Abstract
We design a Copula-based generic randomized truthful mechanism for scheduling on two unrelated machines with approximation ratio within [1.5852, 1.58606], offering an improved upper bound for the two-machine case. Moreover, we provide an upper bound 1.5067711 for the two-machine two-task case, which is almost tight in view of the lower bound of 1.506 for the scale-free truthful mechanisms [6]. Of independent interest is the explicit incorporation of the concept of Copula in the design and analysis of the proposed approximation algorithm. We hope that techniques like this one will also prove useful in solving other problems in the future.
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References
Chen, X., Du, D., Zuluaga, L.F.: Copula-based randomized mechanisms for truthful scheduling on two unrelated machines. CoRR abs/1306.3909 (2013)
Christodoulou, G., Koutsoupias, E., Vidali, A.: A characterization of 2-player mechanisms for scheduling. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 297–307. Springer, Heidelberg (2008)
Dobzinski, S., Sundararajan, M.: On characterizations of truthful mechanisms for combinatorial auctions and scheduling. In: Proceedings of the 9th ACM Conference on Electronic Commerce, EC 2008, pp. 38–47 (2008)
Koutsoupias, E., Vidali, A.: A lower bound of 1 + φ for truthful scheduling mechanisms. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 454–464. Springer, Heidelberg (2007)
Lavi, R., Mu’Alem, A., Nisan, N.: Towards a characterization of truthful combinatorial auctions. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003, pp. 574–583 (2003)
Lu, P.: On 2-player randomized mechanisms for scheduling. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 30–41. Springer, Heidelberg (2009)
Lu, P., Yu, C.: An improved randomized truthful mechanism for scheduling unrelated machines. In: Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008, pp. 527–538 (2008)
Lu, P., Yu, C.: Randomized truthful mechanisms for scheduling unrelated machines. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 402–413. Springer, Heidelberg (2008)
McNeil, A.J., Nešlehová, J.: Multivariate archimedean copulas, d-monotone functions and l 1-norm symmetric distributions. The Annals of Statistics 37(5), 3059–3097 (2009)
Mu’alem, A., Schapira, M.: Setting lower bounds on truthfulness: extended abstract. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, pp. 1143–1152 (2007)
Nisan, N., Ronen, A.: Algorithmic mechanism design. Games and Economic Behavior 35, 166–196 (2001)
Ugray, Z., Lasdon, L., Plummer, J.C., Glover, F., Kelly, J., Martí, R.: Scatter search and local nlp solvers: A multistart framework for global optimization. INFORMS Journal on Computing 19(3), 328–340 (2007)
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Chen, X., Du, D., Zuluaga, L.F. (2013). Copula-Based Randomized Mechanisms for Truthful Scheduling on Two Unrelated Machines. In: Vöcking, B. (eds) Algorithmic Game Theory. SAGT 2013. Lecture Notes in Computer Science, vol 8146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41392-6_20
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DOI: https://doi.org/10.1007/978-3-642-41392-6_20
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