Self-Improving Algorithms

TL;DR

This paper introduces self-improving algorithms that automatically optimize their expected performance for unknown input distributions, demonstrated on sorting and Delaunay triangulation, achieving optimal expected complexity after a training phase.

Contribution

It presents the first self-improving algorithms for sorting and Delaunay triangulation that adapt to unknown distributions and reach optimal expected complexity.

Findings

Algorithms achieve optimal expected complexity after training.

Self-improving algorithms adapt to unknown input distributions.

Effective for sorting and planar point set triangulation.

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.