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Journal of Combinatorial Optimization

, Volume 30, Issue 3, pp 612–626 | Cite as

A 0.5358-approximation for Bandpass-2

  • Liqin Huang
  • Weitian Tong
  • Randy Goebel
  • Tian Liu
  • Guohui Lin
Article

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.

Keywords

The Bandpass problem Maximum weight \(b\)-matching Acyclic 2-matching Approximation algorithm Worst case performance ratio 

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Liqin Huang
    • 1
  • Weitian Tong
    • 2
  • Randy Goebel
    • 2
  • Tian Liu
    • 3
  • Guohui Lin
    • 2
  1. 1.College of Physics and Information EngineeringFuzhou UniversityFuzhouChina
  2. 2.Department of Computing ScienceUniversity of AlbertaEdmontonCanada
  3. 3.Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer SciencePeking UniversityBeijingChina

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