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You searched IISERK - Subject: Red knot MigrationzDelaware Bay (Del. and N.J.)
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Call Number
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512/.7
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Author
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Lovász, László, 1948-
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Title
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An algorithmic theory of numbers, graphs, and convexity [electronic resource] / László Lovász.
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Publication
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Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1986.
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Material Info.
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1 electronic text (iii, 91 p.) : digital file.
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Series
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CBMS-NSF regional conference series in applied mathematics ; 50
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Series
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CBMS-NSF regional conference series in applied mathematics ; 50.
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Summary Note
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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.
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Notes
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Includes bibliographical references (p. 87-91).
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Notes
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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.
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ISBN
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9781611970203 (electronic bk.)
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Subject
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Number theory.
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Subject
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Graph theory.
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Subject
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Convex domains.
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Subject
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Approximation
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Subject
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Lattices
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Subject
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Bases
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Subject
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Reduction problem
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Subject
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Rounding
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Subject
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Combinatorics
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Added Entry
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Society for Industrial and Applied Mathematics.
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Date
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Year, Month, Day:01405141
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Link
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SIAM
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