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 oncombinatorics, 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.

• Allon G. Percus, Gabriel Istrate, and Cristopher Moore: PrefacePart 1: Fundamentals1: Allon G. Percus, Gabriel Istrate, and: Introduction: Where Statistical Physics Meets ComputationCristopher Moore2: Gil Kalai and Shmuel Safra: Threshold Phenomena and Influence: Perspectives from Mathematics, Computer Science, and EconomicsPart 2: Statistical Physics and Algorithms3: Simona Cocco, Remi Monasson, Andrea Montanari, and Guilhem Semerjian: Analyzing Search Algorithms with Physical Methods4: Alfredo Braunstein, Marc Mezard, Martin Weigt, and Riccardo Zecchina: Constraint Satisfaction by Survey Propagation5: Stephan Mertens: The Easiest Hard Problem: Number Partitioning6: Sigismund Kobe and Jarek Krawczyk: Ground States, Energy Landscape and Low-Temperature Dynamics of plus/minus Spin GlassesPart 3: Identifying the Threshold7: Lefteris M. Kirousis, Yannis C. Stamatiou, and Michele Zito: The Satisfiability Threshold Conjecture: Techniques Behind Upper Bound Improvements8: Alexis C. Kaporis, Lefteris M. Kirousis, and Yannis C. Stamatiou: Proving Conditional Randomness Using the Principle of Deferred Decisions9: Demetrios D. Demopoulos, and Moshe Y. Vardi: The Phase Transition in the Random HornSAT ProblemPart 4: Extensions and Applications10: Tad Hogg: Phase Transitions for Quantum Search Algorithms11: Zoltan Toroczkai, Gyorgy Korniss, Mark A. Novotny, and Hasan Guclu: Scalability, Random Surfaces and Synchronized Computing Networks12: Christian M. Reidys: Combinatorics of Genotype-Phenotype Maps: An RNA Case Study13: Harry B. Hunt, III, Madhav V. Marathe, Daniel J. Rosenkrantz, and Richard E. Stearns: Towards a Predictive Computational Complexity Theory for Periodically Specified Problems: A SurveyBibliographyIndex

"This volume provides a comprehensive overview of an exciting new research area at the interface between statistical physics and computer science. It is an excellent exposition, featuring state-of-the-art contributions by renowned researchers in the field. The book will serve as a useful reference for years to come." Bart Selman, Cornell University