Topological properties, communication, and computation on WK‐recursive networks

Abstract

Recently, with the support of the CAPRI (Concurrent Architecture and PRogramming environment for highly Integrated system) project, Vecchia and Sanges proposed a new general class of recursively scalable networks, termed WK-recursive networks, and developed routing and broadcasting algorithms on them. They have also implemented the WK-recursive networks using VLSl technology. This paper studies WK-recursive networks by first investigating their topological properties such as diameter, connectivity, and Hamiltonicity. We then develop new and more efficient routing and broadcasting algorithms. Our routing algorithm can guarantee the shortest paths. Our broadcasting algorithm is much simpler and requires fewer extra bits to be transmitted. The broadcasting tree of our broadcasting algorithm is of minimal height (equal to the diameter), and each node receives the message exactly once. Moreover, we show the execution of descend/ ascend algorithms on the WK-recursive networks using the bitonic sort as an illustrative example.

On the Rabin number problem

“…. , m 1 ) is node-symmetric when m n Å m n01 Å rrr Å m 1 , we obtain works can be found in [8,12]. Among them, W K(d, t) has diameter 2 t 0 1 and connectivity d 0 1.…”

“…, where 1°m°d and Duh [8] showed that Algorithm 3.1 can produce the 0 1 and 1°i°t. Then, there exist m node-disjoint shortest routing path when u Å i £ and u is an i-frontier.…”

The Outer-connected Domination Number of Sierpiński-like Graphs

“…The reader is referred to [2,4,7,13,22,25] for the details. The vertex set of S(n, k) consists of all n-tuples of integers 1, 2, .…”

Topological properties of incomplete WK-recursive networks

“…They offer a high degree of regularity, first proposed a heuristic routing algorithm [22] and an scalability, and symmetry which very well conform to a optimal broadcasting algorithm [23]. Chen and Duh [2] modular design and implementation of distributed systhen improved their work by presenting a shortest-path tems involving a large number of computing elements. A routing algorithm and another optimal, but simpler, VLSI implementation of a 16-node WK-recursive netbroadcasting algorithm.…”

“…A routing algorithm and another optimal, but simpler, VLSI implementation of a 16-node WK-recursive netbroadcasting algorithm. The diameter, Hamiltonicity, and work was realized at the Hybrid Computing Research connectivity were also computed in [2]. Node-disjoint Center [22].…”