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arXiv · 0907.0884

Self-Improving Algorithms

Nir Ailon·Bernard Chazelle·Kenneth L. Clarkson·Ding Liu·Wolfgang Mulzer·C. Seshadhri
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Abstract

We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we need to process a sequence I_1, I_2, ... of inputs I = (x_1, x_2, ..., x_n) of some fixed length n, where each x_i is drawn independently from some arbitrary, unknown distribution D_i. The goal is to design an algorithm for these inputs so that eventually the expected running time will be optimal for the input distribution D = D_1 * D_2 * ... * D_n. We give such self-improving algorithms for two problems: (i) sorting a sequence of numbers and (ii) computing the Delaunay triangulation of a planar point set. Both algorithms achieve optimal expected limiting complexity. The algorithms begin with a training phase during which they collect information about the input distribution, followed by a stationary regime in which the algorithms settle to their optimized incarnations.

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Nir Ailon, Bernard Chazelle, Kenneth L. Clarkson, Ding Liu, Wolfgang Mulzer, C. Seshadhri. 2010-10-18. Self-Improving Algorithms. https://doi.org/10.1137/090766437

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