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Using Finite Experiments to Study Asymptotic Performance

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Experimental Algorithmics

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2547))

Abstract

In the analysis of algorithms we are interested in obtaining closed form expressions for algorithmic complexity, or at least asymptotic expressions in O(·)-notation. It is often possible to use experimental results to make significant progress towards this goal, although there are fundamental reasons why we cannot guarantee to obtain such expressions from experiments alone. This paper investigates two approaches relating to problems of developing theoretical analyses based on experimental data.

We first consider the scientific method, which views experimentation as part of a cycle alternating with theoretical analysis. This approach has been very successful in the natural sciences. Besides supplying preliminary ideas for theoretical analysis, experiments can test falsifiable hypotheses obtained by incomplete theoretical analysis. Asymptotic behavior can also sometimes be deduced from stronger hypotheses which have been induced from experiments. As long as complete mathematical analyses remains elusive, well tested hypotheses may have to take their place. Several examples are given where average complexity can be tested experimentally so that support for hypotheses is quite strong.

A second question is how to approach systematically the problem of inferring asymptotic bounds from experimental data. Five heuristic rules for “empirical curve bounding” are presented, together with analytical results guaranteeing correctness for certain families of functions. Experimental evaluations of the correctness and tightness of bounds obtained by the rules for several constructed functions and real datasets are described.

Partially supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Catherine McGeoch

  2. Amherst College, Amherst, MA, USA

    Peter Sanders

  3. The Hong Kong University of Science and Technology, Hong Kong

    Rudolf Fleischer

  4. University of Massachussetts, Amherst, MA

    Paul R. Cohen & Doina Precup

Authors
  1. Catherine McGeoch
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  2. Peter Sanders
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  3. Rudolf Fleischer
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  4. Paul R. Cohen
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  5. Doina Precup
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Rudolf Fleischer

  2. Department of Computer Science, University of New Mexico, Farris Engineering Bldg, 87131-1386, Albuquerque, NM, USA

    Bernard Moret

  3. Department of Computer Science, University of Aarhus, Bld. 540, Ny Munkegade, 8000, Aarhus C, Denmark

    Erik Meineche Schmidt

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© 2002 Springer-Verlag Berlin Heidelberg

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McGeoch, C., Sanders, P., Fleischer, R., Cohen, P.R., Precup, D. (2002). Using Finite Experiments to Study Asymptotic Performance. In: Fleischer, R., Moret, B., Schmidt, E.M. (eds) Experimental Algorithmics. Lecture Notes in Computer Science, vol 2547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36383-1_5

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  • DOI: https://doi.org/10.1007/3-540-36383-1_5

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  • Print ISBN: 978-3-540-00346-5

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