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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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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, Åbogade 34, 8200, ÅrhusN, 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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