You can start by putting the DO NOT DISTURB sign. Cay, in Desert Hearts (1985). The interplay between randomness and computation is one of the most fas- cinating scientific phenomena uncovered in the last couple of decades. This interplay is at the heart of modern cryptography and plays a fundamental role in complexity theory at large. Specifically, the interplay of randomness and computation is pivotal to several intriguing notions of probabilistic proof systems and is the focal of the computational approach to randomness. This book provides an introduction to these three, somewhat...
You can start by putting the DO NOT DISTURB sign. Cay, in Desert Hearts (1985). The interplay between randomness and computation is one of the most fa...
This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Nesetril. Leading experts have contributed survey and research papers in the areas of Algebraic Combinatorics, Combinatorial Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs, Homomorphisms, Graph Colorings and Graph Embeddings.
This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jar...
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, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research.
What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribut...
You can start by putting the DO NOT DISTURB sign. Cay, in Desert Hearts (1985). The interplay between randomness and computation is one of the most fas- cinating scientific phenomena uncovered in the last couple of decades. This interplay is at the heart of modern cryptography and plays a fundamental role in complexity theory at large. Specifically, the interplay of randomness and computation is pivotal to several intriguing notions of probabilistic proof systems and is the focal of the computational approach to randomness. This book provides an introduction to these three, somewhat...
You can start by putting the DO NOT DISTURB sign. Cay, in Desert Hearts (1985). The interplay between randomness and computation is one of the most fa...
Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant dynamical system are treated by means of graphs and matroids. Special emphasis is laid on the importance of relevant physical observations to successful...
Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illu...
With the advent of computers, algorithmic principles play an ever increasing role in mathematics. Algorithms have to exploit the structure of the underlying mathematical object, and properties exploited by algorithms are often closely tied to classical structural analysis in mathematics. This connection between algorithms and structure is in particular apparent in discrete mathematics, where proofs are often constructive, and can be turned into algorithms more directly. The principle of greediness plays a fundamental role both in the design of continuous algorithms (where it is called the...
With the advent of computers, algorithmic principles play an ever increasing role in mathematics. Algorithms have to exploit the structure of the unde...
In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions.
This contributed volume contains thirty original survey and research...
In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods...
Man wird dem einzelnen nicht gerecht, wenn man es gesondert ins Auge jaftt, ohne seinen Zusammenhang mit dem Ganzen zu beachten und dem Beziehungssystem Rechnung zu tragen, in dem es steht. Thomas Mann Science in general, as well as in each of its individual fields, is a part of human culture. In that sense, this book aims to contribute to uncovering a small part of the connections and relationships which bind image processing, categorized in informatics and technology, with the knowledge accumulated over the years on discrete structures. How does one consider problems, models, mathematical...
Man wird dem einzelnen nicht gerecht, wenn man es gesondert ins Auge jaftt, ohne seinen Zusammenhang mit dem Ganzen zu beachten und dem Beziehungssyst...
One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and...
One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partition...
Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated Dyer-Frieze-Kannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of...
Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as...
