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Partitions : optimality and clustering / Frank K. Hwang, Uriel G. Rothblum and Hong-Bin Chen.

By: Contributor(s): Material type: TextTextSeries: Series on applied mathematics ; v 19, 20.Publication details: New Jersey : World Scientific, c2012-2013.Description: 2 v. : ill. ; 24 cmISBN:
  • 9789812708120 (v. 1 : hardcover : alk. paper)
  • 9789814412346 (v. 2 : hardcover : alk. paper)
Subject(s): DDC classification:
  • 512.73 23 H991
Contents:
v. I. Single-parameter: 1. Formulation and examples-- 2. Sum-Partition problems over single-parameter spaces: Explicit solutions-- 3.Extreme points and optimality-- 4. Permutation polytopes-- 5. Sum-partition problems over single-parameter spaces: polyhedral approach-- 6. Partitions over single-parameter spaces: combinatorial structure-- 7. Partition problems over single-parameter spaces: combinatorial approach-- Bibliography-- Index. v. II. Multi-parameter: 1. Bounded-shape sum-partition problems: polyhedral approach-- 2. Constrained-shape and single-size sum-partition problems: polynomial approach-- 3. Partitions over multi-parameter spaces: combinatorial structure-- 4. Clustering problems over multi-parameter spaces-- 5. Sum-multipartition problems over single-parameter spaces-- 6. Applications-- Bibliography-- Index.
Summary: The need for optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The "clustering" problem, which has received a lot of attention, is a special case of optimal partitioning. This book attempts to collect the theoretical developments of optimal partitions.
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Hong-Bin Chen is co-author of vol.2

Includes bibliographical references and index.

v. I. Single-parameter:
1. Formulation and examples--
2. Sum-Partition problems over single-parameter spaces: Explicit solutions--
3.Extreme points and optimality--
4. Permutation polytopes--
5. Sum-partition problems over single-parameter spaces: polyhedral approach--
6. Partitions over single-parameter spaces: combinatorial structure--
7. Partition problems over single-parameter spaces: combinatorial approach--
Bibliography--
Index.

v. II. Multi-parameter:
1. Bounded-shape sum-partition problems: polyhedral approach--
2. Constrained-shape and single-size sum-partition problems: polynomial approach--
3. Partitions over multi-parameter spaces: combinatorial structure--
4. Clustering problems over multi-parameter spaces--
5. Sum-multipartition problems over single-parameter spaces--
6. Applications--
Bibliography--
Index.

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

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