Computational Complexity and Statistical Physics

Computational Complexity and Statistical Physics

by Allon Percus, Cristopher Moore, Gabriel Istrate
     
 

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… See more details below

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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Product Details

ISBN-13:
9780195177381
Publisher:
Oxford University Press, USA
Publication date:
12/01/2004
Series:
Santa Fe Institute Studies on the Sciences of Complexity Series
Pages:
384
Product dimensions:
9.20(w) x 6.10(h) x 0.70(d)

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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