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Constrained bipartite edge coloring with applications to wavelength routing

  • Session 13: Routing Algorithms
  • Conference paper
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Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

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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].

Partially supported by Progetto MURST 40%, Algoritmi, Modelli di Calcolo e Strutture Informative and by EU Esprit Project GEPPCOM and ALCOM-IT.

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Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Kaklamanis, C., Persiano, P., Erlebach, T., Jansen, K. (1997). Constrained bipartite edge coloring with applications to wavelength routing. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_205

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  • DOI: https://doi.org/10.1007/3-540-63165-8_205

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

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