Partitions :: optimality and clustering. Vol. II, Multi-parameter /
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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2013.
|
| Schriftenreihe: | Series on applied mathematics ;
v. 20. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (x, 291 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 283-288) and index. |
| ISBN: | 9789814412353 981441235X |
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| 520 | |a 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. | ||
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| 700 | 1 | |a Chen, Hong-Bin. | |
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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. |
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| dewey-search | 512.73 |
| dewey-sort | 3512.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:25:21Z |
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| series | Series on applied mathematics ; |
| series2 | Series on applied mathematics ; |
| spelling | Hwang, Frank. http://id.loc.gov/authorities/names/n91024528 Partitions : optimality and clustering. Vol. II, Multi-parameter / Frank K Hwang, Uriel G Rothblum, Hong-Bin Chen. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2013. 1 online resource (x, 291 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on applied mathematics ; v. 20 Includes bibliographical references (pages 283-288) and index. 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. 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. Print version record. Partitions (Mathematics) http://id.loc.gov/authorities/subjects/sh85098392 Partitions (Mathématiques) MATHEMATICS Number Theory. bisacsh Partitions (Mathematics) fast Rothblum, Uriel G. http://id.loc.gov/authorities/names/n2010064555 Chen, Hong-Bin. World Scientific (Firm) http://id.loc.gov/authorities/names/no2001005546 has work: Vol. II Partitions Multi-parameter (Text) https://id.oclc.org/worldcat/entity/E39PCGYPfxtJQGFhcp36FDtKYd https://id.oclc.org/worldcat/ontology/hasWork Print version: Hwang, Frank. Partitions Vol. II, Multi-parameter. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2013 9789814412346 Series on applied mathematics ; v. 20. http://id.loc.gov/authorities/names/n93008796 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=592583 Volltext |
| spellingShingle | Hwang, Frank Partitions : optimality and clustering. Series on applied mathematics ; 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. Partitions (Mathematics) http://id.loc.gov/authorities/subjects/sh85098392 Partitions (Mathématiques) MATHEMATICS Number Theory. bisacsh Partitions (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85098392 |
| title | Partitions : optimality and clustering. |
| title_auth | Partitions : optimality and clustering. |
| title_exact_search | Partitions : optimality and clustering. |
| title_full | Partitions : optimality and clustering. Vol. II, Multi-parameter / Frank K Hwang, Uriel G Rothblum, Hong-Bin Chen. |
| title_fullStr | Partitions : optimality and clustering. Vol. II, Multi-parameter / Frank K Hwang, Uriel G Rothblum, Hong-Bin Chen. |
| title_full_unstemmed | Partitions : optimality and clustering. Vol. II, Multi-parameter / Frank K Hwang, Uriel G Rothblum, Hong-Bin Chen. |
| title_short | Partitions : |
| title_sort | partitions optimality and clustering multi parameter |
| title_sub | optimality and clustering. |
| topic | Partitions (Mathematics) http://id.loc.gov/authorities/subjects/sh85098392 Partitions (Mathématiques) MATHEMATICS Number Theory. bisacsh Partitions (Mathematics) fast |
| topic_facet | Partitions (Mathematics) Partitions (Mathématiques) MATHEMATICS Number Theory. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=592583 |
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