1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
|
{
"abstracts": [
{
"content": "We present a new heuristic for 2D-packing of rectangles inside a rectangular area where the aesthetics of the resulting packing is amenable to generating large collages of photographs or images. The heuristic works by maintaining a sorted collection of vertical segments covering the area to be packed. The segments define the leftmost boundaries of rectangular and possibly overlapping areas that are yet to be covered. The use of this data structure allows for easily defining ahead of time arbitrary rectangular areas that the packing must avoid. The 2D-packing heuristic presented does not allow the rectangles to be rotated during the packing, but could easily be modified to implement this feature. The execution time of the present heuristic on various benchmark problems is on par with recently published research in this area, including some that do allow rotation of items while packing. Several examples of image packing are presented.",
"mimetype": "text/plain",
"sha1": "e5ddba8b6e8fcaf6a58656ded2ee73ffa4e8b8af"
}
],
"contribs": [
{
"index": 0,
"raw_name": "Dominique Thiebaut",
"role": "author"
}
],
"ext_ids": {},
"extra": {
"longtail_oa": true
},
"ident": "crab46jvmvh6hb7njmabej72nm",
"refs": [
{
"extra": {
"authors": [
"B Baker",
"D Brown",
"H Katseff"
],
"volume": null
},
"index": 0,
"key": "b0",
"title": "A 5/4 algorithm for two-dimensional packing",
"year": 1981
},
{
"extra": {
"authors": [
"B Baker",
null,
"R Rivest"
],
"volume": null
},
"index": 1,
"key": "b1",
"title": "Orthogonal packings in two dimensions",
"year": 1980
},
{
"extra": {
"authors": [
"R Baldacci",
"M Boschetti"
],
"issue": null,
"volume": "183"
},
"index": 2,
"key": "b2",
"title": "A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem",
"year": 2007
},
{
"extra": {
"authors": [
"J Beasley"
],
"issue": null,
"volume": "33"
},
"index": 3,
"key": "b3",
"title": "An exact two-dimensional non-guillotine cutting tree search procedure",
"year": 1985
},
{
"extra": {
"authors": [
"E Burke",
"G Kendall",
"G Whitwell"
],
"issue": null,
"volume": "52"
},
"index": 4,
"key": "b4",
"title": "A new placement heuristic for the orthogonal stock-cutting problem",
"year": 2004
},
{
"extra": {
"authors": [
"E Coffman",
"M Gazey",
"D Johnson"
]
},
"index": 5,
"key": "b5",
"title": "Approximation algorithms for bin-packing an updated survey",
"year": 1984
},
{
"extra": {
"authors": [
"R Dietrich",
"S Yakowitz"
],
"volume": "29"
},
"index": 6,
"key": "b6",
"title": "A rule-based approach to the trimloss problem",
"year": 1991
},
{
"extra": {
"authors": [
"H Dyckhoff"
],
"volume": "44"
},
"index": 7,
"key": "b7",
"title": "Typology of cutting and packing problems",
"year": 1990
},
{
"extra": {
"authors": [
"M Garey",
"D Johnson"
]
},
"index": 8,
"key": "b8",
"title": "Computers and Intractability: A Guide to the Theory of NP-Completeness",
"year": 1979
},
{
"extra": {
"authors": [
"L Guibas",
"R Sedgewick"
],
"volume": null
},
"index": 9,
"key": "b9",
"title": "A dichromatic framework for balanced trees",
"year": 1978
},
{
"extra": {
"authors": [
"E Hopper"
]
},
"index": 10,
"key": "b10",
"title": "Two-dimensional packing utilising evolutionary algorithms and other meta-heuristic methods",
"year": 2000
},
{
"extra": {
"authors": [
"E Hopper",
"B Turton"
],
"issue": "128",
"volume": null
},
"index": 11,
"key": "b11",
"title": "An empirical investigation of meta heuristic and heuristic algorithms for a 2d packing problem",
"year": 2000
},
{
"extra": {
"authors": [
"W Huang",
"D Chen"
]
},
"index": 12,
"key": "b12",
"title": "July) Simulated annealing",
"year": 2008
},
{
"extra": {
"url": "http://cdn.intechopen.com/pdfs/4629/InTech"
},
"index": 13,
"key": "b13",
"title": "An efficient quasi human heuristic algorithm for solving the rectangle packing problem"
},
{
"extra": {
"authors": [
"W Huang",
"D Chen",
"R Xu"
],
"issue": "11",
"volume": "34"
},
"index": 14,
"key": "b14",
"title": "A new heuristic algorithm for rectangle packing",
"year": 2007
},
{
"extra": {
"authors": [
"S Imahori",
"M Yagiur"
],
"issue": null,
"volume": "37"
},
"index": 15,
"key": "b15",
"title": "The best-fit heuristic for the rectangular strip packing problem: An efficient implementation and the worst-case approximation ratio",
"year": 2010
},
{
"extra": {
"authors": [
"C Kenyon",
"E Remilia"
]
},
"index": 16,
"key": "b16",
"title": "Approximate strip-packing",
"year": 1996
},
{
"extra": {
"authors": [
"T Leung",
"C Chan",
"M Troutt"
],
"issue": null,
"volume": "145"
},
"index": 17,
"key": "b17",
"title": "Application of a mixed simulated annealing genetic algorithm heuristic for the two-dimensional orthogonal packing problem",
"year": 2003
},
{
"extra": {
"authors": [
"D Liu",
"H Teng"
],
"issue": null,
"volume": "112"
},
"index": 18,
"key": "b18",
"title": "An improved bl-algorithm for genetic algorithm of the orthogonal packing of rectangles",
"year": 1999
},
{
"extra": {
"authors": [
"D Sleator"
],
"volume": "10"
},
"index": 19,
"key": "b19",
"title": "A 2.5 times optimal algorithm for packing in two dimensions",
"year": 1980
},
{
"extra": {
"authors": [
"J Verstichel",
"P Causmaecker",
"G Berghe"
]
},
"index": 20,
"key": "b20",
"title": "An improved best fit heuristic for the orthogonal strip packing problem",
"year": 2013
}
],
"release_type": "article-journal",
"revision": "26300485-268b-43c1-8334-e95eb47eea7e",
"state": "active",
"title": "2D-Packing Images on a Large Scale",
"work_id": "6s3kcsxotregxctxp2upttr2ym"
}
|