Based on a March 2001 workshop, this collection explores connections between random graphs and percolation, between slow mixing and phase transition, and between graph morphisms and hard-constraint models. Topics of the 14 papers include efficient local search near phase transitions in combinatorial optimization, graph homomorphisms and long range action, recent results on parameterized H-colorings, the satisfiability of random k-Horn formulae, a discrete non-Pfaffian approach to the Ising problem, and chromatic numbers of products of tournaments. No indexes are provided. Annotation : 2004 Book News, Inc., Portland, OR (booknews.com).

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.

The intersection of combinatorics and statistical physics has experienced great activity in recent years. This flurry of activity has been fertilized by an exchange not only of techniques, but also of objectives. Computer scientists interested in approximation algorithms have helped statistical physicists and discrete mathematicians overcome language problems. They have found a wealth of common ground in probabilistic combinatorics. Close connections between percolation and random graphs, graph morphisms and hard-constraint models, and slow mixing and phase transition have led to new results and perspectives. These connections can help in understanding typical behavior of combinatorial phenomena such as graph coloring and homomorphisms. Inspired by issues and intriguing new questions surrounding the interplay of combinatorics and statistical physics, a DIMACS/DIMATIA workshop was held at Rutgers University. These proceedings are the outgrowth of that meeting. This volume is intended for graduate students and research mathematicians interested in probabilistic graph theory and its applications.

The 28th International Workshop on Graph-Theoretic Concepts in Computer ? Science (WG 2002) was held in Cesky ́ Krumlov, a beautiful small town in the southern part of the Czech Republic on the river Vltava (Moldau), June 13–15, 2002. The workshop was organized by the Department of Applied Mathematics of the Faculty of Mathematics and Physics of Charles University in Prague. Since 1975, WG has taken place in Germany 20 times, twice in Austria and The Netherlands, and once in Italy, Slovakia, and Switzerland. As in previous years, the workshop aimed at uniting theory and practice by demonstrating how graph-theoretic concepts can be applied to various areas in Computer Science, or by extracting new problems from applications.The workshop was devoted to the theoretical and practical aspects of graph concepts in computer science, and its contributed talks showed how recent research results from algorithmic graph theory can be used in computer science and which graph-theoretic questions arise from new developments in computer science. Altogether 61 research papers were submitted and reviewed by the program committee. The program committee represented the wide scienti?c spectrum, and in a careful reviewing process with four reports per submission it selected 36papersforpresentationattheworkshop.Thereferees’commentsaswellasthe numerous fruitful discussions during the workshop have been taken into account by the authors of these conference proceedings.

This book constitutes the refereed proceedings of the 12th Annual European Symposium on Algorithms, ESA 2004, held in Bergen, Norway, in September 2004. The 70 revised full papers presented were carefully reviewed from 208 submissions. The scope of the papers spans the entire range of algorithmics from design and mathematical issues to real-world applications in various fields, and engineering and analysis of algorithms.

ISAAC 2007, the 18th International Symposium on Algorithms and Compu- tion took place in Sendai, Japan, December 17-19, 2007. In the past, it was held in Tokyo (1990), Taipei (1991), Nagoya (1992), Hong Kong (1993), Beijing (1994), Cairns (1995), Osaka (1996), Singapore (1997), Daejeon (1998), Ch- nai (1999), Taipei (2000), Christchurch(2001), Vancouver(2002), Kyoto (2003), Hong Kong (2004), Hainan (2005), and Kolkata(2006). The symposium provided a forum for researchers working in algorithms and the theory of computation from all over the world. In response to our call for papers we received 220 submissions from 40 countries. The task of selecting the papers in this volume was done by our Program Committee and many other external reviewers. After a thorough review process, the Committee selected 77 papers. We hope all accepted papers will eventually appear in scienti?c journals in a more polished form. Two special issues, one of Algorithmica and one of the International Journal of Computational Geometry and Applications, with selected papers from ISAAC 2007 are in preparation. The best paper awardwasgivenfor "IntegerRepresentationandCounting in the Bit Probe Model" to Mohammad Rhaman and Ian Munro. Selected from 27 submissionsauthoredbyonlystudents, thebeststudentpaperawardsweregiven for "On Mixing and Edge Expansion Properties in Randomized Broadcasting" to Thomas Sauerwald and for "Faster Combinatorial Algorithms for Deter- nant and Pfa?an" to Anna Urbanska. Two eminent invited speakers, Pankaj K. Agarwal, Duke University, USA, and Robin Thomas, Georgia Institute of Technology, USA, also contributed to this volume

A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.

Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.

This book constitutes the refereed proceedings of the 23rd International Symposium on Algorithms and Computation, ISAAC 2012, held in Taipei, Taiwan, in December 2012. The 68 revised full papers presented together with three invited talks were carefully reviewed and selected from 174 submissions for inclusion in the book. This volume contains topics such as graph algorithms; online and streaming algorithms; combinatorial optimization; computational complexity; computational geometry; string algorithms; approximation algorithms; graph drawing; data structures; randomized algorithms; and algorithmic game theory.