A Parallel Iterative Improvement Stable Matching Algorithm

  • Enyue Lu
  • S. Q. Zheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2913)


In this paper, we propose a new approach, parallel iterative improvement (PII), to solving the stable matching problem. This approach treats the stable matching problem as an optimization problem with all possible matchings forming its solution space. Since a stable matching always exists for any stable matching problem instance, finding a stable matching is equivalent to finding a matching with the minimum number (which is always zero) of unstable pairs. A particular PII algorithm is presented to show the effectiveness of this approach by constructing a new matching from an existing matching and using techniques such as randomization and greedy selection to speedup the convergence process. Simulation results show that the PII algorithm has better average performance compared with the classical stable matching algorithms and converges in n iterations with high probability. The proposed algorithm is also useful for some real-time applications with stringent time constraint.


Parallel Algorithm Initiation Phase Stable Match Ranking List Ranking Matrix 
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  1. 1.
    Abeledo, H., Rothblum, U.G.: Paths to marriage stability. Discrete Applied Mathematics 63, 1–12 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Anderson, R.: Parallel algorithms for generating random permutations on a shared memory machine. In: Proc. of the 2nd ACM Symposium on Parallel Algorithms and Architectures, pp. 95–102 (1990)Google Scholar
  3. 3.
    Chuang, S.T., Goel, A., McKeown, N., Prabhakar, B.: Matching output queuing with a combined input/output-queued switch. IEEE Journal on Selected Areas in Communications 17(6), 1030–1039 (1999)CrossRefGoogle Scholar
  4. 4.
    Durstenfeld, R.: Random permutation (Algorithm 235). Communication of ACM 7(7), 420 (1964)CrossRefGoogle Scholar
  5. 5.
    Feder, T., Megiddo, N., Plotkin, S.: A sublinear parallel algorithm for stable matching. Theoretical Computer Science 233, 297–308 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. American Mathematical Monthly 69, 9–15 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gusfield, D.: Three fast algorithms for four problems in stable marriage. SIAM Journal on Computing 16(1), 111–128 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Gusfield, D., Irving, R.W.: The Stable Marriage Problem Structure and Algorithms. MIT Press, Cambridge (1989)zbMATHGoogle Scholar
  9. 9.
    Hagerup, T.: Fast parallel generation of random permutations. In: Proc. of the 18th Annual International Colloquium on Automata, Languages and Programming, pp. 405–416 (1991)Google Scholar
  10. 10.
    Hattori, T., Yamasaki, T., Kumano, M.: New fast iteration algorithm for the solution of generalized stable marriage problem. In: Proc. of IEEE International Conference on Systems, Man, and Cybernetics, vol. 6, pp. 1051–1056 (1999)Google Scholar
  11. 11.
    Hull, M.E.C.: A parallel view of stable marriages. Information Processing Letters 18(1), 63–66 (1984)CrossRefGoogle Scholar
  12. 12.
    Jaja, J.: An Introduction to Parallel Algorithms. Addison-Wesley, Reading (1992)zbMATHGoogle Scholar
  13. 13.
    Kapur, D., Krishnamoorthy, M.S.: Worst-case choice for the stable marriage problem. Information Processing Letters 21, 27–30 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Leighton, F.T.: Introduction to Parallel Algorithms and Architectures: Arrays · Trees · Hypercubes. Morgan Kaufmann Publishers, San Francisco (1992)zbMATHGoogle Scholar
  15. 15.
    McKeown, N.: Scheduling algorithms for input-buffered cell switches. Ph.D. Thesis, University of California, Berkeley (1995)Google Scholar
  16. 16.
    McVitie, D.G., Wilson, L.B.: The stable marriage problem. Communication of the ACM 14(7), 486–490 (1971)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Nong, G., Hamdi, M.: On the provision of quality-of-service guarantees for input queued switches. IEEE Communications Magazine 38(12), 62–69 (2000)CrossRefGoogle Scholar
  18. 18.
    Prabhakar, B., McKeown, N.: On the speedup required for combined input- and output-queued switching. Automatica 35(12), 1909–1920 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Quinn, M.J.: A note on two parallel algorithms to solve the stable marriage problem. BIT 25, 473–476 (1985)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Stoica, I., Zhang, H.: Exact emulation of an output queuing switch by a combined input output queuing switch. In: Proc. of the 6th IEEE/IFIP IWQoS 1998, Napa Valley, CA, pp. 218–224 (1998)Google Scholar
  21. 21.
    Subramanian, A.: A new approach to stable matching problems. SIAM Journal on Computing 23(4), 671–700 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Tseng, S.S., Lee, R.C.T.: A parallel algorithm to solve the stable marriage algorithm. BIT 24, 308–316 (1984)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Enyue Lu
    • 1
  • S. Q. Zheng
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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