| Description |
1 online resource (x, 291 pages) : illustrations |
| Series |
Series on applied mathematics ; v. 20 |
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Series on applied mathematics ; v. 20.
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| Contents |
1. Bounded-shape sum-partition problems: polyhedral approach. 1.1. Linear objective: solution by LP. 1.2. Enumerating vertices of the partition polytopes and corresponding partitions using edge-directions. 1.3. Representation, characterization and enumeration of vertices of partition polytopes: distinct partitioned vectors. 1.4. Representation, characterization and enumeration of vertices of partition polytopes: general case. 2. Constrained-shape and single-size sum-partition problems: polynomial approach. 2.1. Constrained-shape partition polytopes and (almost- ) separable partitions. 2.2. Enumerating separable and limit-separable partitions of constrained-shape. 2.3. Single-size partition polytopes and cone-separable partitions. 2.4. Enumerating (limit- ) cone-separable partitions -- 3. Partitions over multi-parameter spaces: combinatorial structure. 3.1. Properties of partitions. 3.2. Counting and enumerating partition classes of single-size. 3.3. Consistency and sortability of particular partition-properties -- 4. Clustering problems over multi-parameter spaces. 4.1. Geometric properties of optimal partitions. 4.2. Geometric properties of optimal partitions for d = 2 -- 5. Sum-multipartition problems over single-parameter spaces. 5.1. Multipartitions. 5.2. Single-multishape multipartition polytopes. 5.3. Constrained-multishape multipartition polytopes. 5.4. Combinatorial properties of multipartitions. 5.5. Constrained-multishape multipartition problems with asymmetric Schur convex objective: optimization over multipartition polytopes. 5.6. Sum multipartition problems: explicit solutions -- 6. Applications. 6.1. Assembly of systems. 6.2. Group testing. 6.3. Circuit card library. 6.4. Clustering. 6.5. Abstraction of finite state machines. 6.6. Multischeduling. 6.7. Cache assignment. 6.8. The blood analyzer problem. 6.9. Joint replenishment of inventory. 6.10. Statistical hypothesis testing. 6.11. Nearest neighbor assignment. 6.12. Graph partitions. 6.13. The traveling salesman problem. 6.14. Vehicle routing. 6.15. Division of property. 6.16. The consolidation of farmland |
| 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 recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory - or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory |
| Bibliography |
Includes bibliographical references (pages 283-288) and index |
| Notes |
Print version record |
| Subject |
Partitions (Mathematics)
|
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MATHEMATICS -- Number Theory.
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Partitions (Mathematics)
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| Form |
Electronic book
|
| Author |
Rothblum, Uriel G.
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Chen, Hong-Bin
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World Scientific (Firm)
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| ISBN |
9789814412353 |
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981441235X |
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