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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; London :
World Scientific,
2009.
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| Colección: | Series on applied mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; 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; 1.4.1 Assembly of systems; 1.4.2 Group testing; 1.4.3 Circuit card library; 1.4.4 Clustering; 1.4.5 Abstraction of .nite state machines; 1.4.6 Multischeduling; 1.4.7 Cache assignment; 1.4.8 The blood analyzer problem; 1.4.9 Joint replenishment of inventory; 1.4.10 Statistical hypothesis testing; 1.4.11 Nearest neighbor assignment; 1.4.12 Graph partitions.
- 1.4.13 Traveling salesman problem1.4.14 Vehicle routing; 1.4.15 Division of property; 1.4.16 The consolidation of farm land; 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; 3.4 Asymmetric Schur Convexity.
- 3.5 Enumerating Vertices of Polytopes Using Restricted Edge-Directions3.6 Edge-Directions of Polyhedra in Standard Form; 3.7 Edge-Directions of Network Polyhedra; 4. Permutation Polytopes; 4.1 Permutation Polytopes with Respect to Supermodular Functions
- Statement of Results; 4.2 Permutation Polytopes with Respect to Supermodular Functions
- Proofs; 4.3 Permutation Polytopes Corresponding to Strictly Supermodular Functions; 4.4 Permutation Polytopes Corresponding to Strongly Supermodular Functions; 5. Sum-Partition Problems over Single-Parameter Spaces: Polyhedral Approach.
- 5.1 Single-Shape Partition Polytopes5.2 Constrained-Shape Partition Polytopes; 5.3 Supermodularity for Bounded-Shape Sets of Partitions; 5.4 Partition Problems with Asymmetric Schur Convex Objective: Optimization over Partition Polytopes; 6. Partitions over Single-Parameter Spaces: Combinatorial Structure; 6.1 Properties of Partitions; 6.2 Enumerating Classes of Partitions; 6.3 Local Invariance and Local Sortability; 6.4 Localizing Partition Properties: Heredity, Consistency and Sortability; 6.5 Consistency and Sortability of Particular Partition-Properties; 6.6 Extensions.
- 7. Partition Problems over Single-Parameter Spaces: Combinatorial Approach7.1 Applying Sortability to Optimization; 7.2 Partition Problems with Convex and Schur Convex Objective Functions; 7.3 Partition Problems with Objective Functions Depending on Part-Sizes; 7.4 Clustering Problems; 7.5 Other Problems; Bibliography; Index.