An Algorithmic Theory of Numbers, Graphs and Convexity
Seiten
1987
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-203-2 (ISBN)
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-203-2 (ISBN)
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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.
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.
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.
| Erscheint lt. Verlag | 28.2.1987 |
|---|---|
| Reihe/Serie | CBMS-NSF Regional Conference Series in Applied Mathematics |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 151 x 228 mm |
| Gewicht | 202 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| ISBN-10 | 0-89871-203-3 / 0898712033 |
| ISBN-13 | 978-0-89871-203-2 / 9780898712032 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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