Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems

We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They 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 can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard 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 also show how random restarts can effectively eliminate heavy-tailed behavior. Furthermore, for harder problem instances, we observe long tails on the left-hand side of the distribution, which is indicative of a non-negligible fraction of relatively short, successful runs. A r...

• Type: Journal
• Year: 2000
• Where: JAR
• Authors: Carla P. Gomes, Bart Selman, Nuno Crato, Henry A. Kautz
• Keywords: Heavy Tails, JAR 2000, Long Tails, Such Nonstandard Distributions