Computational Complexity and Statistical Physics (Santa Fe Institute Studies on the Sciences of Complexity)

This Santa Fe Institute volume is intended to be a standard reference to statistical physics methods in computer science theory, particularly in relation to the study of phase transitions in combinatorial problems. It will contain both basic pedagogical material and technical tips and discussions to review the field from a broad perspective. The study of phase transitions in combinatorial problems originated about 50 years ago in work on random graphs by Eros and Renyi. During the past 10 years, there has been increasing appreciation of the relevance of phase transitions to algorithmic performance on computationally hard problems. Mathematicians, computer scientists and physicists have been working to develop the theoretical tools to understand the processes fundamental to computation. This book should appeal strongly to the interdisciplinary group of information scientists. Allon Percus is Associate Director of the Institute for Pure and Applied Mathematics at UCLA, and a scientist at Los Alamos National Laboratory. He received his Ph.D. in Theoretical Physics from the University of Paris, Orsay, in 1997. His research has combined statistical physics, discrete mathematics, and computer science, focusing primarily on local search algorithms in combinatorial optimization. He has organized numerous conferences and workshops on combinatorics, phase transitions, and algorithmic complexity. Gabriel Istrate is a scientist at Los Alamos National Laboratory, in the Basic and Applied Simulation Science group. He received his Ph.D. in Computer Science from the University of Rochester in 1999. His primary research interests are in combinatorial, game theoretic, and probabilistic aspects of complex systems. His work in the area of phase transitions has focused on the interplay between threshold properties and computational complexity. Cristopher Moore is an Associate Professor at the University of New Mexico, and holds a joint appointment in the Computer Science and Physics departments. He received his Ph.D. in Physics from Cornell University in 1991. He has published 80 papers at the interface between these two fields, on topics ranging from statistical physics and phase transitions to quantum algorithms and mapping the internet.