Computational Complexity and Statistical Physics

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Overview

Computer science and physics have been closely linked since the birth of modern computing. In recent years, an interdisciplinary area has blossomed at the junction of these fields, connecting insights from statistical physics with basic computational challenges. Researchers have successfully applied techniques from the study of phase transitions to analyze NP-complete problems such as satisfiability and graph coloring. This is leading to a new understanding of the structure of these problems, and of how algorithms perform on them.

Computational Complexity and Statistical Physics will serve as a standard reference and pedagogical aid to statistical physics methods in computer science, with a particular focus on phase transitions in combinatorial problems. Addressed to a broad range of readers, the book includes substantial background material along with current research by leading computer scientists, mathematicians, and physicists. It will prepare students and researchers from all of these fields to contribute to this exciting area.

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Editorial Reviews

From the Publisher

"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

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Product Details

Meet the Author

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.

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Table of Contents

Preface, Allon G. Percus, Gabriel Istrate, and Cristopher Moore
Part 1: Fundamentals
1. Introduction: Where Statistical Physics Meets Computation, Allon G. Percus, Gabriel Istrate, and
Cristopher Moore
2. Threshold Phenomena and Influence: Perspectives from Mathematics, Computer Science, and Economics, Gil Kalai and Shmuel Safra
Part 2: Statistical Physics and Algorithms
3. Analyzing Search Algorithms with Physical Methods, Simona Cocco, Remi Monasson, Andrea Montanari, and Guilhem Semerjian
4. Constraint Satisfaction by Survey Propagation, Alfredo Braunstein, Marc Mezard, Martin Weigt, and Riccardo Zecchina
5. The Easiest Hard Problem: Number Partitioning, Stephan Mertens
6. Ground States, Energy Landscape and Low-Temperature Dynamics of plus/minus Spin Glasses, Sigismund Kobe and Jarek Krawczyk
Part 3: Identifying the Threshold
7. The Satisfiability Threshold Conjecture: Techniques Behind Upper Bound Improvements, Lefteris M. Kirousis, Yannis C. Stamatiou, and Michele Zito
8. Proving Conditional Randomness Using the Principle of Deferred Decisions, Alexis C. Kaporis, Lefteris M. Kirousis, and Yannis C. Stamatiou
9. The Phase Transition in the Random HornSAT Problem, Demetrios D. Demopoulos, and Moshe Y. Vardi
Part 4: Extensions and Applications
10. Phase Transitions for Quantum Search Algorithms, Tad Hogg
11. Scalability, Random Surfaces and Synchronized Computing Networks, Zoltan Toroczkai, Gyorgy Korniss, Mark A. Novotny, and Hasan Guclu
12. Combinatorics of Genotype-Phenotype Maps: An RNA Case Study, Christian M. Reidys
13. Towards a Predictive Computational Complexity Theory for Periodically Specified Problems: A Survey, Harry B. Hunt, III, Madhav V. Marathe, Daniel J. Rosenkrantz, and Richard E. Stearns
Bibliography
Index

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