Preference-Based Resource Allocation: Using Heuristics to Solve Two-Sided Matching Problems with Indifferences

  • Christian Haas
  • Steven O. Kimbrough
  • Simon Caton
  • Christof Weinhardt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8193)


The allocation of resources between providers to consumers is a well-known problem and has received significant attention, typically using notions of monetary exchanges. In this paper, we study resource matching in settings without monetary transactions by using a two-sided matching approach, e.g., in social and collaborative environments where users define preferences for with whom they may be matched. Whereas two-sided matching for strict and complete preference rankings (i.e., without indifferences) has been extensively studied, it is known that the matching problem is NP-hard for more realistic preference structures. We study, via simulation, the applicability of a heuristic procedure in settings with indiffernces in preferences, and compare its performance to existing algorithms. We study performance metrics like fairness and welfare in addition to the classic stability objective. Our results show interesting trade-offs between performance metrics and promising performance of the heuristic.


Two-Sided Matching Preferences with Indifferences Multiple Objectives Heuristics 


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  1. 1.
    Chard, K., Caton, S., Rana, O., Bubendorfer, K.: Social Cloud: Cloud Computing in Social Networks. In: 2010 IEEE 3rd International Conference on Cloud Computing (CLOUD), pp. 99–106 (2010)Google Scholar
  2. 2.
    Chard, K., Caton, S., Rana, O., Katz, D.S.: Social Cloud Computing: A Vision for Socially Motivated Resource Sharing. In: The Third International Workshop on Data Intensive Computing in the Clouds, DataCloud 2012 (2012)Google Scholar
  3. 3.
    Fehr, E., Schmidt, K.M.: 8. In: The Economics of Fairness, Reciprocity and Altruism - Experimental Evidence and New Theories. Handbook on the Economics of Giving, Reciprocity and Altruism, vol. 1, pp. 615–691. Elsevier (2006)Google Scholar
  4. 4.
    Streitberger, W., Eymann, T.: A simulation of an economic, self-organising resource allocation approach for application layer networks. Computer Networks 53(10), 1760–1770 (2009)zbMATHCrossRefGoogle Scholar
  5. 5.
    Roth, A.: Deferred acceptance algorithms: History, theory, practice, and open questions. International Journal of Game Theory 36(3), 537–569 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Halldórsson, M., Iwama, K., Miyazaki, S., Yanagisawa, H.: Improved approximation results for the stable marriage problem. ACM Transactions on Algorithms (TALG) 3(3), 30 (2007)CrossRefGoogle Scholar
  7. 7.
    Kimbrough, S., Kuo, A.: On heuristics for two-sided matching: Revisiting the stable marriage problem as a multiobjective problem. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, pp. 1283–1290. ACM (2010)Google Scholar
  8. 8.
    Nakamura, M., Onaga, K., Kyan, S., Silva, M.: Genetic algorithm for sex-fair stable marriage problem. In: 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, April- May 3, vol. 1, pp. 509–512 (1995)Google Scholar
  9. 9.
    Gale, D., Shapley, L.: College admissions and the stability of marriage. In: American Mathematical Monthly, pp. 9–15 (1962)Google Scholar
  10. 10.
    Erdil, A., Ergin, H.: Two-sided matching with indifferences. Unpublished mimeo, Harvard Business School (2006)Google Scholar
  11. 11.
    Erdil, A., Ergin, H.: What’s the matter with tie-breaking? improving efficiency in school choice. The American Economic Review 98(3), 669–689 (2008)CrossRefGoogle Scholar
  12. 12.
    Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)zbMATHGoogle Scholar
  13. 13.
    Knuth, D.E.: Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms. CRM Proceedings & Lecture Notes, Centre de Recherches Mathématiques Université de Montréal, vol. 10. American Mathematical Society, Providence, RI (1997); Originally published as Knuth, D.E.: Marriages Stables. Les Presses de l’Université de Montreal, Montreal Canada (1976)Google Scholar
  14. 14.
    Irving, R.W., Leather, P., Gusfield, D.: An efficient algorithm for the optimal stable marriage. Journal of the ACM 34(3), 532–543 (1987)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Axtell, R.L., Kimbrough, S.O.: The high cost of stability in two-sided matching: How much social welfare should be sacrificed in the pursuit of stability? In: Proceedings of the 2008 World Congress on Social Simulation, WCSS 2008 (2008)Google Scholar
  16. 16.
    Klaus, B., Klijn, F.: Procedurally fair and stable matching. Economic Theory 27, 431–447 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Iwama, K., Miyazaki, S., Yanagisawa, H.: Approximation algorithms for the sex-equal stable marriage problem. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 201–213. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Aldershof, B., Carducci, O.M.: Stable marriage and genetic algorithms: A fertile union. Journal of Heuristics 5(1), 29–46 (1999)zbMATHCrossRefGoogle Scholar
  19. 19.
    Vien, N.A., Chung, T.C.: Multiobjective fitness functions for stable marriage problem using genetic algorithm. In: International Joint Conference on SICE-ICASE, pp. 5500–5503 (October 2006)Google Scholar
  20. 20.
    Royal Swedish Academy of Sciences: The Sveriges Riksbank prize in economic sciences in memory of Alfred Nobel for 2012. Word Wide Web (October 2012),
  21. 21.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Longman Publishing Co., Inc. (1989)Google Scholar
  22. 22.
    Gusfield, D.: Three fast algorithms for four problems in stable marriage. SIAM J. Comput. 16(1), 111–128 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Haas, C., Caton, S., Trumpp, D., Weinhardt, C.: A Simulator for Social Exchanges and Collaborations - Architecture and Case Study. In: Proceedings of the 8th IEEE International Conference on eScience, eScience 2012 (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Christian Haas
    • 1
  • Steven O. Kimbrough
    • 2
  • Simon Caton
    • 1
  • Christof Weinhardt
    • 1
  1. 1.Karlsruhe Service Research InstituteKarlsruhe Institute of TechnologyGermany
  2. 2.The Wharton SchoolPhiladelphiaUSA

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