Geometric approximation algorithms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2011]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 173 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 362 Seiten Diagramme |
| ISBN: | 9780821849118 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV039528648 | ||
| 003 | DE-604 | ||
| 005 | 20230828 | ||
| 007 | t | ||
| 008 | 110816s2011 xxu|||| |||| 00||| eng d | ||
| 010 | |a 2011002940 | ||
| 020 | |a 9780821849118 |c alk. paper |9 978-0-8218-4911-8 | ||
| 035 | |a (OCoLC)746293065 | ||
| 035 | |a (DE-599)BVBBV039528648 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-703 |a DE-188 |a DE-20 |a DE-706 |a DE-19 |a DE-11 | ||
| 050 | 0 | |a QA448.D38 | |
| 082 | 0 | |a 516/.11 | |
| 084 | |a SK 905 |0 (DE-625)143269: |2 rvk | ||
| 084 | |a ST 600 |0 (DE-625)143681: |2 rvk | ||
| 084 | |a ST 134 |0 (DE-625)143590: |2 rvk | ||
| 100 | 1 | |a Har-Peled, Sariel |d 1971- |e Verfasser |0 (DE-588)1014173817 |4 aut | |
| 245 | 1 | 0 | |a Geometric approximation algorithms |c Sariel Har-Peled |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2011] | |
| 264 | 4 | |c © 2011 | |
| 300 | |a xii, 362 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 173 | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Approximation algorithms | |
| 650 | 4 | |a Geometry |x Data processing | |
| 650 | 4 | |a Computer graphics | |
| 650 | 4 | |a Discrete geometry | |
| 650 | 7 | |a Computer science -- Computing methodologies and applications -- Computer graphics; computational geometry |2 msc | |
| 650 | 7 | |a Computer science -- Algorithms -- Approximation algorithms |2 msc | |
| 650 | 7 | |a Computer science -- Theory of data -- Data structures |2 msc | |
| 650 | 7 | |a Convex and discrete geometry -- Discrete geometry -- Discrete geometry |2 msc | |
| 650 | 0 | 7 | |a Geometrische Approximation |0 (DE-588)4156709-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Geometrische Approximation |0 (DE-588)4156709-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1400-9 |
| 830 | 0 | |a Mathematical surveys and monographs |v Volume 173 |w (DE-604)BV000018014 |9 173 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024380971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024380971 | ||
Datensatz im Suchindex
| _version_ | 1804148339815481344 |
|---|---|
| adam_text | Contents
Preface
xi
Chapter
1.
The Power of Grids
-
Closest Pair and Smallest Enclosing Disk
1
1.1.
Preliminaries
1
1.2.
Closest pair
1
1.3.
A slow 2-approximation algorithm for the fc-enclosing disk
5
1.4.
A linear time 2-approximation for the ¿-enclosing disk
6
1.5.
Bibliographical notes
10
1.6.
Exercises
11
Chapter
2.
Quadtrees
-
Hierarchical Grids
13
2.1.
Quadtrees
-
a simple point-location data-structure
13
2.2.
Compressed quadtrees
15
2.3.
Dynamic quadtrees
20
2.4.
Bibliographical notes
24
2.5.
Exercises
26
Chapter
3.
Well-Separated Pair Decomposition
29
3.1.
Well-separated pair decomposition (WSPD)
29
3.2.
Applications of WSPD
33
3.3.
Semi-separated pair decomposition (SSPD)
40
3.4.
Bibliographical notes
43
3.5.
Exercises
44
Chapter
4.
Clustering
-
Definitions and Basic Algorithms
47
4.1.
Preliminaries
47
4.2.
On ¿-center clustering
49
4.3.
On ¿-median clustering
51
4.4.
On ¿-means clustering
57
4.5.
Bibliographical notes
57
4.6.
Exercises
59
Chapter
5.
On Complexity, Sampling, and
е
-Nets and ir-Samples
61
5.1.
VC dimension
61
5.2.
Shattering dimension and the dual shattering dimension
64
5.3.
On
ε
-nets and e-sampling
70
5.4.
Discrepancy
75
5.5.
Proof of the
éľ-net
theorem
80
5.6.
A better bound on the growth function
82
5.7.
Bibliographical notes
83
5.8.
Exercises
84
vi
CONTENTS
Chapter
6.
Approximation via Reweighting
87
6.1.
Preliminaries
87
6.2.
Computing a spanning tree with low crossing number
88
6.3.
Geometric set cover
94
6.4.
Geometric set cover via linear programming
98
6.5.
Bibliographical notes
100
6.6.
Exercises
100
Chapter
7.
Yet Even More on Sampling
103
7.1.
Introduction
103
7.2.
Applications
106
109
119
119
121
121
125
128
130
131
133
135
135
136
140
142
143
Chapter
10.
Approximating the Depth via Sampling and Emptiness
145
10.1.
From emptiness to approximate range counting
145
10.2.
Application:
Halfplane
and halfspace range counting
148
10.3.
Relative approximation via sampling
149
10.4.
Bibliographical notes
150
10.5.
Exercises
150
Chapter
11.
Random Partition via Shifting
151
11.1.
Partition via shifting
151
11.2.
Hierarchical representation of a point set
155
11.3.
Low quality ANN search
158
11.4.
Bibliographical notes
160
11.5.
Exercises
160
Chapter
12.
Good
Triangulations
and Meshing
163
12.1.
Introduction
-
good
triangulations
163
12.2.
Triangulations
and fat
triangulations
164
12.3.
Analysis
168
12.4.
The result
175
12.5.
Bibliographical notes
176
7.3.
Proof of Theorem
7.7
7.4.
Bibliographical notes
7.5.
Exercises
Chapter
8.
Sampling and the Moments Technique
8.1.
Vertical decomposition
8.2.
General settings
8.3.
Applications
8.4.
Bounds on the probability of a region to be created
8.5.
Bibliographical notes
8.6.
Exercises
Chapter
9.
Depth Estimation via Sampling
9.1.
The at most ¿-levels
9.2.
The crossing lemma
9.3.
A general bound for the at most ¿-weight
9.4.
Bibliographical notes
9.5.
Exercises
CONTENTS
vii
Chapter
13.
Approximating the Euclidean Traveling Salesman Problem (TSP)
177
13.1.
The TSP problem
-
introduction
177
13.2.
When the optimal solution is friendly
178
13.3.
TSP approximation via portals and sliding quadtrees
182
13.4.
Bibliographical notes
190
13.5.
Exercises
190
Chapter
14.
Approximating the Euclidean TSP Using Bridges
191
14.1.
Overview
191
14.2.
Cuts and bridges
192
14.3.
The dynamic programming
198
14.4.
The result
202
14.5.
Bibliographical notes
202
Chapter
15.
Linear Programming in Low Dimensions
203
15.1.
Linear programming
203
15.2.
Low-dimensional linear programming
205
15.3.
Linear programming with violations
208
15.4.
Approximate linear programming with violations
209
15.5.
LP-type problems
210
15.6.
Bibliographical notes
213
15.7.
Exercises
215
Chapter
16.
Polyhedrons, Polytopes, and Linear Programming
217
16.1.
Preliminaries
217
16.2.
Properties of polyhedrons
219
16.3.
Vertices of a poly tope
227
16.4.
Linear programming correctness
230
16.5.
Bibliographical notes
232
16.6.
Exercises
232
Chapter
17.
Approximate Nearest Neighbor Search in Low Dimension
233
17.1.
Introduction
233
17.2.
The bounded spread case
233
17.3.
ANN
-
the unbounded general case
236
17.4.
Low quality ANN search via the ring separator tree
238
17.5.
Bibliographical notes
240
17.6.
Exercises
242
Chapter
18.
Approximate Nearest Neighbor via Point-Location
243
18.1.
ANN using point-location among balls
243
18.2.
ANN using point-location among approximate balls
250
18.3.
ANN using point-location among balls in low dimensions
252
18.4.
Approximate Voronoi diagrams
253
18.5.
Bibliographical notes
255
18.6.
Exercises
256
Chapter
19.
Dimension Reduction
-
The Johnson-Lindenstrauss (JL) Lemma
257
19.1.
The Brunn-Minkowski inequality
257
19.2.
Measure concentration on the sphere
260
viii CONTENTS
19.3.
Concentration
of Lipschitz functions
263
19.4.
The Johnson-Lindenstrauss lemma
263
19.5.
Bibliographical notes
266
19.6.
Exercises
267
Chapter
20.
Approximate Nearest Neighbor (ANN) Search in High Dimensions
269
20.1.
ANN on the hypercube
269
20.2.
LSH and ANN in Euclidean space
274
20.3.
Bibliographical notes
276
Chapter
21.
Approximating a Convex Body by an Ellipsoid
279
21.1.
Ellipsoids
279
21.2.
Bibliographical notes
282
Chapter
22.
Approximating the Minimum Volume Bounding Box of a Point Set
283
22.1.
Some geometry
283
22.2.
Approximating the minimum volume bounding box
284
22.3.
Exact algorithm for the minimum volume bounding box
286
22.4.
Approximating the minimum volume bounding box in three dimensions
288
22.5.
Bibliographical notes
289
22.6.
Exercises
289
Chapter
23.
Coresets
291
23.1.
Coreset for directional width
291
23.2.
Approximating the extent of lines and other creatures
297
23.3.
Extent of polynomials
301
23.4.
Roots of polynomials
302
23.5.
Bibliographical notes
306
23.6.
Exercises
306
Chapter
24.
Approximation Using Shell Sets
307
24.1.
Covering problems, expansion, and shell sets
307
24.2.
Covering by cylinders
310
24.3.
Bibliographical notes
313
24.4.
Exercises
313
Chapter
25.
Duality
315
25.1.
Duality of lines and points
315
25.2.
Higher dimensions
318
25.3.
Bibliographical notes
319
25.4.
Exercises
321
Chapter
26.
Finite Metric Spaces and Partitions
323
26.1.
Finite metric spaces
323
26.2.
Random partitions
325
26.3.
Probabilistic embedding into trees
327
26.4.
Embedding any metric space into Euclidean space
329
26.5.
Bibliographical notes
332
26.6.
Exercises
333
Chapter
27.
Some Probability and Tail Inequalities
335
CONTENTS
ix
27.1.
Some
probability
background
335
27.2.
Tail inequalities
338
27.3.
Hoeffding s inequality
342
27.4.
Bibliographical notes
344
27.5.
Exercises
344
Chapter
28.
Miscellaneous Prerequisite
347
28.1.
Geometry and linear algebra
347
28.2.
Calculus
348
Bibliography
349
Index
357
|
| any_adam_object | 1 |
| author | Har-Peled, Sariel 1971- |
| author_GND | (DE-588)1014173817 |
| author_facet | Har-Peled, Sariel 1971- |
| author_role | aut |
| author_sort | Har-Peled, Sariel 1971- |
| author_variant | s h p shp |
| building | Verbundindex |
| bvnumber | BV039528648 |
| callnumber-first | Q - Science |
| callnumber-label | QA448 |
| callnumber-raw | QA448.D38 |
| callnumber-search | QA448.D38 |
| callnumber-sort | QA 3448 D38 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 905 ST 600 ST 134 |
| ctrlnum | (OCoLC)746293065 (DE-599)BVBBV039528648 |
| dewey-full | 516/.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.11 |
| dewey-search | 516/.11 |
| dewey-sort | 3516 211 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02313nam a2200553 cb4500</leader><controlfield tag="001">BV039528648</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230828 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110816s2011 xxu|||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2011002940</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821849118</subfield><subfield code="c">alk. paper</subfield><subfield code="9">978-0-8218-4911-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)746293065</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV039528648</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA448.D38</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516/.11</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 905</subfield><subfield code="0">(DE-625)143269:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 600</subfield><subfield code="0">(DE-625)143681:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 134</subfield><subfield code="0">(DE-625)143590:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Har-Peled, Sariel</subfield><subfield code="d">1971-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1014173817</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometric approximation algorithms</subfield><subfield code="c">Sariel Har-Peled</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, Rhode Island</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">[2011]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xii, 362 Seiten</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematical surveys and monographs</subfield><subfield code="v">Volume 173</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Informatik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Approximation algorithms</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry</subfield><subfield code="x">Data processing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer graphics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Computer science -- Computing methodologies and applications -- Computer graphics; computational geometry</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Computer science -- Algorithms -- Approximation algorithms</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Computer science -- Theory of data -- Data structures</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Convex and discrete geometry -- Discrete geometry -- Discrete geometry</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrische Approximation</subfield><subfield code="0">(DE-588)4156709-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Geometrische Approximation</subfield><subfield code="0">(DE-588)4156709-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-1400-9</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematical surveys and monographs</subfield><subfield code="v">Volume 173</subfield><subfield code="w">(DE-604)BV000018014</subfield><subfield code="9">173</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024380971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-024380971</subfield></datafield></record></collection> |
| id | DE-604.BV039528648 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:05:34Z |
| institution | BVB |
| isbn | 9780821849118 |
| language | English |
| lccn | 2011002940 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024380971 |
| oclc_num | 746293065 |
| open_access_boolean | |
| owner | DE-703 DE-188 DE-20 DE-706 DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-703 DE-188 DE-20 DE-706 DE-19 DE-BY-UBM DE-11 |
| physical | xii, 362 Seiten Diagramme |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Har-Peled, Sariel 1971- Verfasser (DE-588)1014173817 aut Geometric approximation algorithms Sariel Har-Peled Providence, Rhode Island American Mathematical Society [2011] © 2011 xii, 362 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 173 Datenverarbeitung Informatik Approximation algorithms Geometry Data processing Computer graphics Discrete geometry Computer science -- Computing methodologies and applications -- Computer graphics; computational geometry msc Computer science -- Algorithms -- Approximation algorithms msc Computer science -- Theory of data -- Data structures msc Convex and discrete geometry -- Discrete geometry -- Discrete geometry msc Geometrische Approximation (DE-588)4156709-2 gnd rswk-swf Geometrische Approximation (DE-588)4156709-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1400-9 Mathematical surveys and monographs Volume 173 (DE-604)BV000018014 173 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024380971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Har-Peled, Sariel 1971- Geometric approximation algorithms Mathematical surveys and monographs Datenverarbeitung Informatik Approximation algorithms Geometry Data processing Computer graphics Discrete geometry Computer science -- Computing methodologies and applications -- Computer graphics; computational geometry msc Computer science -- Algorithms -- Approximation algorithms msc Computer science -- Theory of data -- Data structures msc Convex and discrete geometry -- Discrete geometry -- Discrete geometry msc Geometrische Approximation (DE-588)4156709-2 gnd |
| subject_GND | (DE-588)4156709-2 |
| title | Geometric approximation algorithms |
| title_auth | Geometric approximation algorithms |
| title_exact_search | Geometric approximation algorithms |
| title_full | Geometric approximation algorithms Sariel Har-Peled |
| title_fullStr | Geometric approximation algorithms Sariel Har-Peled |
| title_full_unstemmed | Geometric approximation algorithms Sariel Har-Peled |
| title_short | Geometric approximation algorithms |
| title_sort | geometric approximation algorithms |
| topic | Datenverarbeitung Informatik Approximation algorithms Geometry Data processing Computer graphics Discrete geometry Computer science -- Computing methodologies and applications -- Computer graphics; computational geometry msc Computer science -- Algorithms -- Approximation algorithms msc Computer science -- Theory of data -- Data structures msc Convex and discrete geometry -- Discrete geometry -- Discrete geometry msc Geometrische Approximation (DE-588)4156709-2 gnd |
| topic_facet | Datenverarbeitung Informatik Approximation algorithms Geometry Data processing Computer graphics Discrete geometry Computer science -- Computing methodologies and applications -- Computer graphics; computational geometry Computer science -- Algorithms -- Approximation algorithms Computer science -- Theory of data -- Data structures Convex and discrete geometry -- Discrete geometry -- Discrete geometry Geometrische Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024380971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT harpeledsariel geometricapproximationalgorithms |