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 LinEmail author


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.


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



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).


  1. Anstee RP (1987) A polynomial algorithm for \(b\)-matching: an alternative approach. Inf Process Lett 24:153–157MathSciNetCrossRefzbMATHGoogle Scholar
  2. Arkin EM, Hassin R (1998) On local search for weighted packing problems. Math Oper Res 23:640–648MathSciNetCrossRefzbMATHGoogle Scholar
  3. Babayev DA, Bell GI, Nuriyev UG (2009) The bandpass problem: combinatorial optimization and library of problems. J Comb Optim 18:151–172MathSciNetCrossRefzbMATHGoogle Scholar
  4. Bell GI, Babayev DA (2004) Bandpass problem. In: Annual INFORMS meeting, Denver, CO, USA, October 2004Google Scholar
  5. Chandra B, Halldórsson MM (1999) Greedy local improvement and weighted set packing approximation. In: ACM–SIAM proceedings of the tenth annual symposium on discrete algorithms (SODA’99), pp 169–176Google Scholar
  6. Chen Z-Z, Wang L(2012) An improved approximation algorithm for the bandpass-2 problem. In: Proceedings of the 6th annual international conference on combinatorial optimization and applications (COCOA 2012), LNCS, vol 7402, pp 185–196Google Scholar
  7. Chen Z-Z, Okamoto Y, Wang L (2005) Improved deterministic approximation algorithms for Max TSP. Inf Process Lett 95:333–342MathSciNetCrossRefzbMATHGoogle Scholar
  8. Diestel R (2005) Graph theory, 3rd edn. Springer, New YorkzbMATHGoogle Scholar
  9. Gabow H (1983) An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems. In: Proceedings of the 15th annual ACM symposium on theory of computing (STOC’83), pp 448–456Google Scholar
  10. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman and Company, San FranciscozbMATHGoogle Scholar
  11. Harary F (1969) Graph theory. Addison-Wesley, ReadingzbMATHGoogle Scholar
  12. Hassin R, Rubinstein S (2000) Better approximations for Max TSP. Inf Process Lett 75:181–186MathSciNetCrossRefzbMATHGoogle Scholar
  13. Lin G (2011) On the Bandpass problem. J Comb Optim 22:71–77MathSciNetCrossRefzbMATHGoogle Scholar
  14. Miller DL, Pekny JF (1995) A staged primal–dual algorithm for perfect \(b\)-matching with edge capacities. ORSA J Comput 7:298–320CrossRefzbMATHGoogle Scholar
  15. Paluch KE, Mucha M, Madry A (2009) A 7/9-approximation algorithm for the maximum traveling salesman problem. In: Proceedings of the 12th international workshop on APPROX and the 13th international workshop on RANDOM, LNCS, vol 5687, pp 298–311Google Scholar
  16. Serdyukov AI (1984) An algorithms for with an estimate for the traveling salesman problem of the maximum. Upravlyaemye Sistemy 25:80–86MathSciNetzbMATHGoogle Scholar
  17. Tarjan RE (1975) Efficiency of a good but not linear set union algorithm. J ACM 22:215–225MathSciNetCrossRefzbMATHGoogle Scholar
  18. Tong W, Goebel R, Ding W, Lin G (2012) An improved approximation algorithm for the bandpass problem. In: Proceedings of the joint conference of the sixth international frontiers of algorithmics workshop and the eighth international conference on algorithmic aspects of information and management (FAW-AAIM 2012), LNCS, vol 7285, pp 351–358Google Scholar
  19. Tong W, Chen Z-Z, Wang L, Xu Y, Xu J, Goebel R, Lin G (2013) An approximation algorithm for the bandpass-2 problem. arXiv 1307:7089 (under review)Google Scholar

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
    Email author
  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

Personalised recommendations