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Eric Rémila

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15 papers
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15

MFCS Conference 2011 Conference Paper

Transduction on Kadanoff Sand Pile Model Avalanches, Application to Wave Pattern Emergence

  • Kévin Perrot
  • Eric Rémila

Abstract Sand pile models are dynamical systems describing the evolution from N stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be applied. The main interest of sand piles relies in their Self Organized Criticality (SOC), the property that a small perturbation | adding some sand grains | on a fixed configuration has uncontrolled consequences on the system, involving an arbitrary number of grain fall. Physicists L. Kadanoff et al inspire KSPM, a model presenting a sharp SOC behavior, extending the well known Sand Pile Model. In KSPM( D ), we start from a pile of N stacked grains and apply the rule: \(D\! -\! 1\) grains can fall from column i onto the \(D\! -\! 1\) adjacent columns to the right if the difference of height between columns i and \(i\! +\! 1\) is greater or equal to D. This paper develops a formal background for the study of KSPM fixed points. This background, resumed in a finite state word transducer, is used to provide a plain formula for fixed points of KSPM(3).

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FOCS Conference 1996 Conference Paper

Approximate Strip Packing

  • Claire Mathieu
  • Eric Rémila

We present an approximation scheme for strip-packing, or packing rectangles into a rectangle of fixed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm finds a packing of n rectangles whose total height is within a factor of (1+/spl epsiv/) of optimal, and has running time polynomial both in n and in 1//spl epsiv/. It is based on a reduction to fractional bin-packing, and can be performed by 5 stages of guillotine cuts.

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