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