近表明 $$S_n$$ S n , $$BS_n$$ BS n , $$AGN_n$$ 中存在双 CIST AGN n 为 $$n\geqslant 5$$ n ⩾ 5 并提供了它们相应的保护路由。到目前为止,在 $$P_n$$P n 上构建双 CIST 的问题还没有得到解决。在本续集中,我们继续研究在煎饼图中构建双 CIST 作为补充结果。由于$$P_n$$ P n 、$$S_n$$ S n 和$$BS_n$$ BS n 具有相同的规模,我们通过模拟结果实验性地评估保护路由的性能,以便在$$n= 5,6,7$$ n = 5 , 6 , 7 。$$AGN_n$$ AGN n 为 $$n\geqslant 5$$ n ⩾ 5 并提供了它们相应的保护路由。到目前为止,在 $$P_n$$P n 上构建双 CIST 的问题还没有得到解决。在本续集中,我们继续研究在煎饼图中构建双 CIST 作为补充结果。由于$$P_n$$P n 、$$S_n$$ S n 和$$BS_n$$ BS n 具有相同的规模,我们通过模拟结果实验性地评估保护路由的性能,以便在$$n= 5,6,7$$ n = 5 , 6 , 7 。$$AGN_n$$ AGN n 为 $$n\geqslant 5$$ n ⩾ 5 并提供了它们相应的保护路由。到目前为止,在 $$P_n$$P n 上构建双 CIST 的问题还没有得到解决。在本续集中,我们继续研究在煎饼图中构建双 CIST 作为补充结果。由于$$P_n$$ P n 、$$S_n$$ S n 和$$BS_n$$ BS n 具有相同的规模,我们通过模拟结果实验性地评估保护路由的性能,以便在$$n= 5,6,7$$ n = 5 , 6 , 7 。
更新日期:2020-05-04
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