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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-03251-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03250-9
Online ISBN: 978-3-642-03251-6
eBook Packages: Computer ScienceComputer Science (R0)