A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary basics in required detail. Throughout, the algorithms are shown with examples and calculations, while the proofs are given in a way suitable for graduate students, post-docs, and researchers. Ideal for newcomers to this young, multidisciplinary field.

Alexander K. Hartmann, Ph.D. (1998) from the University of Heidelberg, Diplom (1993) from the University of Duisburg. Since January 2003, Head of the Junior Research group "Complex Ground States of Disordered Systems at the University of Göttingen funded by the Volkswagen Stiftung. 1998-2003, Research Assistant in Prof. Annette Zippelius' group at the University of Göttingen. 2001, Visiting Scientist at the University of California, Santa Cruz and the Ecole Normale Superieure. His research interests are the computer simulations of spin glasses, random field systems and diluted antiferromagnets, gas atoms inside polymer systems, combinatorial optimization problems, random surfaces and surface sputtering, and biophysics (RNA secondary structures and sequence alignment). Martin Weigt, born 1970 in Berlin, Germany; Ph.D. (1998) from Otto-von-Guericke University, Magdeburg, Diplom (1993) from Humboldt University Berlin. Since 1999, Research Assistant in Prof. Annette Zippelius' group at the University of Göttingen. In 2000, 2001, and 2002, Visiting Scientist at the International Centre of Theoretical Physics, Trieste, Italy. His research interests are statistical mechanics of disordered systems and application in random combinatorics and theoretical computer science.

Algorithms Introduction to Graphs Introduction to Complexity Theory Statistical Mechanics of the Ising Model Algorithms and Numerical Results for Vertex Covers Statistical Mechanics of Vertex-covers on a Random Graph The Dynamics of Vertex-cover Algorithms Towards new, Statistical-mechanics Motivated Algorithms The Satisfiability Problem Optimization Problems in Physics