Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Martingale inequalities and NP-complete problems
Mathematics of Operations Research
Information Sciences: an International Journal
A threshold for unsatisfiability
Journal of Computer and System Sciences
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Length of prime implicants and number of solutions of random CNF formulae
Theoretical Computer Science
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Asymptotic experimental analysis for the Held-Karp traveling salesman bound
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
2+p-SAT: relation of typical-case complexity to the nature of the phase transition
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
The scaling window of the 2-SAT transition
Random Structures & Algorithms
A physicist's approach to number partitioning
Theoretical Computer Science - Phase transitions in combinatorial problems
Theoretical Computer Science - Phase transitions in combinatorial problems
Complexity of learning in artificial neural networks
Theoretical Computer Science - Phase transitions in combinatorial problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Cut Size Statistics of Graph Bisection Heuristics
SIAM Journal on Optimization
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Complexity of learning in artificial neural networks
Theoretical Computer Science - Phase transitions in combinatorial problems
Annals of Mathematics and Artificial Intelligence
Space Complexity of Estimation of Distribution Algorithms
Evolutionary Computation
Threshold properties of random boolean constraint satisfaction problems
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Discrete Applied Mathematics
Finding critical backbone structures with genetic algorithms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Proof of the local REM conjecture for number partitioning. I: Constant energy scales
Random Structures & Algorithms
Horn complements: towards horn-to-horn belief revision
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Phase transitions and backbones of the asymmetric traveling salesman problem
Journal of Artificial Intelligence Research
How the landscape of random job shop scheduling instances depends on the ratio of jobs to machines
Journal of Artificial Intelligence Research
Threshold properties of random boolean constraint satisfaction problems
Discrete Applied Mathematics
Self-organized combinatorial optimization
Expert Systems with Applications: An International Journal
Implementing survey propagation on graphics processing units
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
| Hi-index | 0.00 |
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer science and statistical physics. This review aims at presenting the tools and concepts designed by physicists to deal with optimization or decision problems in a language accessible for computer scientists and mathematicians, with no prerequisites in physics. We first introduce some elementary methods of statistical mechanics and then progressively cover the tools appropriate for disordered systems. In each case, we apply these methods to study the phase transitions or the statistical properties of the optimal solutions in various combinatorial problems. We cover in detail the Random Graph, the Satisfiability, andthe Traveling Salesman problems. References to the physics literature on optimization are provided. We also give our perspective regarding the interdisciplinary contribution of physics to computer science.