Computational Complexity and Statistical Physics

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.

Preface ; Part 1: Fundamentals ; 1. Introduction: Where Statistical Physics Meets Computation ; 2. Threshold Phenomena and Influence: Perspectives from Mathematics, Computer Science, and Economics ; Part 2: Statistical Physics and Algorithms ; 3. Analyzing Search Algorithms with Physical Methods ; 4. Constraint Satisfaction by Survey Propagation ; 5. The Easiest Hard Problem: Number Partitioning ; 6. Ground States, Energy Landscape and Low-Temperature Dynamics of plus/minus Spin Glasses ; Part 3: Identifying the Threshold ; 7. The Satisfiability Threshold Conjecture: Techniques Behind Upper Bound Improvements ; 8. Proving Conditional Randomness Using the Principle of Deferred Decisions ; 9. The Phase Transition in the Random HornSAT Problem ; Part 4: Extensions and Applications ; 10. Phase Transitions for Quantum Search Algorithms ; 11. Scalability, Random Surfaces and Synchronized Computing Networks ; 12. Combinatorics of Genotype-Phenotype Maps: An RNA Case Study ; 13. Towards a Predictive Computational Complexity Theory for Periodically Specified Problems: A Survey ; Bibliography ; Index