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Posted by Chris Wagner on April 20 2011 11:45pm[Delete] [Edit]

Linear hashing is a bad name considering that it creates a bell curve style distribution. Here are some distribution patterns on a keyed list of integers (0 - 64k) with some associated data volume. The first column is the partition, the second is the number of rows that would go in that partition, and the percentage is that of the total data volume. U can see that if the number of partitions is a power of 2 then the two methods are the same.

Basically, with linear hashing the middle partions will have 2x the size of the outer ones.

8 partitions

Modulo hashing distribution

0 1286793 12.43%
1 1293976 12.50%
2 1281279 12.38%
3 1295948 12.52%
4 1307476 12.63%
5 1291118 12.48%
6 1294605 12.51%
7 1297231 12.54%

Linear hashing distribution

0 1286793 12.43%
1 1293976 12.50%
2 1281279 12.38%
3 1295948 12.52%
4 1307476 12.63%
5 1291118 12.48%
6 1294605 12.51%
7 1297231 12.54%

9 partitions

Modulo hashing distribution

0 1137765 10.99%
1 1152313 11.14%
2 1139055 11.01%
3 1153697 11.15%
4 1150596 11.12%
5 1158082 11.19%
6 1148080 11.09%
7 1155944 11.17%
8 1152894 11.14%

Linear hashing distribution

0 638360 6.17%
1 1293976 12.50%
2 1281279 12.38%
3 1295948 12.52%
4 1307476 12.63%
5 1291118 12.48%
6 1294605 12.51%
7 1297231 12.54%
8 648433 6.27%

7 partitions

Modulo hashing distribution

0 1483555 14.34%
1 1470934 14.21%
2 1487062 14.37%
3 1481081 14.31%
4 1477711 14.28%
5 1468336 14.19%
6 1479747 14.30%

Linear hashing distribution

0 1286793 12.43%
1 1293976 12.50%
2 1281279 12.38%
3 2593179 25.06%
4 1307476 12.63%
5 1291118 12.48%
6 1294605 12.51%

12 partitions

Linear hashing distribution

0 638360 6.17%
1 643268 6.22%
2 637077 6.16%
3 650900 6.29%
4 1307476 12.63%
5 1291118 12.48%
6 1294605 12.51%
7 1297231 12.54%
8 648433 6.27%
9 650708 6.29%
10 644202 6.23%
11 645048 6.23%

For comparison, this is what it looks like just on the integer alone (no data volume).

7 partitions

Modulo hashing distribution

0 9363 14.29%
1 9362 14.29%
2 9362 14.29%
3 9362 14.29%
4 9362 14.29%
5 9362 14.29%
6 9362 14.29%

Linear hashing distribution

0 8192 12.50%
1 8192 12.50%
2 8192 12.50%
3 16383 25.00%
4 8192 12.50%
5 8192 12.50%
6 8192 12.50%

Posted by Steven Roussey on June 22 2011 9:23pm[Delete] [Edit]

For linear, the number of partitions ought to be a power of 2. So 4, 8, 16, 32, etc., would be good choices...