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Information, Physics, and Computation

Marc Mézard and Andrea Montanari

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and ... More


INTRODUCTION TO FIXED-PARAMETER ALGORITHMS

Rolf Niedermeier

in Invitation to Fixed-Parameter Algorithms

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566076
eISBN:
9780191713910
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566076.003.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter discusses three introductory examples for studying exact and fixed-parameter algorithms. It starts with the boolean Satisfiability problem and its numerous parameters, then discusses an ... More


Satisfiability

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Because of Cook's theorem, satisfiability lies at the heart of computational complexity theory. This chapter presents some selected research directions, focusing on ensembles of random satisfiability ... More


The 1RSB cavity method

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0019
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In graphical models whose factor graph has a locally tree-like structure, belief propagation may fail because variables become correlated at large distances. This phenomenon has been observed in many ... More


Random K-satisfiability

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0020
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter studies an ensemble of random satisfiability problems, ‘random K-satisfiability’ (K-SAT). Applying the 1RSB cavity method, it first derives the phase diagram in the limit of large N, in ... More


Introduction to combinatorial optimization

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


Optimization Problems

Hidetoshi Nishimori

in Statistical Physics of Spin Glasses and Information Processing: An Introduction

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198509417
eISBN:
9780191709081
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509417.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A decision-making problem is often formulated as the minimization or maximization of a multivariable function, an optimization problem. This chapter shows that the methods of statistical mechanics ... More


Opting for the Best

Douglas W. Portmore

in Opting for the Best: Oughts and Options

Published in print:
2019
Published Online:
July 2019
ISBN:
9780190945350
eISBN:
9780190945381
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190945350.003.0001
Subject:
Philosophy, Moral Philosophy

This chapter argues for the opting-for-the-best view: the view that, for any subject S and any member ϕ‎ of a certain subset of S’s options, S ought to ϕ‎ if and only if ϕ‎ is the best member of this ... More


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