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Drift Analysis with Tail Bounds

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Parallel Problem Solving from Nature, PPSN XI (PPSN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6238))

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Abstract

We give a simple and short alternative proof of the multiplicative drift theorem published recently (Doerr, Johannsen, Winzen (GECCO 2010)). It completely avoids the use of drift theorems previously used in the theory of evolutionary computation. By this, its proof is fully self-contained.

The new theorem yields exactly the same bounds for expected run-times as the previous theorem. In addition, it also gives good bounds on the deviations from the mean. This shows, for the first time, that the classical O(n logn) run-time bound for the (1+1) evolutionary algorithm for optimizing linear functions holds with high probability (and not just in expectation). Similar improvements are obtained for other classical problems in the evolutionary algorithms literature, for example computing minimum spanning trees, finding single-source shortest paths, and finding Eulerian cycles.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, 66123, Saarbrücken, Germany

    Benjamin Doerr

  2. Department of Computer Science, University of Liverpool, Ashton Bldg, Liverpool, L69 3BX, UK

    Leslie Ann Goldberg

Authors
  1. Benjamin Doerr
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  2. Leslie Ann Goldberg
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Editor information

Editors and Affiliations

  1. Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, Department of ComputerScience, AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Robert Schaefer

  2. Departamento de Lenguajes y Ciencias de la Computación, ETSI Informática, Universidad de Málaga, Campus Teatinos, 29071, Málaga, Spain

    Carlos Cotta

  3. Department of Mathematics and Computer Science, University of Bielsko-Biala, Willowa 2, 43-309, Bielsko-Biala, Poland

    Joanna Kołodziej

  4. Fakultät für Informatik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Günter Rudolph

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Doerr, B., Goldberg, L.A. (2010). Drift Analysis with Tail Bounds. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15844-5_18

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  • DOI: https://doi.org/10.1007/978-3-642-15844-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15843-8

  • Online ISBN: 978-3-642-15844-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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