Polyhedral combinatorics of the quadratic assignment problem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Köln, Univ., Diss., 1997 |
| Beschreibung: | X, 268 S. graph. Darst. |
Internformat
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| 100 | 1 | |a Kaibel, Volker |d 1969- |e Verfasser |0 (DE-588)118199935 |4 aut | |
| 245 | 1 | 0 | |a Polyhedral combinatorics of the quadratic assignment problem |c vorgelegt von Volker Kaibel |
| 264 | 1 | |c 1997 | |
| 300 | |a X, 268 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Köln, Univ., Diss., 1997 | ||
| 650 | 0 | 7 | |a Zuordnungsproblem |0 (DE-588)4068123-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Polyedrische Kombinatorik |0 (DE-588)4132100-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Zuordnungsproblem |0 (DE-588)4068123-3 |D s |
| 689 | 0 | 1 | |a Polyedrische Kombinatorik |0 (DE-588)4132100-5 |D s |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008025274 | |
Datensatz im Suchindex
| _version_ | 1807320157857513472 |
|---|---|
| adam_text |
CONTENTS
PREFACE
V
1
INTRODUCTION
1
2
MATHEMATICAL
CONCEPTS
AND
METHODS
9
2.1
GRAPH
THEORY
.
9
2.2
LINEAR
ALGEBRA
.
11
2.3
POLYHEDRAL
COMBINATORICS
.
12
2.3.1
COMBINATORIAL
OPTIMIZATION
AND
LINEAR
PROGRAMMING
.
12
2.3.2
POLYHEDRAL
THEORY
.
16
2.3.3
PROJECTIONS
OF
POLYTOPES
.
20
3
THE
QUADRATIC
ASSIGNMENT
PROBLEM
23
3.1
A
BRIEF
TOUR
THROUGH
THE
QUADRATIC
ASSIGNMENT
WORLD
.
23
3.2
WORK
RELATED
TO
THE
POLYHEDRAL
APPROACH
.
28
3.3
WORK
ON
THE
QUADRATIC
ASSIGNMENT
POLYTOPE
.
31
4
THE
QUADRATIC
ASSIGNMENT
POLYTOPE
35
4.1
THE
POLYTOPE
QAP
N
.
35
4.1.1
FORMULATION
AS
A
GRAPH
PROBLEM
.
36
4.1.2
DEFINITION
AND
ELEMENTARY
PROPERTIES
OF
QAP
N
.
37
4.1.3
RELATIONS
TO
SOME
OTHER
POLYTOPES
.
38
4.1.4
AN
INTEGER
LINEAR
PROGRAMMING
FORMULATION
.
44
4.2
A
DIFFERENT
REPRESENTATION:
QAPYY
.
46
4.2.1
AN
ISOMORPHIC
PROJECTION
OF
QAP
N
.
46
4.2.2
A
SYSTEM
OF
EQUATIONS
.
48
4.2.3
A
PROOF
TECHNIQUE
.
51
4.2.4
SOME
USEFUL
VECTORS
.
52
4.2.5
AN
INDUCTIVE
CONSTRUCTION
OF
QAP
N
.
55
4.3
AFFINE
HULLS,
DIMENSIONS,
AND
TRIVIAL
INEQUALITIES
.
58
4.3.1
BASIC
FACIAL
STRUCTURES
OF
QAP*
N
.
58
4.3.2
BASIC
FACIAL
STRUCTURES
OF
QAPN
.
62
4.4
THE
RELAXATION
POLYTOPE
EQP
N
.
68
4.4.1
THE
EQUATION
BOUND
.
68
4.4.2
APPROXIMATING
THE
EQUATION
BOUND
.
71
4.4.3
COMPUTATIONAL
EXPERIMENTS
.
72
VIII
C
ONTENTS
5
THE
SYMMETRIC
QUADRATIC
ASSIGNMENT
POLYTOPE
79
5.1
THE
POLYTOPE
SQAP
N
.
80
5.1.1
FORMULATION
AS
A
HYPERGRAPH
PROBLEM
.
81
5.1.2
DEFINITION
AND
ELEMENTARY
PROPERTIES
OF
SQAP
N
.
82
5.1.3
RELATION
TO
QAP
N
.
83
5.1.4
AN
INTEGER
LINEAR
PROGRAMMING
FORMULATION
.
85
5.2
A
DIFFERENT
REPRESENTATION:
SQAPYY
.
86
5.2.1
AN
ISOMORPHIC
PROJECTION
OF
SQAP
N
.
86
5.2.2
A
SYSTEM
OF
EQUATIONS
.
88
5.2.3
A
PROOF
TECHNIQUE
.
89
5.2.4
SOME
USEFUL
VECTORS
.
90
5.2.5
AN
INDUCTIVE
CONSTRUCTION
OF
SQAPN
.
91
5.3
AFFINE
HULLS,
DIMENSIONS,
AND
TRIVIAL
INEQUALITIES
.
92
5.3.1
BASIC
FACIAL
STRUCTURES
OF
SQAPYY
.
92
5.3.2
BASIC
FACIAL
STRUCTURES
OF
SQAP
N
.
94
5.4
THE
CURTAIN
INEQUALITIES
.
99
5.4.1
DEFINITION
OF
THE
INEQUALITIES
.
99
5.4.2
A
FIRST
CLASS
OF
NON-TRIVIAL
FACETS
OF
S2AP
N
.
101
5.5
THE
RELAXATION
POLYTOPE
SQP
N
.
105
5.5.1
THE
SYMMETRIC
EQUATION
BOUND
.
106
5.5.2
RELATION
TO
THE
(NON-SYMMETRIC)
EQUATION
BOUND
.
107
5.5.3
COMPUTATIONAL
EXPERIMENTS
.
108
6
QUADRATIC
ASSIGNMENT
PROBLEMS
WITH
LESS
OBJECTS
THAN
LOCATIONS
113
6.1
THE
POLYTOPES
QAP
M
,N
AND
SQAP
M
,
N
.
114
6.1.1
DEFINITIONS
OF
THE
POLYTOPES
.
115
6.1.2
VARYING
M
AND
N
.
117
6.1.3
RELATIONS
TO
QAP
N
AND
SQAP
N
.
118
6.1.4
INTEGER
LINEAR
PROGRAMMING
FORMULATIONS
.
119
6.1.5
RESTRICTION
TO
M
N
-
2
.
120
6.2
DIFFERENT
REPRESENTATIONS:
QAP^
N
.,
SQAP^.N
.
421
6.2.1
ISOMORPHIC
PROJECTIONS
OF
QAP
M N
AND
SQAP
M
,
N
.
122
6.2.2
TWO
SYSTEMS
OF
EQUATIONS
.
124
6.2.3
MORE
USEFUL
VECTORS
.
125
6.2.4
INDUCTIVE
CONSTRUCTIONS
OF
QAP
M
,N
AND
SQAP
M
,
N
.
128
6.3
AFFINE
HULLS,
DIMENSIONS,
AND
TRIVIAL
INEQUALITIES
.
130
6.3.1
BASIC
FACIAL
STRUCTURES
OF
QAP*
MN
.
AND
SQAP^
N
.
130
6.3.2
BASIC
FACIAL
STRUCTURES
OF
QAP
MN
AND
SQAP
M
,
N
.
131
6.4
THE
PROJECTIONS
OF
QPYY
AND
SQP
N
.
134
6.4.1
LINEAR
DESCRIPTIONS
OF
THE
PROJECTIONS
.
134
6.4.2
AFFINE
HULLS
-
AN
ALTERNATIVE
WAY
.
141
6.4.3
FACETS
OF
THE
LINEAR
DESCRIPTIONS
.
141
6.4.4
COMPUTATIONAL
EXPERIMENTS
.
146
C
ONTENTS
IX
7
SPARSE
QUADRATIC
ASSIGNMENT
PROBLEMS
149
7.1
THE
ASSOCIATED
POLYTOPES
.
150
7.1.1
DEFINITIONS
OF
THE
POLYTOPES
.
150
7.1.2
RELATIONS
TO
THE
GENERAL
POLYTOPES
.
152
7.1.3
INTEGER
LINEAR
PROGRAMMING
FORMULATIONS
.
154
7.1.4
DIFFERENT
REPRESENTATIONS
.
155
7.2
ON
THE
AFFINE
HULLS
AND
THE
DIMENSIONS
OF
THE
POLYTOPES
.
157
7.2.1
THE
N
X
N-CASE
WITH
A
DISPENSABLE
OBJECT
.
157
7.2.2
THE
GENERAL
N
X
N-CASE
.
162
7.2.3
THE
M
X
N-CASE
.
166
8
THE
BOX
INEQUALITIES
171
8.1
DERIVATION
OF
THE
BOX
INEQUALITIES
.
172
8.1.1
ST-INEQUALITIES
FOR
BOOLEAN
QUADRIC
POLYTOPES
.
172
8.1.2
THE
CORRESPONDING
INEQUALITIES
FOR
THE
CUT
POLYTOPE
.
173
8.1.3
THE
BOX
INEQUALITIES:
BASIC
PROPERTIES
.
177
8.2
1-BOX
AND
2-BOX
FACES
IN
THE
FACE
LATTICES
OF
QAP
N
AND
SQAP
N
.
.
183
8.2.1
TWO
THEOREMS
DESCRIBING
THE
RESULTS
.
183
8.2.2
ON
THE
EXISTENCE
OF
CERTAIN
G-CLIQUES
.
187
8.2.3
THE
PROOFS
OF
THE
FIRST
PARTS
OF
THE
THEOREMS
.
190
8.2.4
THE
PROOFS
OF
THE
SECOND
PARTS
OF
THE
THEOREMS
.
195
8.3
CONSEQUENCES
FOR
THE
OTHER
QUADRATIC
ASSIGNMENT
POLYTOPES
.
234
8.4
BOX
INEQUALITIES
AS
CUTTING
PLANES
.
235
8.4.1
A
SEPARATION
HEURISTIC
.
235
8.4.2
COMPUTATIONAL
EXPERIMENTS
.
237
9
DISCUSSION
243
BIBLIOGRAPHY
247
LIST
OF
SYMBOLS
257
INDEX
259
DEUTSCHE
ZUSAMMENFASSUNG
263 |
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| id | DE-604.BV011877812 |
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| indexdate | 2024-08-14T00:20:15Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008025274 |
| oclc_num | 246228560 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-739 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-739 DE-11 |
| physical | X, 268 S. graph. Darst. |
| publishDate | 1997 |
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| spelling | Kaibel, Volker 1969- Verfasser (DE-588)118199935 aut Polyhedral combinatorics of the quadratic assignment problem vorgelegt von Volker Kaibel 1997 X, 268 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Köln, Univ., Diss., 1997 Zuordnungsproblem (DE-588)4068123-3 gnd rswk-swf Polyedrische Kombinatorik (DE-588)4132100-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zuordnungsproblem (DE-588)4068123-3 s Polyedrische Kombinatorik (DE-588)4132100-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008025274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaibel, Volker 1969- Polyhedral combinatorics of the quadratic assignment problem Zuordnungsproblem (DE-588)4068123-3 gnd Polyedrische Kombinatorik (DE-588)4132100-5 gnd |
| subject_GND | (DE-588)4068123-3 (DE-588)4132100-5 (DE-588)4113937-9 |
| title | Polyhedral combinatorics of the quadratic assignment problem |
| title_auth | Polyhedral combinatorics of the quadratic assignment problem |
| title_exact_search | Polyhedral combinatorics of the quadratic assignment problem |
| title_full | Polyhedral combinatorics of the quadratic assignment problem vorgelegt von Volker Kaibel |
| title_fullStr | Polyhedral combinatorics of the quadratic assignment problem vorgelegt von Volker Kaibel |
| title_full_unstemmed | Polyhedral combinatorics of the quadratic assignment problem vorgelegt von Volker Kaibel |
| title_short | Polyhedral combinatorics of the quadratic assignment problem |
| title_sort | polyhedral combinatorics of the quadratic assignment problem |
| topic | Zuordnungsproblem (DE-588)4068123-3 gnd Polyedrische Kombinatorik (DE-588)4132100-5 gnd |
| topic_facet | Zuordnungsproblem Polyedrische Kombinatorik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008025274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kaibelvolker polyhedralcombinatoricsofthequadraticassignmentproblem |