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The Resource An algorithmic theory of numbers, graphs, and convexity, László Lovász, (electronic resource)
An algorithmic theory of numbers, graphs, and convexity, László Lovász, (electronic resource)
Resource Information
The item An algorithmic theory of numbers, graphs, and convexity, László Lovász, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item An algorithmic theory of numbers, graphs, and convexity, László Lovász, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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
 Language
 eng
 Extent
 1 electronic text (iii, 91 p.)
 Contents

 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
 Isbn
 9781611970203
 Label
 An algorithmic theory of numbers, graphs, and convexity
 Title
 An algorithmic theory of numbers, graphs, and convexity
 Statement of responsibility
 László Lovász
 Language
 eng
 Summary
 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
 Cataloging source
 CaBNVSL
 http://library.link/vocab/creatorDate
 1948
 http://library.link/vocab/creatorName
 Lovász, László
 Index
 no index present
 LC call number
 QA241
 LC item number
 .L68 1986eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName

 Society for Industrial and Applied Mathematics
 Society for Industrial and Applied Mathematics
 Series statement
 CBMSNSF regional conference series in applied mathematics
 Series volume
 50
 http://library.link/vocab/subjectName

 Number theory
 Graph theory
 Convex domains
 Target audience
 adult
 Label
 An algorithmic theory of numbers, graphs, and convexity, László Lovász, (electronic resource)
 Bibliography note
 Includes bibliographical references (p. 8791)
 Color
 black and white
 Contents
 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
 Dimensions
 unknown
 Extent
 1 electronic text (iii, 91 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781611970203
 Other physical details
 digital file.
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CaBNVSL)gtp00547315
 (SIAM)9781611970203
 Label
 An algorithmic theory of numbers, graphs, and convexity, László Lovász, (electronic resource)
 Bibliography note
 Includes bibliographical references (p. 8791)
 Color
 black and white
 Contents
 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
 Dimensions
 unknown
 Extent
 1 electronic text (iii, 91 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781611970203
 Other physical details
 digital file.
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CaBNVSL)gtp00547315
 (SIAM)9781611970203
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