Books in the Algorithms and Combinatorics series

This comprehensive textbook on combinatorial optimization emphasizes theoretical results and algorithms with provably good performance, in contrast to heuristics. The text contains complete but concise proofs, and also provides numerous exercises and references.

This book offers a systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is typical of a fuzzy notion, the authors present a unifying classification of general classes of structures.

What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? This book is an accessible and lively introduction to the area of geometric discrepancy theory.

Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron.

One of the important areas of contemporary combinatorics is Ramsey theory. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science.