An Algorithmic Theory of Numbers, Graphs and Convexity - Brossura

Lovasz, Laszlo

Brossura

ISBN 10: 0898712033 ISBN 13: 9780898712032

Casa editrice: Society for Industrial and Applied Mathematics, 1987

Riassunto

A study of how complexity questions in computing interact with classical mathematics in the numerical analysis of issues in algorithm design. Algorithmic designers concerned with linear and nonlinear combinatorial optimization will find this volume especially useful. Two algorithms are studied in detail: the ellipsoid method and the simultaneous diophantine approximation method. Although both were developed to study, on a theoretical level, the feasibility of computing some specialized problems in polynomial time, they appear to have practical applications. The book first describes use of the simultaneous diophantine method to develop sophisticated rounding procedures. Then a model is described to compute upper and lower bounds on various measures of convex bodies. Use of the two algorithms is brought together by the author in a study of polyhedra with rational vertices. The book closes with some applications of the results to combinatorial optimization.

Su questo libro

Descrizione del libro:

Describes use of the simultaneous diophantine method to develop sophisticated rounding procedures. Then a model is described to compute upper and lower bounds on various measures of convex bodies. Use of the two algorithms is brought together by the author in a study of polyhedra with rational vertices.

Contenuti:

How to Round Numbers; Preliminaries: On Algorithms Involving Numbers; Diophantine Approximation, Problems; Lattices, Bases, and the Reduction Problem; Diophantine Approximation and Rounding; What is a Real Number How to Round a Convex Body; Preliminaries: Inputting a Set; Algorithmic Problems on Convex Sets; The Ellipsoid Method; Rational Polyhedra; Some Other Algorithmic Problems on Convex Sets; Integer Programming in Fixed Dimension; Some Applications in Combinatorics; Cuts and Joins; Chromatic Number, Cliques and Perfect Graphs; Minimizing a Submodular Function.

Su questa edizione

• Editore: Society for Industrial and Applied Mathematics
• Data di pubblicazione: 1987
• ISBN 10: 0898712033
• ISBN 13: 9780898712032
• Rilegatura: Copertina flessibile
• Numero di pagine: 97