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A 0.5358-approximation for Bandpass-2

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Abstract

The Bandpass-2 problem is a variant of the maximum traveling salesman problem arising from optical communication networks using wavelength-division multiplexing technology, in which the edge weights are dynamic rather than fixed. The previously best approximation algorithm for this NP-hard problem has a worst-case performance ratio of \(\frac{227}{426}.\) Here we present a novel scheme to partition the edge set of a 4-matching into a number of subsets, such that the union of each of them and a given matching is an acyclic 2-matching. Such a partition result takes advantage of a known structural property of the optimal solution, leading to a \(\frac{70-\sqrt{2}}{128}\approx 0.5358\)-approximation algorithm for the Bandpass-2 problem.

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Acknowledgments

Weitian Tong, Randy Goebel, and Guohui Lin are supported in part by NSERC, the Alberta Innovates Centre for Machine Learning (AICML), and the Alberta Innovates Technology Futures innovates Centre of Research Excellence (AITF iCORE).

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Authors and Affiliations

  1. College of Physics and Information Engineering, Fuzhou University, Fuzhou, 350108, Fujian, China

    Liqin Huang

  2. Department of Computing Science, University of Alberta, Edmonton, AB, T6G 2E8, Canada

    Weitian Tong, Randy Goebel & Guohui Lin

  3. Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing, 100871, China

    Tian Liu

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  1. Liqin Huang
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  2. Weitian Tong
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  3. Randy Goebel
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  4. Tian Liu
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  5. Guohui Lin
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Correspondence to Guohui Lin.

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Huang, L., Tong, W., Goebel, R. et al. A 0.5358-approximation for Bandpass-2. J Comb Optim 30, 612–626 (2015). https://doi.org/10.1007/s10878-013-9656-2

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  • DOI: https://doi.org/10.1007/s10878-013-9656-2

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