Recursive cubes of rings as models for interconnection networks

We study recursive cubes of rings as models for interconnection networks. We first redefine each of them as a Cayley graph on the semidirect product of an elementary abelian group by a cyclic group in order to facilitate the study of them by using algebraic tools. We give an algorithm for computing shortest paths and the distance between any two vertices in recursive cubes of rings, and obtain the exact value of their diameters. We obtain sharp bounds on the Wiener index, vertex-forwarding index, edge-forwarding index and bisection width of recursive cubes of rings. The cube-connected cycles and cube-of-rings are special recursive cubes of rings, and hence all results obtained in the paper apply to these well-known networks

Metaplex networks: influence of the exo-endo structure of complex systems on diffusion

In a complex system the interplay between the internal structure of its entities and their interconnection may play a fundamental role in the global functioning of the system. Here, we define the concept of metaplex, which describes such trade-off between internal structure of entities and their interconnections. We then define a dynamical system on a metaplex and study diffusive processes on them. We provide analytical and computational evidences about the role played by the size of the nodes, the location of the internal coupling areas, and the strength and range of the coupling between the nodes on the global dynamics of metaplexes. Finally, we extend our analysis to two real-world metaplexes: a landscape and a brain metaplex. We corroborate that the internal structure of the nodes in a metaplex may dominate the global dynamics (brain metaplex) or play a regulatory role (landscape metaplex) to the influence of the interconnection between nodes.Comment: 28 pages, 19 figure

CCL: a portable and tunable collective communication library for scalable parallel computers

A collective communication library for parallel computers includes frequently used operations such as broadcast, reduce, scatter, gather, concatenate, synchronize, and shift. Such a library provides users with a convenient programming interface, efficient communication operations, and the advantage of portability. A library of this nature, the Collective Communication Library (CCL), intended for the line of scalable parallel computer products by IBM, has been designed. CCL is part of the parallel application programming interface of the recently announced IBM 9076 Scalable POWERparallel System 1 (SP1). In this paper, we examine several issues related to the functionality, correctness, and performance of a portable collective communication library while focusing on three novel aspects in the design and implementation of CCL: 1) the introduction of process groups, 2) the definition of semantics that ensures correctness, and 3) the design of new and tunable algorithms based on a realistic point-to-point communication model

Online Permutation Routing in Partitioned Optical Passive Star Networks

This paper establishes the state of the art in both deterministic and randomized online permutation routing in the POPS network. Indeed, we show that any permutation can be routed online on a POPS network either with $O(\frac{d}{g}\log g)$ deterministic slots, or, with high probability, with $5c\lceil d/g\rceil+o(d/g)+O(\log\log g)$ randomized slots, where constant $c=\exp (1+e^{-1})\approx 3.927$. When $d=\Theta(g)$, that we claim to be the "interesting" case, the randomized algorithm is exponentially faster than any other algorithm in the literature, both deterministic and randomized ones. This is true in practice as well. Indeed, experiments show that it outperforms its rivals even starting from as small a network as a POPS(2,2), and the gap grows exponentially with the size of the network. We can also show that, under proper hypothesis, no deterministic algorithm can asymptotically match its performance

Algebraic and Computer-based Methods in the Undirected Degree/diameter Problem - a Brief Survey

This paper discusses the most popular algebraic techniques and computational methods that have been used to construct large graphs with given degree and diameter