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Function Evaluation Via Linear Programming in the Priced Information Model

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Automata, Languages and Programming (ICALP 2008)

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

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Abstract

We determine the complexity of evaluating monotone Boolean functions in a variant of the decision tree model introduced in [Charikar et al. 2002]. In this model, reading different variables can incur different costs, and competitive analysis is employed to evaluate the performance of the algorithms. It is known that for a monotone Boolean function f, the size of the largest certificate, aka PROOF(f), is a lower bound for γ(f), the best possible competitiveness achievable by an algorithm on f. This bound has been proved to be achievable for some subclasses of the monotone Boolean functions, e.g., read once formulae, threshold trees. However, determining γ(f) for an arbitrary monotone Boolean function has so far remained a major open question, with the best known upper bound being essentially a factor of 2 away from the above lower bound.

We close the gap and prove that for any monotone Boolean function f, γ(f) = PROOF(f). In fact, we prove that γ(f) ≤ PROOF(f) holds for a class much larger than the set of monotone Boolean functions. This class also contains all Boolean functions.

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Author information

Authors and Affiliations

  1. AG Genominformatik, Technical Faculty, Bielefeld University, Germany

    Ferdinando Cicalese

  2. Departamento de Informática, PUC, Rio de Janeiro, Brazil

    Eduardo Sany Laber

Authors
  1. Ferdinando Cicalese
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  2. Eduardo Sany Laber
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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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Cicalese, F., Laber, E.S. (2008). Function Evaluation Via Linear Programming in the Priced Information Model. 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_15

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  • DOI: https://doi.org/10.1007/978-3-540-70575-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70574-1

  • Online ISBN: 978-3-540-70575-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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