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Truthful Unification Framework for Packing Integer Programs with Choices

  • Conference paper
Automata, Languages and Programming (ICALP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5125))

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Abstract

One of the most interesting research directions within the field of algorithmic mechanism design revolves the study of hard combinatorial optimization problems. In this setting, many common algorithmic techniques cannot be utilized as they violate certain monotonicity properties that are imperative for truthfulness. Consequently, it seems of the essence to develop alternative methods, which can underlie truthful mechanisms. In particular, since many problems can be formulated as instances of integer linear programs, it seems that devising techniques that apply to integer linear programs is significantly important.

In this paper, we focus our attention on packing integer programs with choices. Our main findings can be briefly summarized as follows:

  1. 1

    We develop a framework, which can be used as a building block to approximately solve packing integer programs with choices. The framework is built upon a novel unification technique that approximately solves an instance of a packing integer program with choices, given algorithms that approximately solve sub-instances of it. The framework is deterministic and monotone, and hence can underlie truthful deterministic mechanisms.

  2. 1

    We demonstrate the applicability of the framework by applying it to several NP-hard problems. In particular, we focus on the bandwidth allocation problem in tree networks, and the multiple knapsack problem on bipartite graphs. Notably, using the mentioned framework, we attain the first non-trivial approximation guarantees for these problems in a game theoretic setting.

Proofs and details omitted from this extended abstract appear in the full version of this paper. The first author was supported in part by the Israel Science Foundation and by the German-Israeli Foundation.The second author was supported by the Binational Science Foundation, by the Israel Science Foundation, and by the European Commission under the Integrated Project QAP funded by the IST directorate as Contract Number 015848.

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References

  1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. In: The weighted bipartite mataching problem, ch. 12, Prentice Hall, Englewood Cliffs (1993)

    Google Scholar 

  2. Archer, A., Papadimitriou, C.H., Talwar, K., Tardos, É.: An approximate truthful mechanism for combinatorial auctions with single parameter agents. In: 14th SODA, pp. 205–214 (2003)

    Google Scholar 

  3. Awerbuch, B., Azar, Y., Fiat, A., Leonardi, S., Rosén, A.: On-line competitive algorithms for call admission in optical networks. Algorithmica 31(1), 29–43 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Azar, Y., Gamzu, I., Gutner, S.: Truthful unsplittable flow for large capacity networks. In: 19th SPAA, pp. 320–329 (2007)

    Google Scholar 

  5. Babaioff, M., Lavi, R., Pavlov, E.: Single-value combinatorial auctions and implementation in undominated strategies. In: 17th SODA, pp. 1054–1063 (2006)

    Google Scholar 

  6. Bansal, N., Chakrabarti, A., Epstein, A., Schieber, B.: A quasi-ptas for unsplittable flow on line graphs. In: 38th STOC, pp. 721–729 (2006)

    Google Scholar 

  7. Bar-Noy, A., Bar-Yehuda, R., Freund, A., Naor, J., Schieber, B.: A unified approach to approximating resource allocation and scheduling. J. ACM 48(5), 1069–1090 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bar-Yehuda, R., Beder, M., Cohen, Y., Rawitz, D.: Resource allocation in bounded degree trees. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 64–75. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Briest, P., Krysta, P., Vöcking, B.: Approximation techniques for utilitarian mechanism design. In: 37th STOC, pp. 39–48 (2005)

    Google Scholar 

  10. Calinescu, G., Chakrabarti, A., Karloff, H.J., Rabani, Y.: Improved approximation algorithms for resource allocation. In: 9th IPCO, pp. 439–456 (2001)

    Google Scholar 

  11. Chakrabarti, A., Chekuri, C., Gupta, A., Kumar, A.: Approximation algorithms for the unsplittable flow problem. In: 5th APPROX, pp. 51–66 (2002)

    Google Scholar 

  12. Chekuri, C., Khanna, S.: A polynomial time approximation scheme for the multiple knapsack problem. SICOMP 35(3), 713–728 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chekuri, C., Mydlarz, M., Shepherd, F.B.: Multicommodity demand flow in a tree. In: 30th ICALP, pp. 410–425 (2003)

    Google Scholar 

  14. Clarke, E.H.: Multipart pricing of public goods. Public Choice 8, 17–33 (1971)

    Article  Google Scholar 

  15. Dawande, M., Kalagnanam, J., Keskinocak, P., Salman, F.S., Ravi, R.: Approximation algorithms for the multiple knapsack problem with assignment restrictions. Journal of Combinatorial Optimization 4(2), 171–186 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Feige, U., Vondrák, J.: Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e. In: 47th FOCS, pp. 667–676 (2006)

    Google Scholar 

  17. Fleischer, L., Goemans, M.X., Mirrokni, V.S., Sviridenko, M.: Tight approximation algorithms for maximum general assignment problems. In: 17th SODA, pp. 611–620 (2006)

    Google Scholar 

  18. Garg, N., Vazirani, V.V., Yannakakis, M.: Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18(1), 3–20 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  19. Groves, T.: Incentives in teams. Econemetrica 41(4), 617–631 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lavi, R., Swamy, C.: Truthful and near-optimal mechanism design via linear programming. In: 46th FOCS, pp. 595–604 (2005)

    Google Scholar 

  21. Lehmann, D.J., O’Callaghan, L., Shoham, Y.: Truth revelation in approximately efficient combinatorial auctions. J. ACM 49(5), 577–602 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lewin-Eytan, L., Naor, J., Orda, A.: Admission control in networks with advance reservations. Algorithmica 40(4), 293–304 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  23. Mu’alem, A., Nisan, N.: Truthful approximation mechanisms for restricted combinatorial auctions. In: 18th AAAI, pp. 379–384 (2002)

    Google Scholar 

  24. Nisan, N., Ronen, A.: Computationally feasible vcg mechanisms. In: 2nd EC, pp. 242–252 (2000)

    Google Scholar 

  25. Nisan, N., Ronen, A.: Algorithmic mechanism design. GEB 35, 166–196 (2001)

    MathSciNet  MATH  Google Scholar 

  26. Nutov, Z., Beniaminy, I., Yuster, R.: A (1-1/e)-approximation algorithm for the generalized assignment problem. ORL 34(3), 283–288 (2006)

    MathSciNet  MATH  Google Scholar 

  27. Phillips, C.A., Uma, R.N., Wein, J.: Off-line admission control for general scheduling problems. In: 11th SODA, pp. 879–888 (2000)

    Google Scholar 

  28. Raghavan, P.: Probabilistic construction of deterministic algorithms: Approximating packing integer programs. JCSS 37(2), 130–143 (1988)

    MathSciNet  MATH  Google Scholar 

  29. Raghavan, P., Thompson, C.D.: Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica 7(4), 365–374 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  30. Srinivasan, A.: Improved approximation guarantees for packing and covering integer programs. SICOMP 29(2), 648–670 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  31. Tarjan, R.E.: Decomposition by clique separators. DM 55(2), 221–232 (1985)

    MathSciNet  MATH  Google Scholar 

  32. Vickery, W.: Counterspeculation, auctions and competitive sealed tender. Journal of Finance 16, 8–37 (1961)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Yossi Azar

  2. School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Iftah Gamzu

Authors
  1. Yossi Azar
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  2. Iftah Gamzu
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Editor information

Editors and Affiliations

  1. School of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavík, Iceland

    Luca Aceto

  2. Department of Computer Science, IT-Parken, University of Aarhus, Ã…bogade 34, 8200, Ã…rhusN, Denmark

    Ivan Damgård

  3. Department of Computer Science, University of Liverpool, Ashton Building, L69 3BX, Liverpool, UK

    Leslie Ann Goldberg

  4. School of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavik, Iceland

    Magnús M. Halldórsson

  5. Department of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavík, Iceland

    Anna Ingólfsdóttir

  6. Université de Bordeaux-1, LaBRI, 351, Cours de la Libération, 33405, Talence cedex, France

    Igor Walukiewicz

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© 2008 Springer-Verlag Berlin Heidelberg

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Azar, Y., Gamzu, I. (2008). Truthful Unification Framework for Packing Integer Programs with Choices. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_68

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  • DOI: https://doi.org/10.1007/978-3-540-70575-8_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70574-1

  • Online ISBN: 978-3-540-70575-8

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