Partitions : optimality and clustering /
Hwang, Frank K.
Rothblum, Uriel G.
Chen, Hong-Bin.
text
New Jersey : World Scientific,
c2012-2013.
eng
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.
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.
Partitions (Mathematics).