Abstract
Selfish bin packing can be viewed as the non-cooperative version of bin packing problem, where every item is a selfish agent and wants to minimize his sharing cost with the other items packing in the same bin. In this paper, we focus on designing a new mechanism (a payoff rule) for selfish bin packing, called modified Dutch treatment mechanism. We first show that the pure Nash equilibrium exists and it can be obtained in polynomial time. We then prove that under the new mechanism, the price of anarchy is between 1.47407 and 1.4748, improving the known results.
References
Bilo V (2006) On the packing of selfish items. In: Proceedings 20th IEEE international parallel and distributed processing symposium. IEEE
Coffman JEG, Csirik J (2007) Performance guarantees for one-dimensional bin packing. In: Handbook of approximation algorithms and metaheuristics, 32–1
Coffman JEG, Garey MR, Johnson DS (1996) Approximation algorithms for bin packing: a survey. Approximation algorithms for NP-hard problems. PWS Publishing Co., pp 46–93
Dosa G, Epstein L (2012) Generalized selfish bin packing. arXiv preprint arXiv:1202.4080
Epstein L, Kleiman E (2011) Selfish bin packing. Algorithmica 60(2):368–394
Epstein L, Kleiman E, Mestre J (2016) Parametric packing of selfish items and the subset sum algorithm. Algorithmica 74(1):177–207
Johnson DS, Demers A, Ullman JD, Garey MR, Graham RL (1974) Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J Comput 3(4):299–325
Kleinberg J, Rabani Y, Tardos E (2000) Allocating bandwidth for bursty connections. SIAM J Comput 30(1):191–217
Koutsoupias E, Papadimitriou C (1999) Worst-case equilibria. In: STACS 99. Springer, Berlin, pp 404–413
Li W, Fang Q, Liu W (2016) An incentive mechanism for selfish bin covering. In: International conference on combinatorial optimization and applications. Springer, Berlin, pp 641–654
Ma R, Dósa G, Han X, Ting H, Ye D, Zhang Y (2013) A note on a selfish bin packing problem. J Glob Optim 56(4):1457–1462
Naaman N, Rom R (2002) Packet scheduling with fragmentation. INFOCOM 2
Nong Q, Sun T, Cheng TCE, Fang Q (2018) Bin packing game with a price of anarchy of \(\frac{3}{2}\). J Comb Optim 35(2):632–640
Wang Z, Han X, Dósa G, Tuza Z (2018) A general bin packing game: interest taken into account. Algorithmica 80(5):1534–1555
Yu G, Zhang G (2008) Bin packing of selfish items. In: Internet and network economics. Springer, Berlin, pp 446–453
Zhang C, Zhang G (2017) Cost-sharing mechanisms for selfish bin packing. In: International conference on combinatorial optimization and applications. Springer, Cham, pp 355–368
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A preliminary version of this submission was published in COCOA 2017.
This work is partially supported by National Natural Science Foundation of China (Nos. 11871442 and 11201439) and the Fundamental Research Funds for the Central Universities (No. 201964006).
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Chen, X., Nong, Q. & Fang, Q. An improved mechanism for selfish bin packing. J Comb Optim 42, 636–656 (2021). https://doi.org/10.1007/s10878-019-00476-0
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DOI: https://doi.org/10.1007/s10878-019-00476-0