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Partitions : Optimality and Clustering - Vol Ii.
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 recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific Publishing Company,
2013.
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| Colección: | Series on applied mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; 1. Bounded-Shape Sum-Partition Problems: Polyhedral Approach; 1.1 Linear Objective: Solution by LP; Testing If a Vector (say A) is a Vertex of a given Bounded- Shape Partition Polytope; Solution of Bounded-Shape Partition Problems with Linear Objective Function; 1.2 Enumerating Vertices of the Partition Polytopes and Corresponding Partitions Using Edge-Directions; Enumerating Vertices of Bounded-Shape Partition Polytopes along with Corresponding Partitions Using Edge-Directions; Single-Size Problems.
- Enumerating the Facets of a Constrained-Shape Partition Polytope Using Generic Partitions (along with Supporting Hyperplanes)1.3 Representation, Characterization and Enumeration of Vertices of Partition Polytopes: Distinct Partitioned Vectors; Testing if a Vector A is a Vertex of the Bounded-Shape Partition Polytope When the Columns of A are Nonzero and Distinct; Testing if a Vector A is a Vertex of the Bounded-Shape Partition Polytope When the Columns of A are Distinct, but Contain the Zero Vector; Mean-Partition Problems.
- 1.4 Representation, Characterization and Enumeration of Vertices of Partition Polytopes: General CaseTesting if a Vector A is a Vertex of the Bounded-Shape Partition Polytope; Appendix A; 2. Constrained-Shape and Single-Size Sum-Partition Problems: Polynomial Approach; 2.1 Constrained-Shape Partition Polytopes and (Almost- ) Separable Partitions; Testing for a Point of a Finite Set to be a Vertex of the Convex Hull of that Set; Testing for (Almost) Separability of Partitions; Enumerating the Vertices of Constrained-Shape and Bounded-Shape Partition Polytopes with Underlying Matrix A.
- Generating the Vertices of Bounded-Shape and Constrained- Shape Partition Polytopes2.2 Enumerating Separable and Limit-Separable Partitions of Constrained-Shape; Enumerating all Separable 2-Partitions when A is Generic; Enumerating all Separable p-Partitions when A is Generic; Computing Generic Signs; Enumerating all A-Limit-Separable Partitions; Enumerating all A-Separable Partitions; Solving Constrained-Shape Partition Problems with f(·) (Edge- )Quasi-Convex by Enumerating Limit-Separable Partitions.
- Enumerating the Vertices of Constrained-Shape Partition Polytopes Using Limit-Separable PartitionsEnumerating all Almost-Separable 2-Partitions; Enumerating all Almost-Separable p-Partitions; 2.3 Single-Size Partition Polytopes and Cone-Separable Partitions; Testing for Cone-Separability of Finite Sets; Testing for Cone-Separability of Partitions; 2.4 Enumerating (Limit- )Cone-Separable Partitions; Enumerating All Cone-Separable Partitions when [0,A] is Generic; Enumerating All Cone-Separable Partitions when d 2 and A has no Zero Vectors.