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Model

How wide a block's min–max range is

A zone map is not an index. It is a measurement of how well you sorted.

Block size
rows per block, values uniform on [0, 1]

How it behaves

One input on the horizontal axis, the others held fixed.

Data table
Share of the domain a block's range covers, values in random order
Rows per block bRange covered
10%
1.198.61%
1.4117.1%
1.6825.3%
233.2%
2.3740.7%
2.8247.6%
3.3554%
3.9859.8%
4.7365.1%
5.6269.8%
6.6874%
7.9477.6%
9.4480.8%
11.283.6%
13.386%
15.888.1%
18.889.9%
22.491.4%
26.692.8%
31.693.9%
37.694.8%
44.795.6%
53.196.3%
63.196.9%
7597.4%
89.197.8%
10698.1%
12698.4%
15098.7%
17898.9%
21199.1%
25199.2%
29999.3%
35599.4%
42299.5%
50199.6%
59699.7%
70899.7%
84199.8%
1K99.8%
1.19K99.8%
1.41K99.9%
1.68K99.9%
2K99.9%
2.37K99.9%
2.82K99.9%
3.35K99.9%
3.98K99.9%
4.73K100%
5.62K100%
6.68K100%
7.94K100%
9.44K100%
11.2K100%
13.3K100%
15.8K100%
18.8K100%
22.4K100%
26.6K100%
31.6K100%
37.6K100%
44.7K100%
53.1K100%
63.1K100%
75K100%
89.1K100%
106K100%
126K100%
150K100%
178K100%
211K100%
251K100%
299K100%
355K100%
422K100%
501K100%
596K100%
708K100%
841K100%
1M100%

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.