- Title Pages
- Preface
- 1 Introduction to information theory
- 2 Statistical physics and probability theory
- 3 Introduction to combinatorial optimization
- 4 A probabilistic toolbox
- 5 The random energy model
- 6 The random code ensemble
- 7 Number partitioning
- 8 Introduction to replica theory
- 9 Factor graphs and graph ensembles
- 10 Satisfiability
- 11 Low-density parity-check codes
- 12 Spin glasses
- 13 Bridges: Inference and the Monte Carlo method
- 14 Belief propogation
- 15 Decoding with belief propagation
- 16 The assignment problem
- 17 Ising models on random graph
- 18 Linear equations with Boolean variables
- 19 The 1RSB cavity method
- 20 Random K-satisfiability
- 21 Glassy states in coding theory
- 22 An ongoing story
- Appendix A Symbols and notation
- References
- Index

# Introduction to combinatorial optimization

# Introduction to combinatorial optimization

- Chapter:
- (p.47) 3 Introduction to combinatorial optimization
- Source:
- Information, Physics, and Computation
- Author(s):
### Marc Mézard

### Andrea Montanari

- Publisher:
- Oxford University Press

This chapter provides an elementary introduction to some basic concepts in theoretical computer science. It includes basic notions of graph theory and an informal introduction to computational complexity, presenting the basic classes P, NP, and NP-complete. These notions are illustrated by discussions of the minimal spanning tree and satisfiability problems, and by applications from statistical physics (spin glasses and maximum cuts), and from coding theory (decoding complexity).

*Keywords:*
computational complexity, NP-complete, graph theory, satisfiability, spin glasses, decoding complexity, minimal spanning tree

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- Title Pages
- Preface
- 1 Introduction to information theory
- 2 Statistical physics and probability theory
- 3 Introduction to combinatorial optimization
- 4 A probabilistic toolbox
- 5 The random energy model
- 6 The random code ensemble
- 7 Number partitioning
- 8 Introduction to replica theory
- 9 Factor graphs and graph ensembles
- 10 Satisfiability
- 11 Low-density parity-check codes
- 12 Spin glasses
- 13 Bridges: Inference and the Monte Carlo method
- 14 Belief propogation
- 15 Decoding with belief propagation
- 16 The assignment problem
- 17 Ising models on random graph
- 18 Linear equations with Boolean variables
- 19 The 1RSB cavity method
- 20 Random K-satisfiability
- 21 Glassy states in coding theory
- 22 An ongoing story
- Appendix A Symbols and notation
- References
- Index