Abstract
Winkler and Zhang introduced the FIBER MINIMIZATION problem in [10]. They showed that the problem is NP-complete but left the question of approximation algorithms open. We give a simple 2-approximation algorithm for this problem. We also show how ideas from the Dynamic Storage Allocation algorithm of Buchsbaum et al. [4] can be used to give an approximation ratio arbitrarily close to 1 provided the problem instance satisfies certain criteria. We also show that these criteria are necessary to obtain an approximation scheme. Our 2-approximation algorithm achieves its guarantee unconditionally.
We also consider the extension of the problem to a ring network and give a 2+o(1)-approximation algorithm for this topology. Our techniques also yield a factor-2 approximation for the related problem of PACKING INTERVALS IN INTERVALS, also introduced by Winkler and Zhang in [10].
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Kumar, V., Rudra, A. (2005). Approximation Algorithms for Wavelength Assignment. In: Sarukkai, S., Sen, S. (eds) FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2005. Lecture Notes in Computer Science, vol 3821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11590156_12
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DOI: https://doi.org/10.1007/11590156_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30495-1
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