Abstract
Recently a robustness notion for matching problems based on the concept of a (a, b)-supermatch is proposed for the Stable Marriage problem (SM). In this paper we extend this notion to another matching problem, namely the Stable Roommates problem (SR). We define a polynomial-time procedure based on the concept of reduced rotation poset to verify if a stable matching is a (1, b)-supermatch. Then, we adapt a local search and a genetic local search procedure to find the (1, b)-supermatch that minimises b in a given SR instance. Finally, we compare the two models and also create different SM and SR instances to present empirical results on the robustness of these instances.
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Notes
- 1.
The parentheses are used to indicate priority.
- 2.
Our datasets are publicly available at: github.com/begumgenc/rsmData.
- 3.
The reader is referred to the online version for coloured version.
References
Ashlagi, I., Gonczarowski, Y.A.: Dating strategies are not obvious. CoRR abs/1511.00452 (2015)
Aziz, H., Biró, P., Gaspers, S., de Haan, R., Mattei, N., Rastegari., B.: Stable matching with uncertain linear preferences. CoRR abs/1607.02917 (2016)
Drummond, J., Boutilier, C.: Elicitation and approximately stable matching with partial preferences. In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI 2013, pp. 97–105. AAAI Press (2013)
Genc, B., Siala, M., O’Sullivan, B., Simonin, G.: Finding robust solutions to stable marriage. In: Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, 19–25 August 2017, pp. 631–637 (2017)
Genc, B., Siala, M., O’Sullivan, B., Simonin, G.: Finding robust solutions to stable marriage. CoRR abs/1705.09218 (2017)
Genc, B., Siala, M., Simonin, G., O’Sullivan, B.: Complexity study for the robust stable marriage problem. In: Theoretical Computer Science (2019)
Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)
Hebrard, E.: Robust solutions for constraint satisfaction and optimisation under uncertainty. PhD thesis, University of New South Wales (2007)
Holland, A., O’Sullivan, B.: Super solutions for combinatorial auctions. In: Faltings, B.V., Petcu, A., Fages, F., Rossi, F. (eds.) CSCLP 2004. LNCS (LNAI), vol. 3419, pp. 187–200. Springer, Heidelberg (2005). https://doi.org/10.1007/11402763_14
Irving, R.W.: An efficient algorithm for the “stable roommates” problem. J. Algorithms 6(4), 577–595 (1985)
Irving, R.W., Leather, P.: The complexity of counting stable marriages. SIAM J. Comput. 15(3), 655–667 (1986)
Jacobovic, R.: Perturbation robust stable matching. CoRR abs/1612.08118 (2016)
Kolen, A., Pesch, E.: Genetic local search in combinatorial optimization. Discret. Appl. Math. 48(3), 273–284 (1994)
Lebedev, D., Mathieu, F., Viennot, L., Gai, A.-T., Reynier, J., De Montgolfier, F.: On using matching theory to understand P2P network design. In: INOC 2007, International Network Optimization Conference (2007)
Lussier, B., Chatila, R., Ingrand, F., Killijian, M.O., Powell, D.: On fault tolerance and robustness in autonomous systems. In: Proceedings of the Third IARP/IEEE-RAS/EURON Joint Workshop on Technical Challenge for Dependable Robots in Human Environments, Manchester, GB, 7–9 September 2004
Pittel, B.: The “stable roommates” problem with random preferences. Ann. Probab. 21, 1441–1477 (1993)
Siala, M., O’Sullivan, B.: Rotation-based formulation for stable matching. In: Beck, J.C. (ed.) CP 2017. LNCS, vol. 10416, pp. 262–277. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66158-2_17
Ulder, N.L.J., Aarts, E.H.L., Bandelt, H.-J., van Laarhoven, P.J.M., Pesch, E.: Genetic local search algorithms for the traveling salesman problem. In: Schwefel, H.-P., Männer, R. (eds.) PPSN 1990. LNCS, vol. 496, pp. 109–116. Springer, Heidelberg (1991). https://doi.org/10.1007/BFb0029740
Acknowledgement
This material is based upon works supported by the Science Foundation Ireland under Grant No. 12/RC/2289 which is co-funded under the European Regional Development Fund.
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Genc, B., Siala, M., Simonin, G., O’Sullivan, B. (2019). An Approach to Robustness in the Stable Roommates Problem and Its Comparison with the Stable Marriage Problem. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_21
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