Abstract
In optical networks with wavelength division multiplexing (WDM), multiple connections can share a link if they are transmitted on different wavelengths. We study the problem of satisfying a maximum number of connection requests in a directed tree network if only a limited number W of wavelengths are available. In optical networks without wavelength converters this is the maximum path coloring (MaxPC) problem, in networks with full wavelength conversion this is the max-imum path packing (MaxPP)problem. MaxPC and MaxPP are shown to be polynomial-time solvable to optimality if the tree has height one or if both W and the degree of the tree are bounded by a constant. If either W or the degree of the tree is not bounded by a constant, MaxPC and MaxPP are proved NP-hard. Polynomial-time approximation algorithms with performance ratio 5 /3 + ε for arbitrarily small ε are presented for the case W =1, in which MaxPC and MaxPP are equivalent. For arbitrary W, a 2-approximation for MaxPP in arbitrary trees, a 1.58-approximation for MaxPC in trees of bounded degree, and a 2.22-approximation for MaxPC in arbitrary trees are obtained.
supported by DFG contract SFB 342 TP A7
supported partially by the EU ESPRIT LTR Project NO. 20244 (ALCOM-IT)
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Erlebach, T., Jansen, K. (1998). Maximizing the number of Connections in Optical Tree Networks. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_20
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DOI: https://doi.org/10.1007/3-540-49381-6_20
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