Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph $G$ is a set of oriented paths of $G$, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing $R$ is the number of times it is used (in either direction) by paths of $R$, and the maximum load of an edge is denoted by $\pi(G,R)$. The edge-forwarding index $\pi(G)$ is the minimum of $\pi(G,R)$ over all possible all-to-all routings $R$, and the arc-forwarding index $\overrightarrow{\pi}(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $w(G,R)$ the minimum number of colours required to colour the paths of $R$ such that any two paths having an edge in common receive distinct colours. The optical index $w(G)$ is defined to be the minimum of $w(G,R)$ over all possible $R$, and the directed optical index $\overrightarrow{w}(G)$ is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for $4$-regular circulant graphs with connection set $\{\pm 1,\pm s\}$, $1<s<n/2$. We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of $4$-regular circulant graphs.Comment: 19 pages, no figure in Journal of Discrete Algorithms 201

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

INNOVATIVE DRILLING TECHNOLOGIES FOR ADVANCED MATERIALS

Carbon fibre reinforced polymer (CFRP) composites are among the most widely used composite materials in the aerospace industry, thanks to the high specific mechanical properties offered. These composites combine the fundamental aeronautical requirements of lightness and strength, which have sparked great research interest in improving the properties and the production process of composite materials. CFRP composites can be manufactured in near net shape; however, they often require further machining processes such as drilling, particularly for joining purposes. Fibre orientation plays a fundamental role in CFRP composite materials, affecting the mechanism of chip formation and the quality of the cut surface and making machining of CFRP a challenging task. Proper optimisation of the drilling process can substantially improve CFRP parts quality, which may be affected by several faults generated during the process. In order to simplify the assembly operations and reduce manufacturing costs, efforts are increasingly spent with the aim to optimise CFRP drilling

Satellite Communications

This study is motivated by the need to give the reader a broad view of the developments, key concepts, and technologies related to information society evolution, with a focus on the wireless communications and geoinformation technologies and their role in the environment. Giving perspective, it aims at assisting people active in the industry, the public sector, and Earth science fields as well, by providing a base for their continued work and thinking