Art gallery theorems and algorithms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Oxford Univ. Pr.
1987
|
| Schriftenreihe: | The international series of monographs on computer science
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 282 S. |
| ISBN: | 0195039653 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000800744 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 880912s1987 |||| 00||| eng d | ||
| 020 | |a 0195039653 |9 0-19-503965-3 | ||
| 035 | |a (OCoLC)14130616 | ||
| 035 | |a (DE-599)BVBBV000800744 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91G |a DE-384 |a DE-739 |a DE-20 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA447 | |
| 082 | 0 | |a 516/.0028/5 |2 19 | |
| 084 | |a SK 380 |0 (DE-625)143235: |2 rvk | ||
| 084 | |a MAT 518f |2 stub | ||
| 084 | |a 68K05 |2 msc | ||
| 084 | |a 52A37 |2 msc | ||
| 084 | |a 51D20 |2 msc | ||
| 084 | |a DAT 756f |2 stub | ||
| 100 | 1 | |a O'Rourke, Joseph |d 1951- |e Verfasser |0 (DE-588)114449708 |4 aut | |
| 245 | 1 | 0 | |a Art gallery theorems and algorithms |
| 264 | 1 | |a New York u.a. |b Oxford Univ. Pr. |c 1987 | |
| 300 | |a XIV, 282 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a The international series of monographs on computer science |v 3 | |
| 650 | 4 | |a Géométrie - Informatique | |
| 650 | 4 | |a Géométrie combinatoire | |
| 650 | 7 | |a algorithme graphe |2 inriac | |
| 650 | 7 | |a chiffre de garde |2 inriac | |
| 650 | 7 | |a géométrie algorithmique |2 inriac | |
| 650 | 7 | |a géométrie combinatoire |2 inriac | |
| 650 | 7 | |a géométrie |2 inriac | |
| 650 | 7 | |a polygone |2 inriac | |
| 650 | 7 | |a théorème art gallery |2 inriac | |
| 650 | 7 | |a visibilité |2 inriac | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Combinatorial geometry | |
| 650 | 4 | |a Geometry |x Data processing | |
| 650 | 0 | 7 | |a Algorithmische Geometrie |0 (DE-588)4130267-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kombinatorische Geometrie |0 (DE-588)4140733-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kombinatorische Geometrie |0 (DE-588)4140733-7 |D s |
| 689 | 0 | 1 | |a Algorithmische Geometrie |0 (DE-588)4130267-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Algorithmische Geometrie |0 (DE-588)4130267-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a The international series of monographs on computer science |v 3 |w (DE-604)BV000725123 |9 3 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000501717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-000501717 | ||
Datensatz im Suchindex
| _version_ | 1804115252096270336 |
|---|---|
| adam_text | CONTENTS
1. POLYGON PARTITIONS, 1
1.1. Introduction, 1
1.2. The Original Art Gallery Theorem and Algorithm, 1
1.2.1. The Theorem, 1
1.2.2. The Algorithm of Avis and Toussaint, 10
1.3. Triangulation, 11
1.3.1. Theorems, 12
1.3.2. Algorithms, 14
Monotone Polygons, 14
Triangulation Algorithm of Garey, Johnson, Preparata,
and Tarjan, 19
Recent Triangulation Algorithms, 23
1.4. Convex Partitioning, 27
1.4.1. Theorems, 28
1.4.2. Algorithms for Convex Partitioning, 29
2. ORTHOGONAL POLYGONS, 31
2.1. Introduction, 31
2.2. Kahn, Klawe, Kleitman Proof, 32
2.2.1. Convex Quadrilateralization, 32
Geometric Lemmas, 34
The Three Reductions, 37
2.2.2. The Orthogonal Art Gallery Theorem, 46
2.3. Sack s Quadrilateralization Algorithm, 47
2.3.1. Introduction, 47
2.3.2. Pyramid Quadrilateralization, 47
2.3.3. Orthogonal Monotone Quadrilateralization, 49
2.3.4. Partitioning into Monotone Polygons, 53
2.4. Lubiw s Proof and Algorithm, 56
2.4.1. Introduction, 56
2.4.2. Orthogonal Polygons without Holes, 56
2.4.3. Orthogonal Polygons with Holes, 61
2.4.4. Lubiw s Algorithm, 65
2.5. Partition into L shaped Pieces, 67
2.5.1. Main Inductive Argument, 67
2.5.2. Existence of Odd Cuts, 68
Xii CONTENTS
2.6. Algorithm to Partition into L shaped Pieces, 73
2.6.1. The Algorithm, 74
2.6.2. Discussion, 79
3. MOBILE GUARDS, 81
3.1. Introduction, 81
3.2. General Polygons, 82
3.2.1. Sufficiency Proof, 83
3.2.2. Edge Guards, 89
3.3. Orthogonal Polygons, 90
3.3.1. Properties of Orthogonal Polygons, 92
3.3.2. Sharing Lemmas, 101
3.3.3. Proof of Orthogonal Polygon Theorem, 108
3.4. Discussion, 114
4. MISCELLANEOUS SHAPES, 116
4.1. Introduction, 116
4.2. Star Polygons, 117
4.3. Spiral Polygons, 120
4.4. Monotone Polygons, 123
5. HOLES, 125
5.1. Introduction, 125
5.2. General Polygons with Holes, 127
5.2.1. Reduced Triangulations, 129
5.2.2. Tough Triangulations, 132
5.2.3. Convex Pairs and Triplets, 136
5.3. Orthogonal Polygons with Holes, 140
6. EXTERIOR VISIBILITY, 146
6.1. Introduction, 146
6.2. Fortress Problem, 146
6.2.1. General Polygons, 146
6.2.2. Orthogonal Polygons, 148
6.2.3. Guards in the Plane, 150
6.3. Prison Yard Problem, 154
6.3.1. General Polygons, 154
6.3.2. Orthogonal Polygons, 157
6.4. Algorithms, 158
6.5. Negative Results, 159
6.5.1. Triangulation, 159
6.5.2. Convex Partitioning, 160
6.5.3. Monotone Polygons, 162
CONTENTS Xlii
7. VISIBILITY GRAPHS, 165
7.1. Introduction, 165
7.2. Vertex Visibility Graphs, 166
7.2.1. Maximal Outplanar Graphs, 167
7.2.2. Convex Fans, 171
7.3. Edge Visibility Trees in Orthogonal Polygons, 172
7.3.1. Realization of Visibility Trees, 173
7.3.2. Realization of Labeled Trees, 178
7.3.3. Universal Trees, 187
7.3.4. Discussion, 195
7.4. Bar Visibility Graphs, 195
8. VISIBILITY ALGORITHMS, 202
8.1. Introduction, 202
8.2. Point Visibility Polygon, 203
8.3. Edge Visibility Polygon, 206
8.4. Visibility Graph Algorithm, 211
8.5. Point Visibility Region, 217
8.5.1. Lower Bound, 218
8.5.2. Algorithm, 218
8.6. Edge Visibility Region, 219
8.6.1. Lower Bound, 219
8.6.2. Algorithm, 223
8.7. Recent Algorithms, 226
9. MINIMAL GUARD COVERS, 228
9.1. Introduction, 228
9.2. NP Hard for Polygons with Holes, 231
9.3. NP Hard for Polygons without Holes, 239
9.4. Guards in Grids, 242
9.5. Partitions without Steiner Points, 247
9.6. Discussion, 252
10. THREE DIMENSIONS AND MISCELLANY, 253
10.1. Introduction, 253
10.2. Three Dimensions, 253
10.2.1. Untetrahedralizable Polyhedra, 253
10.2.2. Q(n3a) Guards Necessary, 255
10.2.3. Convex Partitions, 256
10.2.4. Satellite Sentries, 257
10.3. Line Segment Obstacles, 258
10.4. Point Obstacles, 263
Xiv CONTENTS
10.5. Mirrors, 265
10.6. Table of Theorems, 266
REFERENCES, 268
INDEX, 273
|
| any_adam_object | 1 |
| author | O'Rourke, Joseph 1951- |
| author_GND | (DE-588)114449708 |
| author_facet | O'Rourke, Joseph 1951- |
| author_role | aut |
| author_sort | O'Rourke, Joseph 1951- |
| author_variant | j o jo |
| building | Verbundindex |
| bvnumber | BV000800744 |
| callnumber-first | Q - Science |
| callnumber-label | QA447 |
| callnumber-raw | QA447 |
| callnumber-search | QA447 |
| callnumber-sort | QA 3447 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 380 |
| classification_tum | MAT 518f DAT 756f |
| ctrlnum | (OCoLC)14130616 (DE-599)BVBBV000800744 |
| dewey-full | 516/.0028/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.0028/5 |
| dewey-search | 516/.0028/5 |
| dewey-sort | 3516 228 15 |
| 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>02350nam a2200625 cb4500</leader><controlfield tag="001">BV000800744</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">880912s1987 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0195039653</subfield><subfield code="9">0-19-503965-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)14130616</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000800744</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA447</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516/.0028/5</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 518f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">68K05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">52A37</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">51D20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">DAT 756f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">O'Rourke, Joseph</subfield><subfield code="d">1951-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)114449708</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Art gallery theorems and algorithms</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York u.a.</subfield><subfield code="b">Oxford Univ. Pr.</subfield><subfield code="c">1987</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 282 S.</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">The international series of monographs on computer science</subfield><subfield code="v">3</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Géométrie - Informatique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Géométrie combinatoire</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">algorithme graphe</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">chiffre de garde</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">géométrie algorithmique</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">géométrie combinatoire</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">géométrie</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">polygone</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">théorème art gallery</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">visibilité</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Combinatorial geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry</subfield><subfield code="x">Data processing</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algorithmische Geometrie</subfield><subfield code="0">(DE-588)4130267-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorische Geometrie</subfield><subfield code="0">(DE-588)4140733-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kombinatorische Geometrie</subfield><subfield code="0">(DE-588)4140733-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Algorithmische Geometrie</subfield><subfield code="0">(DE-588)4130267-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Algorithmische Geometrie</subfield><subfield code="0">(DE-588)4130267-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">The international series of monographs on computer science</subfield><subfield code="v">3</subfield><subfield code="w">(DE-604)BV000725123</subfield><subfield code="9">3</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=000501717&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:BVB01-000501717</subfield></datafield></record></collection> |
| id | DE-604.BV000800744 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:19:39Z |
| institution | BVB |
| isbn | 0195039653 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000501717 |
| oclc_num | 14130616 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-20 DE-83 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-20 DE-83 DE-188 |
| physical | XIV, 282 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Oxford Univ. Pr. |
| record_format | marc |
| series | The international series of monographs on computer science |
| series2 | The international series of monographs on computer science |
| spelling | O'Rourke, Joseph 1951- Verfasser (DE-588)114449708 aut Art gallery theorems and algorithms New York u.a. Oxford Univ. Pr. 1987 XIV, 282 S. txt rdacontent n rdamedia nc rdacarrier The international series of monographs on computer science 3 Géométrie - Informatique Géométrie combinatoire algorithme graphe inriac chiffre de garde inriac géométrie algorithmique inriac géométrie combinatoire inriac géométrie inriac polygone inriac théorème art gallery inriac visibilité inriac Datenverarbeitung Combinatorial geometry Geometry Data processing Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 s Algorithmische Geometrie (DE-588)4130267-9 s DE-604 The international series of monographs on computer science 3 (DE-604)BV000725123 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000501717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Rourke, Joseph 1951- Art gallery theorems and algorithms The international series of monographs on computer science Géométrie - Informatique Géométrie combinatoire algorithme graphe inriac chiffre de garde inriac géométrie algorithmique inriac géométrie combinatoire inriac géométrie inriac polygone inriac théorème art gallery inriac visibilité inriac Datenverarbeitung Combinatorial geometry Geometry Data processing Algorithmische Geometrie (DE-588)4130267-9 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| subject_GND | (DE-588)4130267-9 (DE-588)4140733-7 |
| title | Art gallery theorems and algorithms |
| title_auth | Art gallery theorems and algorithms |
| title_exact_search | Art gallery theorems and algorithms |
| title_full | Art gallery theorems and algorithms |
| title_fullStr | Art gallery theorems and algorithms |
| title_full_unstemmed | Art gallery theorems and algorithms |
| title_short | Art gallery theorems and algorithms |
| title_sort | art gallery theorems and algorithms |
| topic | Géométrie - Informatique Géométrie combinatoire algorithme graphe inriac chiffre de garde inriac géométrie algorithmique inriac géométrie combinatoire inriac géométrie inriac polygone inriac théorème art gallery inriac visibilité inriac Datenverarbeitung Combinatorial geometry Geometry Data processing Algorithmische Geometrie (DE-588)4130267-9 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| topic_facet | Géométrie - Informatique Géométrie combinatoire algorithme graphe chiffre de garde géométrie algorithmique géométrie combinatoire géométrie polygone théorème art gallery visibilité Datenverarbeitung Combinatorial geometry Geometry Data processing Algorithmische Geometrie Kombinatorische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000501717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000725123 |
| work_keys_str_mv | AT orourkejoseph artgallerytheoremsandalgorithms |