/**
* Fill the list recursively with collideNum numbers that sum to <i>sum</i>. Assuming items
* already in the array p sum to <i>usedSum</i>. The numbers must be > min. It stops if it finds
* <i>limit</i> patterns and the probability of those found patterns become very small comparing
* to the other patterns found (probability <1/freq)
*
* @param patterns
* @param collideNum
* @param sum
* @param usedSum sum of items in array <i>p</i>
* @param min: is used to make p a sorted array
* @param level what is the current level of recursion (number of items in array <i>p</i>)
* @param p keeps track of already decided items in the pattern, it will be a sorted array
* @param oldDistribution
* @param limit the number of patterns to be found
* @param freqI the frequency of the sum items in the sketch
* @return
*/
private boolean getPatternRecursive(
List<Map<Integer, Integer>> patterns,
int collideNum,
int sum,
int usedSum,
int min,
int level,
int[] p,
Distribution oldDistribution,
double limit,
int freqI) {
if (min > sum - usedSum) { // repetitive
return false;
}
if (level == collideNum - 1) { // create the pattern with whatever remained out of sum
p[level] = sum - usedSum;
if (oldDistribution.getFreq(p[level]) == 0) {
return false;
}
Map<Integer, Integer> pattern = getPattern(p);
patterns.add(pattern);
double prob = getProb(oldDistribution, pattern);
if (sumProb == 0) {
meanProb = prob * (level + 1);
} else {
meanProb = alpha * meanProb + (1 - alpha) * prob * (level + 1);
}
sumProb += prob;
} else {
for (int j = min; j <= sum - usedSum - (collideNum - level - 1); j++) {
p[level] = j;
if (oldDistribution.getFreq(p[level]) == 0) {
continue;
}
// if I have found enough patterns and the probability of found items are very small
if (patterns.size() > limit && meanProb / sumProb < 1.0 / freqI) {
return true;
}
getPatternRecursive(
patterns,
collideNum,
sum,
usedSum + j,
Math.max(min, j),
level + 1,
p,
oldDistribution,
limit,
freqI);
}
}
return false;
}
/**
* Returns te probability of each of the key items in the pattern. It leverages Poisson
* distribution. See the paper for its description
*
* @param distribution
* @param pattern
* @return
*/
private double getProb(Distribution distribution, Map<Integer, Integer> pattern) {
return pattern
.entrySet()
.stream()
.mapToDouble(
e -> {
double l = distribution.getFreq(e.getKey()) / capwidth;
return l == 0
? 0
: (new PoissonDistribution(l).probability(e.getValue()) / FastMath.exp(-l));
})
.reduce((a, b) -> (a * b))
.getAsDouble();
}