超级扭立方体互连网络及其性质

扭立方体是超立方体的一类变体,它具有比超立方体更好的性质。但是,同超立方体一样,它也是具有2n个顶点的n-正则图,故要使一个扭立方体的维数(即顶点度数)增加1(称为升级),就必须成倍地增加扭立方体中的顶点个数。为了解决这一问题,将具有2n个顶点的扭立方体的拓扑结构加以改变,得到了包含任意多个顶点的互连网络——超级扭立方体(STN)。证明了超级扭立方体保持了扭立方体的最高连通度、对数级的直径和顶点度数、Hamilton性质、连通度级的tp-可诊断度等方面的优良性质,更进一步地,由于它包含了任意多个顶点,所以对它的升级只需增加任意多个顶点,从而克服了扭立方体的升级必须成倍增加其顶点个数的缺点。     

LHL-立方体互连网络及其性质

并行计算系统一直是计算机科学中的重要研究领域,其互连网络的拓扑性质对整个网络的性能起着非常重要的作用.目前已经提出多种互连网络,其中超立方体具有对数级的直径、高连通度、对称性等很好的性质,故被用作多种并行机的处理器连接的拓扑结构.然而,超立方体并非所有性质都是最优的互连网络,且超立方体的许多变型结构具有许多比超立方体更好的性质,其中已经证明了局部扭立方体在直径、Hamilton连通性等方面都优于超立方体.给出在超立方体与局部扭立方体的顶点间的一种连接方式--超连接,从而得到一种称为LHL-立方体的新型网络,并对这种网络的以下性质进行了研究:顶点连通度、边连通度、Hamilton连通性、直径.研究结果表明,一个n维LHL-立方体是一个具有2n个顶点和n2n-1条边的n-正则图,n维LHL-立方体的顶点连通度和边连通度均为n,且是Hamilton连通的,直径上界为[n/2 ]+3.     

超级交叉立方体互连网络及其拓扑性质

交叉立方体是近年提出的超立方体的一种变种。由于它的许多优越性质（如直径、嵌入性等）,在并行处理领域越来越受到人们的重视。然而,像超立方体一样,它也有一个缺点,即要使交叉立方体升级,就必须成倍地增加其顶点个数。为了解决这一问题,本文将顶点个数的２的次幂的交叉立方体推广到具有任意个顶点的互连网络,提出了超级交叉立方体的定义,并证明它保持了交叉立方体在高速通度、对数级的直径和顶点度数等方面的优良性质,从     

超级M(o)bius立方体一类最优容错的小直径互连网络

文中将具有2n个顶点的M(o)bius立方体的拓扑结构加以改变,得到了包含任意个顶点的互连网络--超级M(o)bius立方体,并证明它保持了M(o)bius立方体的高连通度、对数级的直径和顶点度数等优良性质,并且当顶点个数N=2n+2n-1 时,0-型超级M(o)bius立方体是一个(n+1)-正则图;更进一步地,由于它包含任意个顶点,所以其升级只需增加任意个顶点,从而克服了M(o)bius立方体的升级必须成倍增加其顶点个数的缺点.     

超级Mbius立方体──一类最优容错的小直径互连网络

文中将具有２ｎ个顶点的Ｍｏｂｉｕｓ立方体的拓扑结构加以改变,得到了包含任意个顶点的互连网络——超级Ｍｏｂｉｕｓ立方体,并证明它保持了Ｍｏｂｉｕｓ立方体的高连通度、对数级的直径和顶点度数等优良性质,并且当顶点个数Ｎ＝２ｎ＋２ｎ－１时,０－型超级Ｍｏｂｉｕｓ立方体是一个（ｎ＋１）－正则图;更进一步地,由于它包含任意个顶点,所以其升级只需增加任意个顶点,从而克服了Ｍｏｂｉｕｓ立方体的升级必须成倍增加其顶点个数的缺点．     

局部扭立方体环互连网络及其性质

优化网络的拓扑结构是互连网络研究的重要研究方向。局部扭立方体（locally twisted cube,LTQn ）是对超立方体（hypercube,Qn ）互连网络的优化变种,然而当对LTQn 升级时,需要成倍地增加网络的节点,这不利于LTQn的应用和发展。为了克服LTQn 这一缺陷,提出了一种新的互连网络拓扑结构：局部扭立方体环互连网络（locally twisted cube-connected ring interconnect network,LRN）,给出了LRN的定义及其拓扑结构,并研究了LRN的网络直径、连接度、汉密尔顿连通性、泛圈性、路由等问题,证明了LRN是一种易于升级又具有LTQn 许多优良性质的层次环互连网络（hierarchical ring interconnection networks,HRN）。     

交叉扭立方体互联网络及其性质

扭N立方体是近年来提出的一种新型变体网络结构.通过X-变换操作使得存在2n个顶点的超立方体的网络直径从N减少到N-1,减少了网络规模增大时所需要的网络开销,从而受到了广泛的欢迎.与超立方体一样,扭N立方体也存在缺点,如果增加扭N立方体的维数,会成倍增加扭N立方体的顶点个数.为了解决这一问题,本文通过扭N立方体的结构,提出了交叉扭立方体的定义,并给出了相应的拓扑结构网络图,证明了交叉扭立方体的部分子网与超立方体网络同构,同时研究了交叉扭立方体的网络直径、连通度等问题.通过上述拓扑结构的基本性质的研究,得到了交叉扭立方体的性能优于扭N立方体的重要结论.     

超级交叉立方体互连网络上的圈嵌入

作为超立方体的变型，交叉立方体同时具有一些比超立方体优越的性质，但类似于超立方体，它的升级也伴随着顶点个数的增加而成倍中增加。为了解决这一问题，一种称为超级交叉立方体（SCC）的互连网络被提了出来。有关文献已证明，SCC很好地保持了交叉立方体在顶点度数，直径和连通度方面的优越性质，而且其升级可以增加任意多个顶点。用图嵌入技术讨论了SCC模拟环网络的能力，证明了长度为4到N的任一圈都能以扩张1嵌入具有N个顶点的SCC，从而证明了SCC模拟环网络的能力与交叉立方体完全相同。     

超有Moebius立方体———一类最优容错的小直径互连网络

文中将具有２＾ｎ个顶点的Ｍｏｅｂｉｕｓ立方体的拓扑结构加以改变,得到了包含任意个顶点的互连网络－－超级Ｍｏｅｂｉｕｓ立方体,并证明它保持了Ｍｏｅｂｉｕｓ立方本的高连通度、对数级的直径和顶点度数等优良性质,并且当顶点个数Ｎ＝２＾ｎ＋２＾ｎ－１时,０－型超级Ｍｏｅｂｉｕｓ立方体是一个（ｎ＋１）－正则图;更进一步地,由于它包含任意一个顶点,所以其升级只需增加任意个顶点,从而克服了Ｍｏｅｂｉｕｓ立方体的升     

局部扭立方体网络中网络嵌入问题的研究

局部扭立方体网络LTQ_n(Locally Twisted Cube)作为超立方体网络Q_n(Hypercube)的优化变种网络,具有很多优良的特性。依据局部扭立方体网络的性质及图嵌入的理论提出二项树、交换超立方体网络和超立方体网络嵌入到局部扭立方体网络的方案,并严格证明了这几种嵌入映射的扩张率、拥塞度及负载等都是最小的,这说明了局部扭立方体网络具有很好的通用性。     

基于局部扭曲立方体的多播路由算法

局部扭曲立方体是一种新提出来用于并行计算的互联网络。经研究发现,局部扭曲立方体中已有最小路由算法存在着死锁。因此,在原有算法的基础上,提出了一种新的无死锁路由算法并给出了无死锁证明。利用将物理通道分成两条虚拟通道进而形成两个不相交的虚拟网络,将不同的点对之间的路由限定在某一个虚拟网络中,从而有效地避免了死锁的产生。同时,利用一个局部扭曲立方体可由两个低维子立文体和2-扭曲立方体构成这一性质,在局部的低维子立方体和2-扭曲立方体中均采用自适应路由,从而提高了算法的自适应性。在此基础上提出了一种多播路由算法。     

One-to-one communication in twisted cubes under restricted connectivity

The dimensions of twisted cubes are only limited to odd integers. In this paper, we first extend the dimensions of twisted cubes to all positive integers. Then, we introduce the concept of the restricted faulty set into twisted cubes. We further prove that under the condition that each node of the n-dimensional twisted cube TQ_n has at least one fault-free neighbor, its restricted connectivity is 2n − 2, which is almost twice as that of TQ_n under the condition of arbitrary faulty nodes, the same as that of the n-dimensional hypercube. Moreover, we provide an O(NlogN) fault-free unicast algorithm and simulations result of the expected length of the fault-free path obtained by our algorithm, where N denotes the node number of TQ_n. Finally, we propose a polynomial algorithm to check whether the faulty node set satisfies the condition that each node of the n-dimensional twisted cube TQ_n has at least one fault-free neighbor.     

Node-pancyclicity and edge-pancyclicity of hypercube variants

Twisted cubes, crossed cubes, Möbius cubes, and locally twisted cubes are some of the widely studied hypercube variants. The 4-pancyclicity of twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes and the 4-edge-pancyclicity of twisted cubes, crossed cubes, Möbius cubes are proven in [C.P. Chang, J.N. Wang, L.H. Hsu, Topological properties of twisted cube, Inform. Sci. 113 (1999) 147-167; C.P. Chang, T.Y. Sung, L.H. Hsu, Edge congestion and topological properties of crossed cubes, IEEE Trans. Parall. Distr. 11 (1) (2000) 64-80; J. Fan, Hamilton-connectivity and cycle embedding of the Möbius cubes, Inform. Process. Lett. 82 (2002) 113-117; X. Yang, G.M. Megson, D.J. Evans, Locally twisted cubes are 4-pancyclic, Appl. Math. Lett. 17 (2004) 919-925; J. Fan, N. Yu, X. Jia, X. Lin, Embedding of cycles in twisted cubes with edge-pancyclic, Algorithmica, submitted for publication; J. Fan, X. Lin, X. Jia, Node-pancyclic and edge-pancyclic of crossed cubes, Inform. Process. Lett. 93 (2005) 133-138; M. Xu, J.M. Xu, Edge-pancyclicity of Möbius cubes, Inform. Process. Lett. 96 (2005) 136-140], respectively. It should be noted that 4-edge-pancyclicity implies 4-node-pancyclicity which further implies 4-pancyclicity. In this paper, we outline an approach to prove the 4-edge-pancyclicity of some hypercube variants and we prove in particular that Möbius cubes and locally twisted cubes are 4-edge-pancyclic.     

Changing the diameter of the locally twisted cube

The hypercube network Q _n has been proved to be one of the most popular interconnection networks. The n-dimensional locally twisted cube LTQ _n is an important variant of Q _n . One of the critical performance factors of an interconnection network is the diameter which determines the maximum communication time between any pair of processors. In this paper, we investigate the diameter variability problems arising from the addition and deletion of edges in LTQ _n . We obtain three results in this paper: (1) for any integer n≥2, we find the least number of edges (denoted by ch ^?(LTQ _n )), whose deletion from LTQ _n causes the diameter to increase, (2) for any integer n≥2, when ch ^?(LTQ _n ) edges are deleted, the diameter will increase by 1 and (3) for any integer n≥4, the least number of edges whose addition to LTQ _n will decrease the diameter is at most 2 ^n?1.     

The twisted crossed cube

The topology of interconnection networks plays an important role in the performance of parallel and distributed computing systems. In this paper, we propose a new interconnection network called twisted crossed cube (TCQ_n) and investigate its basic network properties in terms of the regularity, connectivity, fault tolerance, recursiveness, hamiltonicity and ability to simulate other architectures, and so on. Then, we develop an effective routing algorithm Route (u, v) for TCQ_n that takes no more than d(u, v) + 1 steps for any two nodes (u, v) to communicate with each other, and the routing process shows that the diameter, wide diameter, and fault‐tolerant diameter of TCQ_n are about half of the corresponding diameters of the equivalent hypercube with the same dimension. In the end, by combining TCQ_n with crossed cube (CQ_n), we propose a preferable dynamic network structure, that is, the dynamic crossed cube, which has the same network diameter as TCQ_n/CQ_n and better properties in other respects, for example, its connection complexity is half of that of TCQ_n/CQ_n when the network scale is large enough, and the number of its average routing steps is also much smaller than that in TCQ_n/CQ_n. Copyright © 2015 John Wiley & Sons, Ltd.     

The spined cube: A new hypercube variant with smaller diameter

Bijective connection graphs (in brief, BC graphs) are a family of hypercube variants, which contains hypercubes, twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes, etc. It was proved that the smallest diameter of all the known n-dimensional bijective connection graphs (BC graphs) is , given a fixed dimension n. An important question about the smallest diameter among all the BC graphs is: Does there exist a BC graph whose diameter is less than the known BC graphs such as crossed cubes, twisted cubes, Möbius cubes, etc., with the same dimension? This paper answers this question. In this paper, we find that there exists a kind of BC graphs called spined cubes and we prove that the n-dimensional spined cube has the diameter ⌈n/3⌉+3 for any integer n with n?14. It is the first time in literature that a hypercube variant with such a small diameter is presented.