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Partitions : optimality and clustering /

The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The "clustering" problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect a...

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Bibliographic Details
Main Authors: Hwang, Frank
Corporate Authors: World Scientific Firm
Group Author: Rothblum, Uriel G
Published: World Scientific Pub. Co.,
Publisher Address: Singapore ; Hackensack, N.J. :
Publication Dates: 2012.
Literature type: eBook
Language: English
Subjects:
Partitions Mathematics
Electronic books
Online Access: http://www.worldscientific.com/worldscibooks/10.1142/6518#t=toc
Summary: The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The "clustering" problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical pr
Carrier Form: 1 online resource (xi,350pages) : illustrations
Bibliography: Includes bibliographical references (pages 341-346) and index.
ISBN: 9789812770158 (electronic bk.)
CLC: O156.4
Contents: 1. Formulation and examples. 1.1. Formulation and classification of partitions. 1.2. Formulation and classification of partition problems over parameter spaces. 1.3. Counting partitions. 1.4. Examples -- 2. Sum-partition problems over single-parameter spaces: explicit solutions. 2.1. Bounded-shape problems with linear objective. 2.2. Constrained-shape problems with Schur convex objective. 2.3. Constrained-shape problems with Schur concave objective: uniform (over f) solution -- 3. Extreme points and optimality. 3.1. Preliminaries. 3.2. Partition polytopes. 3.3. Optimality of extreme points.

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