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
|
// Copyright Verizon Media. Licensed under the terms of the Apache 2.0 license. See LICENSE in the project root.
package com.yahoo.search.dispatch;
import org.junit.Test;
import static org.junit.Assert.assertEquals;
public class TopKEstimatorTest {
@Test
public void requireHitsAreEstimatedAccordingToPartitionsAndProbability() {
TopKEstimator estimator = new TopKEstimator(30, 0.999);
assertEquals(91.97368471911312, estimator.estimateExactK(200, 3), 0.0);
assertEquals(92, estimator.estimateK(200, 3));
assertEquals(37.96328109101396, estimator.estimateExactK(200, 10), 0.0);
assertEquals(38, estimator.estimateK(200, 10));
assertEquals(23.815737601023095, estimator.estimateExactK(200, 20), 0.0);
assertEquals(24, estimator.estimateK(200, 20));
assertEquals(37.96328109101396, estimator.estimateExactK(200, 10, 0.999), 0.0);
assertEquals(38, estimator.estimateK(200, 10, 0.999));
assertEquals(34.36212304875885, estimator.estimateExactK(200, 10, 0.99), 0.0);
assertEquals(35, estimator.estimateK(200, 10, 0.99));
assertEquals(41.44244358524574, estimator.estimateExactK(200, 10, 0.9999), 0.0);
assertEquals(42, estimator.estimateK(200, 10, 0.9999));
assertEquals(44.909040374464155, estimator.estimateExactK(200, 10, 0.99999), 0.0);
assertEquals(45, estimator.estimateK(200, 10, 0.99999));
}
@Test
public void requireHitsAreEstimatedAccordingToPartitionsAndProbabilityForVaryingN_K200() {
TopKEstimator estimator = new TopKEstimator(30, 0.99999);
assertEquals(200, estimator.estimateExactK(200, 1), 0.0);
assertEquals(200, estimator.estimateK(200, 1));
assertEquals(137.4727798056239, estimator.estimateExactK(200, 2), 0.0);
assertEquals(102.95409291533568, estimator.estimateExactK(200, 3), 0.0);
assertEquals(44.909040374464155, estimator.estimateExactK(200, 10), 0.0);
assertEquals(28.86025772029091, estimator.estimateExactK(200, 20), 0.0);
}
@Test
public void requireHitsAreEstimatedAccordingToPartitionsAndProbabilityForVaryingN_K20() {
TopKEstimator estimator = new TopKEstimator(30, 0.99999);
assertEquals(20, estimator.estimateExactK(20, 1), 0.0);
assertEquals(20, estimator.estimateK(20, 1));
assertEquals(21.849933444373328, estimator.estimateExactK(20, 2), 0.0);
assertEquals(18.14175840378403, estimator.estimateExactK(20, 3), 0.0);
assertEquals(9.87693019124002, estimator.estimateExactK(20, 10), 0.0);
assertEquals(6.964137165389415, estimator.estimateExactK(20, 20), 0.0);
}
@Test
public void requireHitsAreEstimatedAccordingToPartitionsAndProbabilityForVaryingN_K10_Five9() {
TopKEstimator estimator = new TopKEstimator(30, 0.99999);
assertEquals(10, estimator.estimateExactK(10, 1), 0.0);
assertEquals(10, estimator.estimateK(10, 1));
assertEquals(13.379168295125641, estimator.estimateExactK(10, 2), 0.0);
assertEquals(11.447448515386741, estimator.estimateExactK(10, 3), 0.0);
assertEquals(6.569830753158866, estimator.estimateExactK(10, 10), 0.0);
assertEquals(4.717281833573569, estimator.estimateExactK(10, 20), 0.0);
}
@Test
public void requireHitsAreEstimatedAccordingToPartitionsAndProbabilityForVaryingN_K10_Four9() {
TopKEstimator estimator = new TopKEstimator(30, 0.9999);
assertEquals(10, estimator.estimateExactK(10, 1), 0.0);
assertEquals(10, estimator.estimateK(10, 1));
assertEquals(12.087323848369289, estimator.estimateExactK(10, 2), 0.0);
assertEquals(10.230749855131009, estimator.estimateExactK(10, 3), 0.0);
assertEquals(5.794676146031378, estimator.estimateExactK(10, 10), 0.0);
assertEquals(4.152394782937266, estimator.estimateExactK(10, 20), 0.0);
}
@Test
public void requireEstimatesAreRoundeUp() {
TopKEstimator estimator = new TopKEstimator(30, 0.9999);
assertEquals(5.794676146031378, estimator.estimateExactK(10, 10), 0.0);
assertEquals(6, estimator.estimateK(10, 10));
}
@Test
public void requireEstimatesAreCappedAtInputK() {
TopKEstimator estimator = new TopKEstimator(30, 0.9999);
assertEquals(12.087323848369289, estimator.estimateExactK(10, 2), 0.0);
assertEquals(10, estimator.estimateK(10, 2));
}
@Test
public void requireThatLargeKAreSane() {
TopKEstimator estimator = new TopKEstimator(30, 0.9999);
assertEquals(6, estimator.estimateK(10, 10));
assertEquals(9, estimator.estimateK(20, 10));
assertEquals(14, estimator.estimateK(40, 10));
assertEquals(22, estimator.estimateK(80, 10));
assertEquals(26, estimator.estimateK(100, 10));
assertEquals(42, estimator.estimateK(200, 10));
assertEquals(71, estimator.estimateK(400, 10));
assertEquals(123, estimator.estimateK(800, 10));
assertEquals(148, estimator.estimateK(1000, 10));
assertEquals(268, estimator.estimateK(2000, 10));
assertEquals(496, estimator.estimateK(4000, 10));
assertEquals(936, estimator.estimateK(8000, 10));
assertEquals(1152, estimator.estimateK(10000, 10));
assertEquals(2215, estimator.estimateK(20000, 10));
assertEquals(4304, estimator.estimateK(40000, 10));
assertEquals(8429, estimator.estimateK(80000, 10));
assertEquals(10480, estimator.estimateK(100000, 10));
String expected =
"Prob/Hits: 1.0000000000 0.9999000000 0.9999900000 0.9999990000 0.9999999000 0.9999999900 0.9999999990 0.9999999999\n" +
" 10: 10.000 6.000 7.000 8.000 9.000 10.000 10.000 10.000\n" +
" 20: 10.000 4.500 5.000 5.500 6.500 7.000 7.500 8.000\n" +
" 40: 10.000 3.500 4.000 4.250 4.750 5.250 5.500 6.000\n" +
" 80: 10.000 2.750 3.000 3.250 3.625 3.875 4.250 4.500\n" +
" 100: 10.000 2.600 2.800 3.100 3.300 3.600 3.900 4.200\n" +
" 200: 10.000 2.100 2.250 2.450 2.650 2.800 3.000 3.200\n" +
" 400: 10.000 1.775 1.900 2.025 2.150 2.275 2.425 2.575\n" +
" 800: 10.000 1.538 1.625 1.713 1.813 1.900 2.000 2.100\n" +
" 1000: 10.000 1.480 1.560 1.640 1.720 1.810 1.890 1.990\n" +
" 2000: 10.000 1.340 1.395 1.450 1.510 1.570 1.630 1.695\n" +
" 4000: 10.000 1.240 1.280 1.320 1.360 1.403 1.445 1.493\n" +
" 8000: 10.000 1.170 1.198 1.225 1.254 1.284 1.315 1.348\n" +
" 10000: 10.000 1.152 1.177 1.202 1.227 1.254 1.282 1.311\n" +
" 20000: 10.000 1.108 1.125 1.143 1.161 1.180 1.199 1.220\n" +
" 40000: 10.000 1.076 1.088 1.101 1.114 1.127 1.141 1.156\n" +
" 80000: 10.000 1.054 1.062 1.071 1.080 1.090 1.100 1.110\n" +
" 100000: 10.000 1.048 1.056 1.064 1.072 1.080 1.089 1.098\n";
assertEquals(expected, dumpProbability(10));
}
/**
* This make a table showing how many more hits will be fetched as a factor of hits requested.
* It shows how it varies with probability and hits requested for a given number of partitions.
*/
private String dumpProbability(int numPartitions) {
TopKEstimator estimator = new TopKEstimator(30, 0.9999);
int [] K = {10, 20, 40, 80, 100, 200, 400, 800, 1000, 2000, 4000, 8000, 10000, 20000, 40000, 80000, 100000};
double [] P = {1.0, 0.9999, 0.99999, 0.999999, 0.9999999, 0.99999999, 0.999999999, 0.9999999999};
int n = numPartitions;
StringBuilder sb = new StringBuilder();
sb.append(String.format("Prob/Hits:"));
for (double p : P) {
sb.append(String.format(" %1.10f", p));
}
sb.append("\n");
for (int k : K) {
sb.append(String.format("%9d:", k));
for (double p : P) {
sb.append(String.format("%13.3f", (double)(estimator.estimateK(k, n, p)*n) / k));
}
sb.append("\n");
}
return sb.toString();
}
}
|
