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Coreset

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is an arbitrary positive number. When this is the case, one obtains a linear-time or near-linear time approximation scheme, based on the idea of finding a coreset and then applying an exact optimization algorithm to the coreset. Regardless of how slow the exact optimization algorithm is, for any
34:) results in approximately equal numbers. Many natural geometric optimization problems have coresets that approximate an optimal solution to within a factor of 27:
is a small set of points that approximates the shape of a larger point set, in the sense that applying some geometric measure to the two sets (such as their
238: 214: 150: 116:, Mathematical Sciences Research Institute Publications, vol. 52, Cambridge Univ. Press, Cambridge, pp. 1–30, 233: 207: 137:"10. Fast approximate optimization in high dimensions with core-sets and fast dimension reduction" 200: 20: 121: 28: 8: 146: 136: 89: 101: 93: 188: 140: 117: 184: 180: 227: 105: 42: 176: 109: 97: 45:
or near-linear time), and that have size bounded by a function of
31: 168: 88: 65:, the running time of this approximation scheme will be 225: 208: 142:Introduction to HPC with MPI for Data Science 215: 201: 114:Combinatorial and Computational Geometry 134: 226: 98:"Geometric approximation via coresets" 82: 52:independent of the input size, where 239:Algorithms and data structures stubs 163: 72:plus the time to find the coreset. 13: 96:; Varadarajan, Kasturi R. (2005), 14: 250: 167: 41:, that can be found quickly (in 145:. Springer. pp. 259–272. 128: 16:Computational geometry concept 1: 75: 187:. You can help Knowledge by 7: 10: 255: 162: 135:Nielsen, Frank (2016). 234:Computational geometry 183:-related article is a 21:computational geometry 29:minimum bounding box 90:Agarwal, Pankaj K. 196: 195: 152:978-3-319-21903-5 102:Goodman, Jacob E. 94:Har-Peled, Sariel 246: 217: 210: 203: 171: 164: 157: 156: 132: 126: 124: 86: 71: 64: 59:fixed choice of 57: 51: 40: 254: 253: 249: 248: 247: 245: 244: 243: 224: 223: 222: 221: 181:data structures 161: 160: 153: 133: 129: 87: 83: 78: 66: 60: 53: 46: 35: 17: 12: 11: 5: 252: 242: 241: 236: 220: 219: 212: 205: 197: 194: 193: 172: 159: 158: 151: 127: 80: 79: 77: 74: 15: 9: 6: 4: 3: 2: 251: 240: 237: 235: 232: 231: 229: 218: 213: 211: 206: 204: 199: 198: 192: 190: 186: 182: 178: 173: 170: 166: 165: 154: 148: 144: 143: 138: 131: 123: 119: 115: 111: 107: 103: 99: 95: 91: 85: 81: 73: 69: 63: 56: 50: 44: 39: 33: 30: 26: 22: 189:expanding it 174: 141: 130: 113: 84: 67: 61: 54: 48: 37: 24: 18: 106:Pach, János 43:linear time 228:Categories 177:algorithms 110:Welzl, Emo 76:References 112:(eds.), 122:2178310 25:coreset 149:  120:  32:volume 175:This 100:, in 185:stub 147:ISBN 36:1 + 23:, a 179:or 70:(1) 19:In 230:: 139:. 118:MR 108:; 104:; 92:; 47:1/ 216:e 209:t 202:v 191:. 155:. 125:. 68:O 62:ε 55:ε 49:ε 38:ε

Index

computational geometry
minimum bounding box
volume
linear time
Agarwal, Pankaj K.
Har-Peled, Sariel
"Geometric approximation via coresets"
Goodman, Jacob E.
Pach, János
Welzl, Emo
MR
2178310
"10. Fast approximate optimization in high dimensions with core-sets and fast dimension reduction"
Introduction to HPC with MPI for Data Science
ISBN
978-3-319-21903-5
Stub icon
algorithms
data structures
stub
expanding it
v
t
e
Categories
Computational geometry
Algorithms and data structures stubs

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