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This paper proposes an offline wavelength assignment technique for de Bruijn (d, k) optical wavelength division multiplexing (WDM) networks having nodal degree d and diameter k that can support lightpaths between pair of nodes. Each lightpath uses a channel (wavelength) along each link in its route. An efficient algorithm is proposed that can be used to assign wavelengths to lightpath requests in O(k|V|) time, where |V| represents the number of nodes of the de Bruijn network and V represents the set of nodes. The proposed algorithm can be efficiently used for wavelength assignment in de Bruijn WDM networks having limited wavelength conversion capabilities. This work shows that de Bruijn graph can be expressed as union of edge-disjoint rings. Wavelengths are assigned for the individual rings in the graph thus resulting in the assignment for the graph itself. Results are shown for a given de Bruijn graph and for an arbitrary request. The proposed algorithm is compared with two other algorithms, which use two other known works of wavelength assignment on ring topology. Comparisons of the time complexity and the type of wavelength conversion required for these algorithms clearly show that the proposed algorithm is a faster and more efficient way of assigning wavelengths. [ABSTRACT FROM PUBLISHER]

Metacyclic graphs, which include supertoroids as a subclass, have been shown to possess interesting properties and potential applications in implementing moderate- to large-size parallel processors with fairly small node degrees. Wu, Lakshmivarahan, and Dhall (J. Parallel Distrib. Comput. 60 (2000), pp. 539-565) have described a deterministic, distributed routing scheme for certain subclasses of metacyclic graphs. However, they offer no proof that the scheme is a shortest-path routing algorithm and do not indicate whether or how their scheme may be extended to the entire class of metacyclic graphs. In this paper, we provide a near-shortest-path, deterministic routing algorithm that is applicable to any metacyclic graph and derive a bound for the diameter of such graphs. [ABSTRACT FROM AUTHOR]

This paper introduces a new variant of the popular n-dimensional hypercube network Qn, known as the n-dimensional locally twisted cube LTQn, which has the same number of nodes and the same number of connections per node as Qn, Furthermore, LTQn, is similar to Qn, in the sense that the nodes can be one-to-one labeled with 0-1 binary sequences of length n, so that the labels of any two adjacent nodes differ in at most two successive hits. One advantage of LTQn, is that the diameter is only about half of the diameter ot Qn. We develop a simple routing algorithm tor LTQn, which creates a shortest path from the source to the destination in 0(n) time. We find that LTQn, consists of two disjoint copies of Qn-1, by adding a matching between their nodes. On this basis, we show that LTQn has a connectivity of n. [ABSTRACT FROM AUTHOR]

A minimum spanning tree (MST) with a small diameter is required in numerous practical situations such as when distributed mutual-exclusion algorithms are used, or when information retrieval algorithms need to compromise between fast access and small storage. The Diameter-Constrained MST (DCMST) problem can be stated as follows: given an undirected, edge-weighted graph, G , with n nodes and a positive integer, k , find a spanning tree with the smallest weight among all spanning trees of G which contain no path with more than k edges. This problem is known to be NP-complete, for all values of k ; 4≤ k ≤( n -2). In this paper, we investigate the behavior of the diameter of an MST in randomly generated graphs. Then, we present heuristics that produce approximate solutions for the DCMST problem in polynomial time. We discuss convergence, relative merits, and implementation of these heuristics. Our extensive empirical study shows that the heuristics produce good solutions for a wide variety of inputs. [ABSTRACT FROM AUTHOR]