Low-dimensional k-ary n-cubes have been popular in recent multicomputers. These networks, however, suffer from high switching delays due to their high message distance. To overcome this problem, Dally has proposed a variation, called express k-ary n-cubes, with express channels that allow non-local messages to partially bypass clusters of nodes within a dimension. K-ary n-cubes are graph topolo...

In this paper, we present a strongly fault-tolerant design for the k-ary n-cube multiprocessor and examine its reconfigurability. Our design augments the k-ary n-cube with ( j ) n spare nodes; each set of j regular nodes is connected to a spare node and the spare nodes are interconnected as a ( j )-ary n-cube. Our approach utilizes the circuit-switched capabilities of the communication modules ...

An (n, a, b)-perfect double cube is a b × b × b sized n-ary periodic array containing all possible a × a × a sized n-ary array exactly once as subarray. A growing cube is an array whose cj × cj × cj sized prefix is an (nj, a, cj)-perfect double cube for j = 1, 2, . . ., where cj = n v/3 j , v = a 3 and n1 < n2 < · · ·. We construct the smallest possible perfect double cube (a 256×256×256 sized ...

The diierence among diierent topologies in interconnection networks is a debated issue among highly parallel machine designers, since opposing parameters innuence the network performance. This paper presents a new model, k-ary n-cube m-diags, which generalizes existing k-ary n-cube topologies to include hexagonal networks and their n-dimensional extensions. A performance analysis based on this ...

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative binary star products are associative and require the use of the Baker-Campbell-Hausdorff formula. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X, X, ......, X] and the poly-vector valued coordinates X in noncommutative Clifford spaces is expl...

This paper presents three simple and efficient algorithms for generating, ranking and unranking t-ary trees in a lexicographic order. The simplest idea of encoding a t-ary tree with n nodes as a bit-string of length t*n is exploited to its full advantages. It is proved that the lexicographic order in the set of t-ary trees with n nodes is preserved in the set of bit-strings of length t*n, using...

Inspired by engineering of high-speed switching with quality of service, this paper introduces a new approach to classify finite lattices by the concept of cut-through coding. An n-ary cut-through code of a finite lattice encodes all lattice elements by distinct n-ary strings of a uniform length such that for all j, the initial j encoding symbols of any two elements x and y determine the initia...