Single-parameter /:
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...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, N.J. :
World Scientific,
2012.
|
| Schriftenreihe: | Series on applied mathematics ;
v. 19. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 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 prob. |
| Beschreibung: | 1 online resource (xi, 350 pages) : illustrations. |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812770158 9812770151 |
Internformat
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| 245 | 1 | 0 | |a Single-parameter / |c by Frank K. Hwang & Uriel G. Rothblum. |
| 260 | |a Hackensack, N.J. : |b World Scientific, |c 2012. | ||
| 300 | |a 1 online resource (xi, 350 pages) : |b illustrations. | ||
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| 490 | 1 | |a Series on applied mathematics ; |v v. 19 | |
| 490 | 0 | |a Partitions : optimality and clustering ; |v v. 1 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; Contents; 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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 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 prob. | ||
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| 650 | 6 | |a Partitions (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
| 650 | 7 | |a Partitions (Mathematics) |2 fast | |
| 700 | 1 | |a Rothblum, Uriel G. | |
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Datensatz im Suchindex
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| _version_ | 1816881789627531264 |
| adam_text | |
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| author | Hwang, Frank |
| author2 | Rothblum, Uriel G. |
| author2_role | |
| author2_variant | u g r ug ugr |
| author_facet | Hwang, Frank Rothblum, Uriel G. |
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| contents | Preface; Contents; 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 |
| ctrlnum | (OCoLC)781539382 |
| dewey-full | 512.7/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/3 |
| dewey-search | 512.7/3 |
| dewey-sort | 3512.7 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn781539382 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:18Z |
| institution | BVB |
| isbn | 9789812770158 9812770151 |
| language | English |
| oclc_num | 781539382 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 350 pages) : illustrations. |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific, |
| record_format | marc |
| series | Series on applied mathematics ; |
| series2 | Series on applied mathematics ; Partitions : optimality and clustering ; |
| spelling | Hwang, Frank. Single-parameter / by Frank K. Hwang & Uriel G. Rothblum. Hackensack, N.J. : World Scientific, 2012. 1 online resource (xi, 350 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on applied mathematics ; v. 19 Partitions : optimality and clustering ; v. 1 Includes bibliographical references and index. Preface; Contents; 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 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 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 prob. Partitions (Mathematics) http://id.loc.gov/authorities/subjects/sh85098392 Partitions (Mathématiques) MATHEMATICS Number Theory. bisacsh Partitions (Mathematics) fast Rothblum, Uriel G. has work: Single-parameter (Text) https://id.oclc.org/worldcat/entity/E39PCGWjJydg7dhCrXkJyjYGd3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Hwang, Frank. Single-parameter. Hackensack, N.J. : World Scientific, 2012 (DLC) 2010038315 Series on applied mathematics ; v. 19. 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=518616 Volltext |
| spellingShingle | Hwang, Frank Single-parameter / Series on applied mathematics ; Preface; Contents; 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 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 | Single-parameter / |
| title_auth | Single-parameter / |
| title_exact_search | Single-parameter / |
| title_full | Single-parameter / by Frank K. Hwang & Uriel G. Rothblum. |
| title_fullStr | Single-parameter / by Frank K. Hwang & Uriel G. Rothblum. |
| title_full_unstemmed | Single-parameter / by Frank K. Hwang & Uriel G. Rothblum. |
| title_short | Single-parameter / |
| title_sort | single parameter |
| 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=518616 |
| work_keys_str_mv | AT hwangfrank singleparameter AT rothblumurielg singleparameter |