Appendix 4
Determination of WLS for various partionings

Table a4.1 shows AS values (derived using equation 4.8) for the QS values used by queries referencing AGE, CRED_LIM and JOIN_DATE. The appropriate AS values are used in table a4.2, in which total WLS is calculated for each of the six partitionings shown in table 6.9, as well as for the calculation of maximum possible STS (not WLS) assuming maximum possible partitioning (i.e. in each dimension there is a partition for each data value).

Table a4.1 AS for QS values used in following example queries
n QS
  0.04 0.05 0.117 0.167 0.333
1 1.000 1.000 1.000 1.000 1.000
2 0.521 0.526 0.566 0.600 0.750
3 0.361 0.368 0.422 0.467 0.666
4 0.281 0.289 0.349 0.400 0.562
5 0.233 0.242 0.306 0.360 0.520
6 0.201 0.211 0.277 0.334 0.500
7 0.179 0.188 0.256 0.306 0.469
8 0.161 0.171 0.241 0.288 0.453
9 0.148 0.158 0.227 0.274 0.444
10 0.138 0.147 0.215 0.264 0.430
11 0.129 0.139 0.206 0.257 0.421
12 0.122 0.132 0.198 0.250 0.416
13 0.115 0.126 0.192 0.243 0.408
14 0.110 0.120 0.187 0.237 0.403
15 0.106 0.116 0.183 0.232 0.400
16 0.102 0.112 0.179 0.228 0.394
17 0.098 0.108 0.176 0.225 0.391
18 0.095 0.105 0.172 0.223 0.389
19 0.092 0.102 0.169 0.219 0.385
20 0.090 0.100 0.166 0.216 0.382
21 0.087 0.098 0.164 0.214 0.381
22 0.085 0.095 0.162 0.212 0.378
23 0.083 0.093 0.160 0.210 0.376

Table a4.2 - view or download the PDF file

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