A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange

  • Xiang YanEmail author
  • Wei Zhu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11458)


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.


Polynomial algorithm Fair allocation Resource exchange Bottleneck decomposition 


  1. 1.
    Arrow, K.J., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica: J. Econometric Soc. 265–290 (1954)MathSciNetCrossRefGoogle Scholar
  2. 2.
    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). Scholar
  3. 3.
    Cheng, Y., Deng, X., Qi, Q., Yan, X.: Truthfulness of a proportional sharing mechanism in resource exchange. In: IJCAI, pp. 187–193 (2016)Google Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    Eaves, B.C.: A finite algorithm for the linear exchange model. Technical report, Systems Optimization Laboratory, Stanford University, California (1975)Google Scholar
  6. 6.
    Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM (JACM) 19(2), 248–264 (1972)CrossRefGoogle Scholar
  7. 7.
    Felson, M., Spaeth, J.L.: Community structure and collaborative consumption: a routine activity approach. Am. Behav. Sci. 21(4), 614–624 (1978)CrossRefGoogle Scholar
  8. 8.
    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)MathSciNetCrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
  11. 11.
  12. 12.
  13. 13.
  14. 14.
  15. 15.
    Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Courier Corporation (1998)Google Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    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)Google Scholar
  18. 18.
    Ye, Y.: A path to the Arrow-Debreu competitive market equilibrium. Math. Program. 111(1–2), 315–348 (2008)MathSciNetzbMATHGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Shanghai Jiao Tong UniversityShanghaiChina
  2. 2.China Academy of Aerospace Standardization and Product AssuranceBeijingChina

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