Statistics of Partial Minima

Details Statistics of Partial Minima Statistics of Partial Minima

2007-09-19

arxiv.org/abs/0709.3117v1

J. Phys. A 40, F1021 (2007)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 1 figure

Scientific paper

10.1088/1751-8113/40/47/F02

Motivated by multi-objective optimization, we study extrema of a set of N points independently distributed inside the d-dimensional hypercube. A point in this set is k-dominated by another point when at least k of its coordinates are larger, and is a k-minimum if it is not k-dominated by any other point. We obtain statistical properties of these partial minima using exact probabilistic methods and heuristic scaling techniques. The average number of partial minima, A, decays algebraically with the total number of points, A ~ N^{-(d-k)/k}, when 1<=k

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