Partitions : optimality and clustering / Frank K. Hwang, Uriel G. Rothblum and Hong-Bin Chen.
Material type: TextSeries: 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)
- 512.73 23 H991
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Books | ISI Library, Kolkata | 512.73 H991 (Browse shelf(Opens below)) | Available | 135959 |
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512.73 H986 Area, lattice points, and exponential sums | 512.73 H986 Distribution of prime numbers : large sieves and zero-density theorems | 512.73 H991 Partitions : | 512.73 H991 Partitions : | 512.73 In48 Distribution of prime numbers | 512.73 In61 Analytic number theory | 512.73 J35 Analytic number theory |
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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