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A 0.5358-approximation for Bandpass-2

Author

Listed:
  • Liqin Huang

    (Fuzhou University)

  • Weitian Tong

    (University of Alberta)

  • Randy Goebel

    (University of Alberta)

  • Tian Liu

    (Peking University)

  • Guohui Lin

    (University of Alberta)

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 $$\frac{227}{426}.$$ 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 $$\frac{70-\sqrt{2}}{128}\approx 0.5358$$ 70 - 2 128 ≈ 0.5358 -approximation algorithm for the Bandpass-2 problem.

Suggested Citation

  • Liqin Huang & Weitian Tong & Randy Goebel & Tian Liu & Guohui Lin, 2015. "A 0.5358-approximation for Bandpass-2," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 612-626, October.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9656-2
    DOI: 10.1007/s10878-013-9656-2
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    References listed on IDEAS

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    1. Esther M. Arkin & Refael Hassin, 1998. "On Local Search for Weighted k -Set Packing," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 640-648, August.
    2. Donald L. Miller & Joseph F. Pekny, 1995. "A Staged Primal-Dual Algorithm for Perfect b-Matching with Edge Capacities," INFORMS Journal on Computing, INFORMS, vol. 7(3), pages 298-320, August.
    3. Guohui Lin, 2011. "On the Bandpass problem," Journal of Combinatorial Optimization, Springer, vol. 22(1), pages 71-77, July.
    4. Djangir A. Babayev & George I. Bell & Urfat G. Nuriyev, 2009. "The bandpass problem: combinatorial optimization and library of problems," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 151-172, August.
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