Abstract
In this work we represent the Optimal Stable Marriage problem as a Soft Constraint Satisfaction Problem. In addition, we extend this problem from couples of individuals to coalitions of generic agents, in order to define new coalition-formation principles and stability conditions. In the coalition case, we suppose the preference value as a trust score, since trust can describe the belief of a node in the capabilities of another node, in its honesty and reliability. Semiring-based soft constraints represent a general and expressive framework that is able to deal with distinct concepts of optimality by only changing the related c-semiring structure, instead of using different ad-hoc algorithms. At last, we propose an implementation of the classical OSM problem using integer linear programming tools.
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References
Bistarelli, S.: Semirings for Soft Constraint Solving and Programming. LNCS, vol. 2962. Springer, Heidelberg (2004)
Bistarelli, S., Martinelli, F., Santini, F.: A semantic foundation for trust management languages with weights: An application to the RT family. In: Rong, C., Jaatun, M.G., Sandnes, F.E., Yang, L.T., Ma, J. (eds.) ATC 2008. LNCS, vol. 5060, pp. 481–495. Springer, Heidelberg (2008)
Bistarelli, S., Montanari, U., Rossi, F.: Soft concurrent constraint programming. ACM Trans. Comput. Logic 7(3), 563–589 (2006)
Bistarelli, S., Montanari, U., Rossi, F.: Semiring-based Constraint Solving and Optimization. Journal of the ACM 44(2), 201–236 (1997)
Bistarelli, S., O’Sullivan, B.: Combining branch & bound and SBDD to solve soft CSPs. In: Proc. of CP 2004 Fourth International Workshop on Symmetry and Constraint Satisfaction Problems (SymCon 2004) (2004)
Bistarelli, S., Santini, F.: Propagating multitrust within trust networks. In: SAC 2008: Proceedings of the 2008 ACM symposium on Applied computing, pp. 1990–1994. ACM, New York (2008)
Breban, S., Vassileva, J.: A coalition formation mechanism based on inter-agent trust relationships. In: AAMAS 2002: Proceedings of the first international joint conference on Autonomous agents and multiagent systems, pp. 306–307. ACM, New York (2002)
Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Programming. Brooks/Cole Publishing Company, Monterey (2002)
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. The American Mathematical Monthly 69(1), 9–15 (1962)
Gent, I.P., Irving, R.W., Manlove, D., Prosser, P., Smith, B.M.: A constraint programming approach to the stable marriage problem. In: Conference on Principles and Practice of Constraint Programming, pp. 225–239. Springer, London (2001)
Griffiths, N., Luck, M.: Coalition formation through motivation and trust. In: AAMAS 2003: Proceedings of the second international joint conference on Autonomous agents and multiagent systems, pp. 17–24. ACM, New York (2003)
Gusfield, D.: Three fast algorithms for four problems in stable marriage. SIAM J. Comput. 16(1), 111–128 (1987)
Gusfield, D., Irving, R.W.: The stable marriage problem: structure and algorithms. MIT Press, Cambridge (1989)
Horling, B., Lesser, V.: A survey of multi-agent organizational paradigms. Knowl. Eng. Rev. 19(4), 281–316 (2004)
Irving, R.W., Leather, P., Gusfield, D.: An efficient algorithm for the “optimal” stable marriage. J. ACM 34(3), 532–543 (1987)
Iwama, K., Miyazaki, S.: A survey of the stable marriage problem and its variants. In: International Conference on Informatics Education and Research for Knowledge-Circulating Society (icks 2008), pp. 131–136. IEEE Computer Society Press, Los Alamitos (2008)
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)
Jøsang, A., Ismail, R., Boyd, C.: A survey of trust and reputation systems for online service provision. Decis. Support Syst. 43(2), 618–644 (2007)
Knuth, D.E.: Stable marriage and its relation to other combinatorial problems: An introduction to the mathematical analysis of algorithms. American Mathematical Society, Providence (1997)
Leenen, L., Ghose, A.: Branch and bound algorithms to solve semiring constraint satisfaction problems. In: Ho, T.-B., Zhou, Z.-H. (eds.) PRICAI 2008. LNCS, vol. 5351, pp. 991–997. Springer, Heidelberg (2008)
Lerman, K., Shehory, O.: Coalition formation for large-scale electronic markets. In: ICMAS, pp. 167–174. IEEE Computer Society, Los Alamitos (2000)
Theodorakopoulos, G., Baras, J.S.: Trust evaluation in ad-hoc networks. In: WiSe 2004: Proceedings of the 3rd ACM workshop on Wireless security, pp. 1–10. ACM, New York (2004)
Unsworth, C., Prosser, P.: Specialised constraints for stable matching problems. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, p. 869. Springer, Heidelberg (2005)
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Bistarelli, S., Foley, S., O’Sullivan, B., Santini, F. (2009). From Marriages to Coalitions: A Soft CSP Approach. In: Oddi, A., Fages, F., Rossi, F. (eds) Recent Advances in Constraints. CSCLP 2008. Lecture Notes in Computer Science(), vol 5655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03251-6_1
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DOI: https://doi.org/10.1007/978-3-642-03251-6_1
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