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A review of routing and wavelength assignment approaches for wavelengthrouted optical WDM networks
 Optical Networks Magazine
, 2000
"... This study focuses on the routing and WavelengthAssignment (RWA) problem in wavelengthrouted optical WDM networks. Most of the attention is devoted to such networks operating under the wavelengthcontinuity constraint, in which lightpaths are set up for connection requests between node pairs, and ..."
Abstract

Cited by 307 (11 self)
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This study focuses on the routing and WavelengthAssignment (RWA) problem in wavelengthrouted optical WDM networks. Most of the attention is devoted to such networks operating under the wavelengthcontinuity constraint, in which lightpaths are set up for connection requests between node pairs, and a single lightpath must occupy the same wavelength on all of the links that it spans. In setting up a lightpath, a route must be selected and a wavelength must be assigned to the lightpath. If no wavelength is available for this lightpath on the selected route, then the connection request is blocked. We examine the RWA problem and review various routing approaches and wavelengthassignment approaches proposed in the literature. We also briefly consider the characteristics of wavelengthconverted networks (which do not have the wavelengthcontinuity constraint), and we examine the associated research problems and challenges. Finally, we propose a new wavelengthassignment scheme, called Distributed Relative Capacity Loss (DRCL), which works well in distributedcontrolled networks, and we demonstrate the performance of DRCL through simulation. 1
Treewidth and Small Separators for Graphs with Small Chordality
, 1995
"... A graph G kchordal, if it does not contain chordless cycles of length larger than k. The chordality cl of a graph G is the minimum k for which G is kchordal. The degeneracy or the width of a graph is the maximum mindegree of any of its subgraphs. Our results are the following: 1. The problem of ..."
Abstract

Cited by 3 (1 self)
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A graph G kchordal, if it does not contain chordless cycles of length larger than k. The chordality cl of a graph G is the minimum k for which G is kchordal. The degeneracy or the width of a graph is the maximum mindegree of any of its subgraphs. Our results are the following: 1. The problem of treewidth remains NPcomplete when restricted on graphs with small maximum degree. 2. An upper bound is given for the treewidth of a graph as a function of its maximum degree and chordality. A consequence of this result is that when maximum degree and chordality are fixed constants, then there is a linear algorithm for treewidth and a polynomial algorithm for pathwidth. 3. For any constant s 1, it is shown that any (s + 2)chordal graph with degeneracy d contains a 1 2 separator of size O((dn) s\Gamma1 s ), computable in linear time. Our results extent the many applications of the separator theorems in [1, 33, 34] to the class of kchordal graphs. Several natural classes of graphs have ...