Bloom filter

The bloon filter

Definition

The bloon filter is ⼀ A probabilistic data structure , It is characterized by ⾼ Effective insert ⼊ and Inquire about , Can clearly tell a string ⼀ Must not exist perhaps Possible ;
Bloom filter phase ⽐ Traditional query structure （ for example ： hash, set, map And so on ） more ⾼ effect , Occupy ⽤ More space ⼩; But the drawback is that it returns The result is probability Of , That is to say, there are errors in the results , Although this error is controllable ; At the same time, it No ⽀ Hold delete operation ;

form

Bitmap （bit Array ） + n individual hash function

principle

When ⼀ Elements plus ⼊ Bitmap time , adopt k individual hash Function maps this element to the of the bitmap k A little bit , And set them as
1; When retrieving , Re pass k individual hash Function operation to detect the of bitmap k Whether all points are 1; If there is any reason not to 1 The point of , So think
non-existent ; If it's all 1, There may be （ There is an error ）;

• There are only two states for each slot in the bitmap （0 perhaps 1）,⼀ Slots are set to 1 state , But it is not clear how many times it has been set ; I don't know how many str1 Hash mapping and which hash Function mapping ; So don't ⽀ Hold the delete operation ;

• In practice, we should ⽤ In the process , How the bloom filter makes ⽤？ How many hash function , Bitmap of how much space to allocate , How many elements are stored ？ In addition, how to control the false positive rate （ The bloan filter can define ⼀ Must not exist , Not clear ⼀ There must be , Then there is an error in the judgment of existence , False positive rate is the probability of wrong judgment ）？

• In practice, we should ⽤ in , We are sure that n and p, Pass on ⾯ The calculation of m and k; It can also be in ⽹ Select the appropriate value on the station ：
  https://hur.st/bloomfilter

• It is known that k, How to choose k individual hash function ？

//  Mining ⽤⼀ individual hash function , to hash Pass on different species ⼦ Offset value 
// #define MIX_UINT64(v) ((uint32_t)((v>>32)^(v)))
uint64_t hash1 = MurmurHash2_x64(key, len, Seed);
uint64_t hash2 = MurmurHash2_x64(key, len, MIX_UINT64(hash1));
for (i = 0; i < k; i++) // k  yes hash Number of functions 
{
    
Pos[i] = (hash1 + i*hash2) % m; // m  It's a bitmap ⼤⼩
}
//  Through this kind of ⽅ To simulate  k  individual hash function   Before us ⾯ Open addressing   double hash yes ⼀ What kind of thinking