Heavy - Tailed Distributions in CombinatorialSearchCarla

Combinatorial search methods often exhibit a large variability in performance. We study the cost prooles of combinatorial search procedures. Our study reveals some intriguing properties of such cost prooles. The distributions are often characterized by very long tails or \heavy tails". We will show that these distributions are best characterized by a general class of distributions that have no moments (i.e., an innnite mean, variance, etc.). Such non-standard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We believe this is the rst nd-ing of these distributions in a purely computational setting. We also show how random restarts can eeectively eliminate heavy-tailed behavior , thereby dramatically improving the overall performance of a search procedure.