Laszlo Lovasz's Books

Geometric Algorithms and Combinatorial Optimization

By: Martin Grötschel,Laszlo Lovasz,Alexander Schrijver

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Geometric Algorithms and Combinatorial Optimization

By: Martin Grötschel,Laszlo Lovasz,Alexander Schrijver

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 Nevertheless, we do not feel that the ongoing research has made this book outdated.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 optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs.

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374

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364278240X

ISBN 13

9783642782404

An Algorithmic Theory of Numbers, Graphs and Convexity

By: Laszlo Lovasz

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An Algorithmic Theory of Numbers, Graphs and Convexity

By: Laszlo Lovasz

Studies two algorithms in detail: the ellipsoid method and the simultaneous diophantine approximation method.

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SIAM

Published Date

ISBN 10

0898712033

ISBN 13

9780898712032

Greedoids

By: Bernhard Korte,Laszlo Lovasz,Rainer Schrader

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Greedoids

By: Bernhard Korte,Laszlo Lovasz,Rainer Schrader

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 steepest descent or gradient method) and of discrete algorithms. The discrete structure most closely related to greediness is a matroid; in fact, matroids may be characterized axiomatically as those independence systems for which the greedy solution is optimal for certain optimization problems (e.g. linear objective functions, bottleneck functions). This book is an attempt to unify different approaches and to lead the reader from fundamental results in matroid theory to the current borderline of open research problems. The monograph begins by reviewing classical concepts from matroid theory and extending them to greedoids. It then proceeds to the discussion of subclasses like interval greedoids, antimatroids or convex geometries, greedoids on partially ordered sets and greedoid intersections. Emphasis is placed on optimization problems in greedois. An algorithmic characterization of greedoids in terms of the greedy algorithm is derived, the behaviour with respect to linear functions is investigated, the shortest path problem for graphs is extended to a class of greedoids, linear descriptions of antimatroid polyhedra and complexity results are given and the Rado-Hall theorem on transversals is generalized. The self-contained volume which assumes only a basic familarity with combinatorial optimization ends with a chapter on topological results in connection with greedoids.

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Page Count

213

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642581919

ISBN 13

9783642581915

Ways Of Thinking: The Limits Of Rational Thought And Artificial Intelligence

By: Mero Laszlo

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Ways Of Thinking: The Limits Of Rational Thought And Artificial Intelligence

By: Mero Laszlo

This book goes right into the the causes and reasons of the diversity of ways of thinking. It is about the tricks of how our thinking works and about the efforts and failures of artificial intelligence. It discusses what can and cannot be expected of `intelligent' computers, and provides an insight into the deeper layers of the mechanism of our thinking.-An enjoyable piece of reading, this thought-provoking book is also an exciting mental adventure for those with little or no computer competence at all.

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Page Count

266

Publisher

World Scientific

Published Date

ISBN 10

9814506842

ISBN 13

9789814506847

Advanced Quantum Communications

An Engineering Approach

By: Sandor Imre,Laszlo Gyongyosi

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Advanced Quantum Communications

An Engineering Approach

By: Sandor Imre,Laszlo Gyongyosi

The book provides an overview of the most advanced quantum informational geometric techniques, which can help quantum communication theorists analyze quantum channels, such as security or additivity properties. Each section addresses an area of major research of quantum information theory and quantum communication networks. The authors present the fundamental theoretical results of quantum information theory, while also presenting the details of advanced quantum ccommunication protocols with clear mathematical and information theoretical background. This book bridges the gap between quantum physics, quantum information theory, and practical engineering.

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Page Count

437

Publisher

John Wiley & Sons

Published Date

ISBN 10

111833745X

ISBN 13

9781118337455

An Algorithmic Theory of Numbers, Graphs and Convexity

By: Laszlo Lovasz

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An Algorithmic Theory of Numbers, Graphs and Convexity

By: Laszlo Lovasz

Studies two algorithms in detail: the ellipsoid method and the simultaneous diophantine approximation method.

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SIAM

Published Date

ISBN 10

0898712033

ISBN 13

9780898712032

Greedoids

By: Bernhard Korte,Laszlo Lovasz,Rainer Schrader

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Greedoids

By: Bernhard Korte,Laszlo Lovasz,Rainer Schrader

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Page Count

213

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642581919

ISBN 13

9783642581915

Book's by Laszlo Lovasz

Geometric Algorithms and Combinatorial Optimization

Geometric Algorithms and Combinatorial Optimization

An Algorithmic Theory of Numbers, Graphs and Convexity

An Algorithmic Theory of Numbers, Graphs and Convexity

Greedoids

Greedoids

Ways Of Thinking: The Limits Of Rational Thought And Artificial Intelligence

Ways Of Thinking: The Limits Of Rational Thought And Artificial Intelligence

Advanced Quantum Communications

Advanced Quantum Communications

An Algorithmic Theory of Numbers, Graphs and Convexity

An Algorithmic Theory of Numbers, Graphs and Convexity

Greedoids

Greedoids

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