On Shortest-Path All-Optical Networks without Wavelength Conversion Requirements

Abstract

In all-optical networks with wavelength division multiplexing, every connection is routed along a certain path and assigned a wavelength such that no two connections use the same wavelength on the same link. For a given set P of paths (a routing), let χ(P) denote the minimum number of wavelengths in a valid wavelength assignment and let L(P) denote the maximum link load. We always have L(P) ≤ χ(P). Motivated by practical concerns, we consider routings containing only shortest paths. We give a complete characterization of undirected networks for which any set P of shortest paths admits a wavelength assignment with L(P) wavelengths. These are exactly the networks that do not benefit from the use of (expensive) wavelength converters if shortest-path routing is used. We also give an efficient algorithm for computing a wavelength assignment with L(P) wavelengths in these networks.

Wavelength Conversion in All-Optical Networks with Shortest-Path Routing

“…This generalizes the result of [6], which only allows us to decide whether the empty set is SP-sufficient for a given undirected graph, and also extends it to the directed case. We note that the proof given here, although for a much more general result, is substantially simpler and more elegant than the one given in [6]. In their most general form, our algorithms apply to networks with other routings as well (for example, arbitrary routings).…”

“…Therein, it was shown that lines (paths) are the only undirected graphs that do not need converters, and an optimal polynomial-time algorithm for finding a minimum sufficient set was given. Networks with shortest-path routings were considered in [6]. A complete characterization of the undirected graphs which admit the empty SP-sufficient set, as well as efficient optimal coloring algorithms for this class of graphs, were given.…”

“…The characterization of the undirected graphs which admit the empty SPsufficient set given in [6] implies that the restriction to shortest-path routings can reduce the converter requirements of a given network significantly. Furthermore, the known algorithms for MIN SUFFICIENT SET from [5] and [12] indicate that by allowing arbitrary routings we end up with unduly pessimistic placements of converters since they can result in picking half or even all vertices of degree greater than 2.…”

Optimization in telecommunication networks

“…The only exception are rings, where an arbitrary node of degree 2 must be selected. Erlebach and Stefanakos (2002a) restrict themselves to sets of paths 𝒫 which contain shortest paths only, bearing in mind that these paths are the ones generally used in network routings. They characterize graphs with MSS of size 0.…”

Minimizing maximum fiber requirement in optical networks

“…However, in many practical situations arising in optical network design, routing is determined by some higher-level specifications (e.g. carriers may require min-hop routing, see [10,8]). Hence, it is important to consider the wavelength assignment problem in isolation.…”