Geometry of cuts and metrics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Edition: | 1st., softcover pr. |
| Series: | Algorithms and combinatorics
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XII, 587 S. graph. Darst. |
| ISBN: | 9783642042942 |
Staff View
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Record in the Search Index
| _version_ | 1804142782889066496 |
|---|---|
| adam_text | 5.4 THE BOOLE PROBLEM 61 CONTENTS 1. OUTLINE OF THE BOOK 1 1.1 OUTLINE
OF PART I. MEASURE ASPECTS: I-EMBEDDABILITY AND PROBABILITY 2 1.2
OUTLINE OF PART II. HYPERMETRIC SPACES: AN APPROACH VIA GEOMETRY OF
NUMBERS 4 1.3 OUTLINE OF PART III. EMBEDDINGS OF GRAPHS 6 1.4 OUTLINE OF
PART IV. HYPERCUBE EMBEDDINGS AND DESIGNS . . . . 7 1.5 OUTLINE OF PART
V. FACETS OF THE CUT CONE AND POLYTOPE . . . . 8 2. BASIC DEFINITIONS 11
2.1 GRAPHS 11 2.2 POLYHEDRA 14 2.3 ALGORITHMS AND COMPLEXITY 18 2.4
MATRICES 19 PART I. MEASURE ASPECTS: ^-EMBEDDABILITY AND PROBABILITY 23
3. PRELIMINARIES ON DISTANCES 27 3.1 DISTANCE SPACES AND P-SPACES 27
3.2 MEASURE SPACES AND L P -SPACES 32 4. THE CUT CONE AND -METRICS 37
4.1 THE CUT CONE AND POLYTOPE 37 4.2 I-SPACES 39 4.3 REALIZATIONS,
RIGIDITY, SIZE AND SCALE 43 4.4 COMPLEXITY QUESTIONS 48 4.5 AN
APPLICATION TO STATISTICAL PHYSICS 51 5. THE CORRELATION CONE AND {0,
LJ-COVARIANCES 53 5.1 THE CORRELATION CONE AND POLYTOPE 53 5.2 THE
COVARIANCE MAPPING 55 5.3 COVARIANCES 58 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/996064737 DIGITALISIERT DURCH V »I CONTENTS 6.
CONDITIONS FOR LI-EMBEDDABILITY 67 6.1 HYPERMETRIC AND NEGATIVE TYPE
CONDITIONS 67 6.1.1 HYPERMETRIC AND NEGATIVE TYPE INEQUALITIES 67 6.1.2
HYPERMETRIC AND NEGATIVE TYPE DISTANCE SPACES 71 6.1.3 ANALOGUES FOR
COVARIANCES 72 6.2 CHARACTERIZATION OF L 2 -EMBEDDABILITY 73 6.2.1
SCHOENBERG S RESULT AND CAYLEY-MENGER DETERMINANTS . . 74 6.2.2 MENGER S
RESULT 78 6.2.3 FURTHER CHARACTERIZATIONS 80 6.3 A CHAIN OF IMPLICATIONS
82 6.4 AN EXAMPLE: THE SPHERICAL DISTANCE SPACE 86 6.5 AN EXAMPLE:
KALMANSON DISTANCES 91 7. OPERATIONS 93 7.1 THE GATE EXTENSION OPERATION
93 7.2 THE ANTIPODAL EXTENSION OPERATION 94 7.3 THE SPHERICAL EXTENSION
OPERATION 97 7.4 AN EXAMPLE: THE COCKTAIL-PARTY GRAPH 98 7.5 THE DIRECT
PRODUCT AND TENSOR PRODUCT OPERATIONS 101 7.6 THE 1-SUM OPERATION 103 8.
I-METRICS FROM LATTICES, SEMIGROUPS AND NORMED SPACES 105 8.1
II-METRICS FROM LATTICES 105 8.2 II-METRICS FROM SEMIGROUPS 107 8.3
I-METRICS FROM NORMED SPACES 109 9. METRIC TRANSFORMS OF LJ-SPACES 113
9.1 THE SCHOENBERG TRANSFORM 115 9.2 THE BIOTOPE TRANSFORM 118 9.3 THE
POWER TRANSFORM 120 10. LIPSCHITZ EMBEDDINGS 125 10. CONTENTS IX 12.
EXAMPLES OF THE USE OF THE LI-METRIC 161 12.1 THE I-METRIC IN
PROBABILITY THEORY 161 12.2 THE I-METRIC IN STATISTICAL DATA ANALYSIS
162 12.3 THE I-METRIC IN COMPUTER VISION AND PATTERN RECOGNITION . .
163 PART II. HYPERMETRIC SPACES: AN APPROACH VIA GEOMETRY OF NUMBERS 167
13. PRELIMINARIES ON LATTICES 175 13.1 DISTANCE SPACES 175 13.2 LATTICES
AND DELAUNAY POLYTOPES 177 13.2.1 LATTICES 177 13.2.2 DELAUNAY POLYTOPES
179 13.2.3 BASIC FACTS ON DELAUNAY POLYTOPES 182 13.2.4 CONSTRUCTION OF
DELAUNAY POLYTOPES 184 13.2.5 ADDITIONAL NOTES 187 13.3 FINITENESS OF
THE NUMBER OF TYPES OF DELAUNAY POLYTOPES . . 189 14. HYPERMETRICS AND
DELAUNAY POLYTOPES 193 14.1 CONNECTION BETWEEN HYPERMETRICS AND DELAUNAY
POLYTOPES . . 193 14.2 POLYHEDRALITY OF THE HYPERMETRIC CONE 199 14.3
DELAUNAY POLYTOPES IN ROOT LATTICES 206 14.4 ON THE RADIUS OF DELAUNAY
POLYTOPES 211 15. DELAUNAY POLYTOPES: RANK AND HYPERMETRIC FACES 217
15.1 RANK OF A DELAUNAY POLYTOPE 217 15.2 DELAUNAY POLYTOPES RELATED TO
FACES 222 15.2.1 HYPERMETRIC FACES 222 15.2.2 HYPERMETRIC FACETS 226
15.3 BOUNDS ON THE RANK OF BASIC DELAUNAY POLYTOPES 230 16. EXTREME
DELAUNAY POLYTOPES 235 16.1 EXTREME DELAUNAY POLYTOPES AND EQUIANGULAR
SETS OF LINES . . 236 16. X CONTENTS PART III. ISOMETRIC EMBEDDINGS OF
GRAPHS 275 18. PRELIMINARIES ON GRAPHS 279 19. ISOMETRIC EMBEDDINGS OF
GRAPHS INTO HYPERCUBES 283 19.1 DJOKOVIC S CHARACTERIZATION 283 19.2
FURTHER CHARACTERIZATIONS 286 19.3 ADDITIONAL NOTES 293 20. ISOMETRIC
EMBEDDINGS OF GRAPHS INTO CARTESIAN PRODUCTS 297 20.1 CANONICAL METRIC
REPRESENTATION OF A GRAPH 297 20.2 THE PRIME FACTORIZATION OF A GRAPH
305 20.3 METRIC DECOMPOSITION OF BIPARTITE GRAPHS 306 20.4 ADDITIONAL
NOTES 308 21. -GRAPHS 313 21.1 RESULTS ON I-GRAPHS 313 21.2
CONSTRUCTION OF G VIA THE ATOM GRAPH 316 21.3 PROOFS 322 21.4 MORE ABOUT
IJ-GRAPHS 325 PART IV. HYPERCUBE EMBEDDINGS AND DESIGNS 331 22. RIGIDITY
OF THE EQUIDISTANT METRIC 335 23. HYPERCUBE EMBEDDINGS OF THE
EQUIDISTANT METRIC 341 23.1 PRELIMINARIES ON DESIGNS 341 23.1.1 (R, A,
N)-DESIGNS AND BIBD S 341 23.1.2 INTERSECTING SYSTEMS 344 23.2
EMBEDDINGS OF 2IL N AND DESIGNS 345 23.3 THE MINIMUM *-SIZE OF 2IL* 347
23.4 ALL HYPERCUBE EMBEDDINGS OF 2 1* FOR SMALL N, T 35 CONTENTS XI 25.
CUT LATTICES, QUASI /I-DISTANCES AND HUBERT BASES 381 25.1 CUT LATTICES
381 25.2 QUASI *-DISTANCES 385 25.3 HUBERT BASES OF CUTS 391 PART V.
FACETS OF THE CUT CONE AND POLYTOPE 395 26. OPERATIONS ON VALID
INEQUALITIES AND FACETS 401 26.1 CUT AND CORRELATION VECTORS 401 26.2
THE PERMUTATION OPERATION 403 26.3 THE SWITCHING OPERATION 403 26.3.1
SWITCHING: A GENERAL DEFINITION 403 26.3.2 SWITCHING: CUT POLYTOPE
VERSUS CUT CONE 405 26.3.3 THE SYMMETRY GROUP OF THE CUT POLYTOPE 409
26.4 THE COLLAPSING OPERATION 410 26.5 THE LIFTING OPERATION 413 26.6
FACETS BY PROJECTION 416 27. TRIANGLE INEQUALITIES 421 27.1 TRIANGLE
INEQUALITIES FOR THE CORRELATION POLYTOPE 423 27.2 ROOTED TRIANGLE
INEQUALITIES 424 27.2.1 AN INTEGER PROGRAMMING FORMULATION FOR MAX-CUT .
. . 425 27.2.2 VOLUME OF THE ROOTED SEMIMETRIC POLYTOPE 426 27.2.3
ADDITIONAL NOTES 428 27.3 PROJECTING THE TRIANGLE INEQUALITIES 430
27.3.1 THE SEMIMETRIC POLYTOPE OF A GRAPH 431 27.3.2 THE CUT POLYTOPE
FOR GRAPHS WITH NO A S-MINOR 434 27.4 AN EXCURSION TO CYCLE POLYTOPES OF
BINARY MATROIDS 435 27.4.1 PRELIMINARIES ON BINARY MATROIDS 436 27.4.2
THE CYCLE CONE AND THE CYCLE POLYTOPE 438 27.4.3 MORE ABOUT CYCLE SPACES
441 28. HYPERMETRIC INEQUALITIES 445 28.1 HYPERMETRIC INEQUALITIES:
VALIDITY 445 28. XII CONTENTS 29.5 SEPARATION OF CLIQUE-WEB INEQUALITIES
481 29.6 AN EXAMPLE OF PROOF FOR CLIQUE-WEB FACETS 483 30. OTHER VALID
INEQUALITIES AND FACETS 487 30.1 SUSPENDED-TREE INEQUALITIES 487 30.2
PATH-BLOCK-CYCLE INEQUALITIES 492 30.3 CIRCULANT INEQUALITIES 496 30.4
THE PARACHUTE INEQUALITY 497 30.4.1 ROOTS AND FIBONACCI NUMBERS 498
30.4.2 GENERALIZING THE PARACHUTE INEQUALITY 500 30.5 SOME SPORADIC
EXAMPLES 502 30.6 COMPLETE DESCRIPTION OF CUT N AND CUT FOR N 7 503
30.7 ADDITIONAL NOTES 506 31. GEOMETRIC PROPERTIES 511 31.1 DISPROVAI OF
A CONJECTURE OF BORSUK USING CUTS 512 31.2 INEQUALITIES FOR ANGLES OF
VECTORS 514 31.3 THE POSITIVE SEMIDEFINITE COMPLETION PROBLEM 515 31.3.1
RESULTS 516 31.3.2 CHARACTERIZING GRAPHS WITH EXCLUDED INDUCED WHEELS .
522 31.4 THE EUCLIDEAN DISTANCE MATRIX COMPLETION PROBLEM 527 31.4.1
RESULTS 529 31.4.2 LINKS BETWEEN THE TWO COMPLETION PROBLEMS 531 31.5
GEOMETRY OF THE ELLIPTOPE 534 31.6 ADJACENCY PROPERTIES 539 31.6.1 LOW
DIMENSION FACES 539 31.6.2 SMALL POLYTOPES 542 31.7 DISTANCE OF FACETS
TO THE BARYCENTRUM 546 31.8 SIMPLEX FACETS 549 BIBLIOGRAPHY 551 NOTATION
INDEX 575 SUBJECT INDEX 57
|
| any_adam_object | 1 |
| author | Deza, Michel 1939- Laurent, Monique |
| author_GND | (DE-588)118064495 |
| author_facet | Deza, Michel 1939- Laurent, Monique |
| author_role | aut aut |
| author_sort | Deza, Michel 1939- |
| author_variant | m d md m l ml |
| building | Verbundindex |
| bvnumber | BV025599511 |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)501319614 (DE-599)BVBBV025599511 |
| dewey-full | 519.64 511.6 516.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics 511 - General principles of mathematics 516 - Geometry |
| dewey-raw | 519.64 511.6 516.11 |
| dewey-search | 519.64 511.6 516.11 |
| dewey-sort | 3519.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st., softcover pr. |
| format | Book |
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| id | DE-604.BV025599511 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:37:15Z |
| institution | BVB |
| isbn | 9783642042942 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020195103 |
| oclc_num | 501319614 |
| open_access_boolean | |
| owner | DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-11 DE-19 DE-BY-UBM |
| physical | XII, 587 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Algorithms and combinatorics |
| series2 | Algorithms and combinatorics |
| spelling | Deza, Michel 1939- Verfasser (DE-588)118064495 aut Geometry of cuts and metrics Michel Marie Deza ; Monique Laurent 1st., softcover pr. Berlin [u.a.] Springer 2010 XII, 587 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithms and combinatorics 15 Literaturangaben Geometrie der Zahlen (DE-588)4227477-1 gnd rswk-swf Schnitt Mathematik (DE-588)4458889-6 gnd rswk-swf Diskrete Geometrie (DE-588)4130271-0 gnd rswk-swf Metrik Mathematik (DE-588)4193458-1 gnd rswk-swf Geometrische Kombinatorik (DE-588)4156713-4 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Schnitt Mathematik (DE-588)4458889-6 s Metrik Mathematik (DE-588)4193458-1 s Diskrete Geometrie (DE-588)4130271-0 s Geometrie der Zahlen (DE-588)4227477-1 s Geometrische Kombinatorik (DE-588)4156713-4 s Kombinatorische Optimierung (DE-588)4031826-6 s DE-604 Graphentheorie (DE-588)4113782-6 s 1\p DE-604 Laurent, Monique Verfasser aut Algorithms and combinatorics 15 (DE-604)BV000617357 15 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195103&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Deza, Michel 1939- Laurent, Monique Geometry of cuts and metrics Algorithms and combinatorics Geometrie der Zahlen (DE-588)4227477-1 gnd Schnitt Mathematik (DE-588)4458889-6 gnd Diskrete Geometrie (DE-588)4130271-0 gnd Metrik Mathematik (DE-588)4193458-1 gnd Geometrische Kombinatorik (DE-588)4156713-4 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4227477-1 (DE-588)4458889-6 (DE-588)4130271-0 (DE-588)4193458-1 (DE-588)4156713-4 (DE-588)4031826-6 (DE-588)4113782-6 |
| title | Geometry of cuts and metrics |
| title_auth | Geometry of cuts and metrics |
| title_exact_search | Geometry of cuts and metrics |
| title_full | Geometry of cuts and metrics Michel Marie Deza ; Monique Laurent |
| title_fullStr | Geometry of cuts and metrics Michel Marie Deza ; Monique Laurent |
| title_full_unstemmed | Geometry of cuts and metrics Michel Marie Deza ; Monique Laurent |
| title_short | Geometry of cuts and metrics |
| title_sort | geometry of cuts and metrics |
| topic | Geometrie der Zahlen (DE-588)4227477-1 gnd Schnitt Mathematik (DE-588)4458889-6 gnd Diskrete Geometrie (DE-588)4130271-0 gnd Metrik Mathematik (DE-588)4193458-1 gnd Geometrische Kombinatorik (DE-588)4156713-4 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Geometrie der Zahlen Schnitt Mathematik Diskrete Geometrie Metrik Mathematik Geometrische Kombinatorik Kombinatorische Optimierung Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195103&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000617357 |
| work_keys_str_mv | AT dezamichel geometryofcutsandmetrics AT laurentmonique geometryofcutsandmetrics |