Abstract
The rapid growth of wireless and mobile Internet has led to wide applications of exchanging resources over network, in which how to fairly allocate resources has become a critical challenge. To motivate sharing, a BD Mechanism is proposed for resource allocation, which is based on a combinatorial structure called bottleneck decomposition. The mechanism has been shown with properties of fairness, economic efficiency [17], and truthfulness against two kinds of strategic behaviors [2, 3]. Unfortunately, the crux on how to compute a bottleneck decomposition of any graph is remain untouched. In this paper, we focus on the computation of bottleneck decomposition to fill the blanks and prove that the bottleneck decomposition of a network \(G=(V,E;w_v)\) can be computed in \(O(n^6\log (nU))\), where \(n=|V|\) and \(U=max_{v\in V}w_v\). Based on the bottleneck decomposition, a fair allocation in resource exchange system can be obtained in polynomial time. In addition, our work completes the computation of a market equilibrium and its relationship to two concepts of fairness in resource exchange.
Supported by the National Nature Science Foundation of China (No. 11301475, 61632017, 61761146005).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Arrow, K.J., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica: J. Econometric Soc. 265–290 (1954)
Cheng, Y., Deng, X., Pi, Y., Yan, X.: Can bandwidth sharing be truthful? In: Hoefer, M. (ed.) SAGT 2015. LNCS, vol. 9347, pp. 190–202. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48433-3_15
Cheng, Y., Deng, X., Qi, Q., Yan, X.: Truthfulness of a proportional sharing mechanism in resource exchange. In: IJCAI, pp. 187–193 (2016)
Duan, R., Garg, J., Mehlhorn, K.: An improved combinatorial polynomial algorithm for the linear Arrow-Debreu market. In: Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 90–106. SIAM (2016)
Eaves, B.C.: A finite algorithm for the linear exchange model. Technical report, Systems Optimization Laboratory, Stanford University, California (1975)
Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM (JACM) 19(2), 248–264 (1972)
Felson, M., Spaeth, J.L.: Community structure and collaborative consumption: a routine activity approach. Am. Behav. Sci. 21(4), 614–624 (1978)
Garg, J., Mehta, R., Sohoni, M., Vazirani, V.V.: A complementary pivot algorithm for market equilibrium under separable, piecewise-linear concave utilities. SIAM J. Comput. 44(6), 1820–1847 (2015)
Georgiadis, L., Iosifidis, G., Tassiulas, L.: Exchange of services in networks: competition, cooperation, and fairness. In: ACM SIGMETRICS Performance Evaluation Review, vol. 43, pp. 43–56. ACM (2015)
Getridapp. http://getridapp.com
Homeexchange. http://www.homeexchange.com
Nestia. http://www.nestia.com
Opengarden. http://www.opengarden.com
Swap. http://www.swap.com
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Courier Corporation (1998)
Schollmeier, R.: A definition of peer-to-peer networking for the classification of peer-to-peer architectures and applications. In: Proceedings of First International Conference on Peer-to-Peer Computing, pp. 101–102. IEEE (2001)
Wu, F., Zhang, L.: Proportional response dynamics leads to market equilibrium. In: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, pp. 354–363. ACM (2007)
Ye, Y.: A path to the Arrow-Debreu competitive market equilibrium. Math. Program. 111(1–2), 315–348 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Yan, X., Zhu, W. (2019). A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange. In: Chen, Y., Deng, X., Lu, M. (eds) Frontiers in Algorithmics. FAW 2019. Lecture Notes in Computer Science(), vol 11458. Springer, Cham. https://doi.org/10.1007/978-3-030-18126-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-18126-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-18125-3
Online ISBN: 978-3-030-18126-0
eBook Packages: Computer ScienceComputer Science (R0)