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An Experimental Investigation on the Pancake Problem

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Computer Games (CGW 2015, GIGA 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 614))

Abstract

In this paper, we present an experimental investigation on the pancake problem. Also called sorting by prefix reversals (SBPR), this problem is linked to the genome rearrangement problem also called sorting by reversals (SBR). The pancake problem is a NP-hard problem. Until now, the best theoretical R-approximation was 2 with an algorithm, which gives a 1.22 experimental R-approximation on stacks with a size inferior to 70. In the current work, we used a Monte-Carlo Search (MCS) approach with nested levels and specific domain-dependent simulations. First, in order to sort large stacks of pancakes, we show that MCS is a relevant alternative to Iterative Deepening Depth First Search (IDDFS). Secondly, at a given level and with a given number of polynomial-time domain-dependent simulations, MCS is a polynomial-time algorithm as well. We observed that MCS at level 3 gives a 1.04 experimental R-approximation, which is a breakthrough. At level 1, MCS solves stacks of size 512 with an experimental R-approximation value of 1.20.

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Author information

Authors and Affiliations

  1. LIPADE, Université Paris Descartes, Paris, France

    Bruno Bouzy

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  1. Bruno Bouzy
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Correspondence to Bruno Bouzy .

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Editors and Affiliations

  1. Université Paris-Dauphine, Paris, France

    Tristan Cazenave

  2. Maastricht University, Maastricht, The Netherlands

    Mark H.M. Winands

  3. Universität Bremen, Bremen, Bremen, Germany

    Stefan Edelkamp

  4. Reykjavik University, Reykjavik, Iceland

    Stephan Schiffel

  5. The University of New South Wales, Sydney, New South Wales, Australia

    Michael Thielscher

  6. New York University, Brooklyn, New York, USA

    Julian Togelius

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Bouzy, B. (2016). An Experimental Investigation on the Pancake Problem. In: Cazenave, T., Winands, M., Edelkamp, S., Schiffel, S., Thielscher, M., Togelius, J. (eds) Computer Games. CGW GIGA 2015 2015. Communications in Computer and Information Science, vol 614. Springer, Cham. https://doi.org/10.1007/978-3-319-39402-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-39402-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39401-5

  • Online ISBN: 978-3-319-39402-2

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