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Online Computation with Advice

  • Conference paper
Automata, Languages and Programming (ICALP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5555))

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Abstract

We consider a model for online computation in which the online algorithm receives, together with each request, some information regarding the future, referred to as advice. The advice provided to the online algorithm may allow an improvement in its performance, compared to the classical model of complete lack of information regarding the future. We are interested in the impact of such advice on the competitive ratio, and in particular, in the relation between the size b of the advice, measured in terms of bits of information per request, and the (improved) competitive ratio. Since b = 0 corresponds to the classical online model, and \( b = \lceil \log |\mathcal{A}| \rceil \), where \(\mathcal{A}\) is the algorithm’s action space, corresponds to the optimal (offline) one, our model spans a spectrum of settings ranging from classical online algorithms to offline ones.

In this paper we propose the above model and illustrate its applicability by considering two of the most extensively studied online problems, namely, metrical task systems (MTS) and the k-server problem. For MTS we establish tight (up to constant factors) upper and lower bounds on the competitive ratio of deterministic and randomized online algorithms with advice for any choice of 1 ≤ b ≤ Θ(logn) , where n is the number of states in the system: we prove that any randomized online algorithm for MTS has competitive ratio Ω( log(n) / b) and we present a deterministic online algorithm for MTS with competitive ratio O (log(n) / b) . For the k-server problem we construct a deterministic online algorithm for general metric spaces with competitive ratio k O (1 / b) for any choice of Θ(1) ≤ b ≤ logk .

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Author information

Authors and Affiliations

  1. Tel Aviv University, Tel Aviv, 69978, Israel

    Yuval Emek

  2. CNRS and University Paris Diderot, France

    Pierre Fraigniaud & Amos Korman

  3. CNRS and University of Paris 11, France

    Adi Rosén

Authors
  1. Yuval Emek
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  2. Pierre Fraigniaud
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  3. Amos Korman
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  4. Adi Rosén
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer and Systems Sciences, Sapienza University of Rome, Via Ariosto 25, 00184, Roma, Italy

    Alberto Marchetti-Spaccamela

  3. Google R&D Center, School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Yossi Matias

  4. University of Patras and CTI, N. Kazantzaki Street 1, 26504 Rion, Patras, Greece

    Sotiris Nikoletseas

  5. RWTH Aachen, Lehrstuhl Informatik 7, Ahornstraße 55, 52056, Aachen, Germany

    Wolfgang Thomas

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© 2009 Springer-Verlag Berlin Heidelberg

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Emek, Y., Fraigniaud, P., Korman, A., Rosén, A. (2009). Online Computation with Advice. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02927-1_36

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  • DOI: https://doi.org/10.1007/978-3-642-02927-1_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02926-4

  • Online ISBN: 978-3-642-02927-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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