A local algorithm is a distributed algorithm that runs in constant time, independently of the
size of the network. Being highly scalable and fault tolerant, such algorithms are ideal in the …

Szemerédi's Regularity Lemma is an important tool in discrete mathematics. It says that, in
some sense, all graphs can be approximated by random-looking graphs. Therefore the …

Communication complexity is the mathematical study of scenarios where several parties
need to communicate to achieve a common goal, a situation that naturally appears during …

Graph Theory has proved to be an extremely useful tool for solving combinatorial problems
in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations …

Combinatorics on words, or finite sequences, is a field that grew from the disparate
mathematics branches of group theory and probability. In recent times, it has gained …

Additive combinatorics is the theory of counting additive structures in sets. This theory has
seen exciting developments and dramatic changes in direction in recent years thanks to its …

Page 1 Graduate Texts in Mathematics David Marker Model Theory: An Introduction Page 2
Graduate Texts in Mathematics 2 1 7 Springer New York Berlin Heidelberg Hong Kong London …

3.4. Isoperimetric inequalities in Riemannian manifolds 25 4. Filling in Banach spaces 28
4.1. Normalization of Haar's measure 28 4.2. Isoperimetric inequalities in Banach spaces 34 …

This is a book about graph homomorphisms. Graph theory is now an established discipline
but the study of graph homomorphisms has only recently begun to gain wide acceptance …

A linear algebraic model of computation the span program, is introduced, and several upper
and lower bounds on it are proved. These results yield applications in complexity and …