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How Much Information about the Future Is Needed?

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SOFSEM 2008: Theory and Practice of Computer Science (SOFSEM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4910))

Abstract

We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request, and minimized over all algorithm-oracle pairs) communicated between the algorithm and the oracle in order to solve the problem optimally. Hence, the advice complexity measures the amount of problem-relevant information contained in the input.

We introduce two modes of communication between the algorithm and the oracle based on whether the oracle offers an advice spontaneously (helper) or on request (answerer). We analyze the Paging and DiffServ problems in terms of advice complexity and deliver tight bounds in both communication modes.

Supported by APVV-0433-06 and VEGA 1/3106/06.

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Authors and Affiliations

  1. Institute of Mathematics, Slovak Academy of Sciences,  

    Stefan Dobrev

  2. Department of Computer Science, Comenius University, Bratislava, Slovakia

    Rastislav Královič & Dana Pardubská

Authors
  1. Stefan Dobrev
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  2. Rastislav Královič
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  3. Dana Pardubská
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Editor information

Viliam Geffert Juhani Karhumäki Alberto Bertoni Bart Preneel Pavol Návrat Mária Bieliková

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Dobrev, S., Královič, R., Pardubská, D. (2008). How Much Information about the Future Is Needed?. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds) SOFSEM 2008: Theory and Practice of Computer Science. SOFSEM 2008. Lecture Notes in Computer Science, vol 4910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77566-9_21

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  • DOI: https://doi.org/10.1007/978-3-540-77566-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77565-2

  • Online ISBN: 978-3-540-77566-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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