Constrained bipartite edge coloring with applications to wavelength routing
Identifieur interne : 002926 ( Main/Merge ); précédent : 002925; suivant : 002927Constrained bipartite edge coloring with applications to wavelength routing
Auteurs : Christos Kaklamanis [Grèce] ; Pino Persiano [Italie] ; Thomas Erlebach [Allemagne] ; Klaus Jansen [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 1997.
Abstract
Abstract: Motivated by the problem of efficient routing in all-optical networks, we study a constrained version of the bipartite edge coloring problem. We show that if the edges adjacent to a pair of opposite vertices of an L-regular bipartite graph are already colored with αL different colors, then the rest of the edges can be colored using at most (1+α/2)L colors. We also show that this bound is tight by constructing instances in which (1+α/2)L colors are indeed necessary. We also obtain tight bounds on the number of colors that each pair of opposite vertices can see. Using the above results, we obtain a polynomial time greedy algorithm that assigns proper wavelengths to a set of requests of maximum load L per directed fiber link on a directed fiber tree using at most 5/3L wavelengths. This improves previous results of [9, 7, 6, 10]. We also obtain that no greedy algorithm can in general use less than 5/3L wavelengths for a set of requests of load L in a directed fiber tree, and thus that our algorithm is optimal in the class of greedy algorithms which includes the algorithms presented in [9, 7, 6, 10].
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DOI: 10.1007/3-540-63165-8_205
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<front><div type="abstract" xml:lang="en">Abstract: Motivated by the problem of efficient routing in all-optical networks, we study a constrained version of the bipartite edge coloring problem. We show that if the edges adjacent to a pair of opposite vertices of an L-regular bipartite graph are already colored with αL different colors, then the rest of the edges can be colored using at most (1+α/2)L colors. We also show that this bound is tight by constructing instances in which (1+α/2)L colors are indeed necessary. We also obtain tight bounds on the number of colors that each pair of opposite vertices can see. Using the above results, we obtain a polynomial time greedy algorithm that assigns proper wavelengths to a set of requests of maximum load L per directed fiber link on a directed fiber tree using at most 5/3L wavelengths. This improves previous results of [9, 7, 6, 10]. We also obtain that no greedy algorithm can in general use less than 5/3L wavelengths for a set of requests of load L in a directed fiber tree, and thus that our algorithm is optimal in the class of greedy algorithms which includes the algorithms presented in [9, 7, 6, 10].</div>
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