超级局部扭立方体互连网络及其性质

局部扭立方体是近年来提出的超立方体的一个变型,由于它的许多优越性质(如低直径),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,即要使局部扭立方体升级,就必须成倍地增加其顶点个数.为了解决这一问题,文中将顶点个数为2的次幂的局部扭立方体推广到具有任意个顶点的互连网络,提出了超级局部扭立方体(SLTC)的定义,并证明它保持了局部扭立方体的最高连通度、对数级的直径和顶点度数、Hamilton性质等方面的优良性质,从而证明了超级局部扭立方体是既保持了局部扭立方体的多种优越性质又易于升级的互连网络.

The Super Locally Twisted Cube Interconnection Networks and Their Properties

The recently introduced interconnection network,the locally twisted cube,has attracted much attention in the parallel processing area due to its many attractive features,for example: the diameter of the locally twisted cube is approximately half that of the hypercube.However,like the hypercube,it is necessary to double the node number to upgrade the locally twisted cube.In order to solve the problem,this paper generalizes the locally twisted cube with node number of power 2 to the interconnection network with arbitrary node number,and proposes a definition of the super locally twisted cube(SLTC).We prove that,the super locally twisted cube has the greatest connectivity,the logarithm node degree and diameter,and the Hamilton property.Thus,it is proved that the super locally twisted cubes are a kind of interconnection networks which keep the advantageous properties of locally twisted cubes and are easy to be upgraded.