The linear ordering problem: algorithms and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Heldermann
1985
|
| Series: | Reserch and exposition in mathematics
8 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Augsburg, Univ., Diss. |
| Physical Description: | XI, 158 S. |
| ISBN: | 3885382083 |
Staff View
MARC
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Record in the Search Index
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| adam_text | vi
CONTENTS
Introduction viii
1. Mathematical preliminaries 1
1.1 Graph theory 1
1.2 Polyhedral theory 6
1.3 Complexity theory 10
2. The facial structure of the linear ordering polytope 13
2.1 Notations and basic results 13
2.2 Facets induced by dicycles 18
2.3 Facets induced by A fences 22
2.4 Facets induced by Mobius ladders 26
2.5 Further classes of facets 46
2.6 Adjacency and diameter 55
3. An algorithm for the solution of the linear ordering problem 60
3.1 The conception of the algorithm 60
3.2 Preprocessing 63
3.3 Detection of violated inequalities 65
3.4 The cutting plane part 72
3.5 The branch k bound part 75
4. Applications of the cutting plane algorithm 79
4.1 Description of the input data 79
4.2 Computational results 82
4.3 Comparison of cutting plane generation strategies 88
4.4 Aspects of the optimization process 90
4.5 Random problems 93
4.6 Heuristics 95
vii
5. Triangulation of input output tables 98
5.1 Economical background 98
5.2 Coefficients for interpreting triangulated tables 99
5.3 Discussion of the computational results 103
5.4 Conclusion Ill
6. Review of algorithms for the linear ordering problem 112
6.1 Heuristic methods 112
6.2 Branch bound algorithms 114
6.3 Linear programming methods 117
7. Further applications and final remarks 118
7.1 Aggregation of individual preferences 118
7.2 An application in sports 121
7.3 Final remarks 123
References 124
Index of definitions 128
Appendix A: Optimum triangulations of input output tables 130
Appendix B: Optimum triangulations of Bundesliga tables 148
|
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| publishDate | 1985 |
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| series2 | Reserch and exposition in mathematics |
| spelling | Reinelt, Gerhard Verfasser aut The linear ordering problem algorithms and applications G. Reinelt Berlin Heldermann 1985 XI, 158 S. txt rdacontent n rdamedia nc rdacarrier Reserch and exposition in mathematics 8 Zugl.: Augsburg, Univ., Diss. Mathématiques Optimisation combinatoire ram Combinatorial optimization Graph theory Linear orderings Lineare Ordnung (DE-588)4167706-7 gnd rswk-swf Ordnung Mathematik (DE-588)4043745-0 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Reihenfolgeplanung (DE-588)4261341-3 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Lineares Ordnungsproblem (DE-588)4120676-9 gnd rswk-swf Ordnung (DE-588)4043744-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kombinatorische Optimierung (DE-588)4031826-6 s Ordnung (DE-588)4043744-9 s Algorithmus (DE-588)4001183-5 s DE-604 Lineares Ordnungsproblem (DE-588)4120676-9 s Lineare Ordnung (DE-588)4167706-7 s Ordnung Mathematik (DE-588)4043745-0 s Optimierung (DE-588)4043664-0 s Reihenfolgeplanung (DE-588)4261341-3 s Reserch and exposition in mathematics 8 (DE-604)BV000017533 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000284426&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reinelt, Gerhard The linear ordering problem algorithms and applications Reserch and exposition in mathematics Mathématiques Optimisation combinatoire ram Combinatorial optimization Graph theory Linear orderings Lineare Ordnung (DE-588)4167706-7 gnd Ordnung Mathematik (DE-588)4043745-0 gnd Optimierung (DE-588)4043664-0 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Reihenfolgeplanung (DE-588)4261341-3 gnd Algorithmus (DE-588)4001183-5 gnd Lineares Ordnungsproblem (DE-588)4120676-9 gnd Ordnung (DE-588)4043744-9 gnd |
| subject_GND | (DE-588)4167706-7 (DE-588)4043745-0 (DE-588)4043664-0 (DE-588)4031826-6 (DE-588)4261341-3 (DE-588)4001183-5 (DE-588)4120676-9 (DE-588)4043744-9 (DE-588)4113937-9 |
| title | The linear ordering problem algorithms and applications |
| title_auth | The linear ordering problem algorithms and applications |
| title_exact_search | The linear ordering problem algorithms and applications |
| title_full | The linear ordering problem algorithms and applications G. Reinelt |
| title_fullStr | The linear ordering problem algorithms and applications G. Reinelt |
| title_full_unstemmed | The linear ordering problem algorithms and applications G. Reinelt |
| title_short | The linear ordering problem |
| title_sort | the linear ordering problem algorithms and applications |
| title_sub | algorithms and applications |
| topic | Mathématiques Optimisation combinatoire ram Combinatorial optimization Graph theory Linear orderings Lineare Ordnung (DE-588)4167706-7 gnd Ordnung Mathematik (DE-588)4043745-0 gnd Optimierung (DE-588)4043664-0 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Reihenfolgeplanung (DE-588)4261341-3 gnd Algorithmus (DE-588)4001183-5 gnd Lineares Ordnungsproblem (DE-588)4120676-9 gnd Ordnung (DE-588)4043744-9 gnd |
| topic_facet | Mathématiques Optimisation combinatoire Combinatorial optimization Graph theory Linear orderings Lineare Ordnung Ordnung Mathematik Optimierung Kombinatorische Optimierung Reihenfolgeplanung Algorithmus Lineares Ordnungsproblem Ordnung Hochschulschrift |
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