学习笔记－bloom filter

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实例学习Bloom Filter

0. 科普
1. 为什么需要Bloom Filter
2. 基本原理
3. 如何设计Bloom Filter
4. 实例操作
5. 扩展

0. 科普

Bloom Filter是由Bloom在1970年提出的一种多哈希函数映射的快速查找算法。通常应用在一些需要快速判断某个元素是否属于集合，但是并不严格要求100%正确的场合。

1. 为什么需要Bloom Filter

举例说明：假设有2000万个url，现在判断一个新的url是否在这2000万个之中。可以有的思路：

将访问过的URL保存到数据库。
用HashSet将访问过的URL保存起来。那只需接近O(1)的代价就可以查到一个URL是否被访问过了。
URL经过MD5等单向哈希后再保存到HashSet或数据库。
Bit-Map方法。建立一个BitSet，将每个URL经过一个哈希函数映射到某一位。

分析

思路1：当数据量很大时，查询数据库变得效率底下

思路2：太消耗内存，还得把字符串全部储存起来

思路3：字符串经过MD5处理后有128个bit,比思路2省了很多空间

思路4：一个字符串仅用一位来表示，比思路3还节省空间

当然前提是会出现误判（哈希后表示相同），为了继承这么好的思路，同时减少误判的情况，可以来个折衷：一个哈希函数生成一个位，用多个哈希函数生成多个位来存储一个字符串。这样比Bit-Map多用了些空间，但是减少了误判率。

2. 基本原理

这样把大量的字符串存起来。查找时，用同样的哈希处理待查串，如果对应的各位上都为1，说明该字符串可能在这些字符串中，否则一定不在其中。

3. 如何设计Bloom Filter

如何降低误判率是关键，这需要

选取区分度高的哈希函数
根据存储数组、哈希函数个数、误判率之间的关系，分配空间、个数

直接利用前人的结论：

其中f'是自己期望的误判率，m是总共开辟的存储空间位数，n是待存储字符串的个数，k是哈希函数的个数，f是真正的误判率。

4. 实例操作

需求：2000万个已知url，100个待查url

设计：

1. 设定误判率为0.1， n=2000万，计算

m = n * 1.44 * math.log(1/f)/math.log(2)=287014588k = 0.693 * m / n= 10f = (1 - math.exp(-1 * k * n / m)) ** k = 0.00101298781512

参考代码(c++)

makefile

objects = main.o hash.o bloomfilter.omain : $(objects)    g++ -o main $(objects)main.o : hash.h bloomfilter.hbloomfilter.o : bloomfilter.hhash.o : hash.hclean:    rm *.o main

main.cc

#include <iostream>#include <fstream>#include <sstream>#include <cstring>#include <string>#include "bloomfilter.h"using namespace std;const int MAXSIZE = 400000000; int main(int argc, char **argv){    char *poolfile = argv[1];    char *testfile = argv[2];    cout << poolfile << endl;    ifstream fpool(poolfile);    ifstream ftest(testfile);    if(!fpool)    {        cout << "cannot open the file:" << poolfile << endl;        return 0;    }    if(!ftest)    {        cout << "cannot open the file:" << testfile << endl;        return 0;    }    BloomFilter bf(MAXSIZE);    bf.setBit(fpool);    cout << "Store OK" << endl;    bf.checkBit(ftest);    cout << "Check OK" << endl;    fpool.close();    ftest.close();}

bloomfilter.h

#include <iostream>#include <string>#include <fstream>#include <vector>#include "hash.h"using namespace std;class BloomFilter{    public:        BloomFilter(int size) : SIZE(size) { vec.resize(size); };        void setBit(ifstream &f);        void setBit(const string &s);        void setBit(unsigned int count);        bool checkBit(ifstream &f);        bool checkBit(const string &s);        bool checkBit(unsigned int count);    private:        vector<char> vec;        const unsigned int SIZE;};

bloomfilter.cc

#include "bloomfilter.h"void BloomFilter::setBit(ifstream &f){    string line;    while(f >> line)    {        setBit(line);    }}bool BloomFilter::checkBit(ifstream &f){    string line;    while(f >> line)    {        if(!checkBit(line))            cout << line << endl;    }}void BloomFilter::setBit(const string &s){    unsigned int bitpos = 0;    const char *str = s.c_str();    int len = s.size();    bitpos = RSHash(str, len);    setBit(bitpos);    bitpos = JSHash(str, len);    setBit(bitpos);    bitpos = PJWHash(str, len);    setBit(bitpos);    bitpos = ELFHash(str, len);    setBit(bitpos);    bitpos = BKDRHash(str, len);    setBit(bitpos);    bitpos = SDBMHash(str, len);    setBit(bitpos);    bitpos = DJBHash(str, len);    setBit(bitpos);    bitpos = DEKHash(str, len);    setBit(bitpos);    bitpos = BPHash(str, len);    setBit(bitpos);    bitpos = FNVHash(str, len);    setBit(bitpos);}bool BloomFilter::checkBit(const string &s){    unsigned int bitpos = 0;    const char *str = s.c_str();    int len = s.size();    bool rev = true;    bitpos = RSHash(str, len);    rev &= checkBit(bitpos);    bitpos = JSHash(str, len);    rev &= checkBit(bitpos);    bitpos = PJWHash(str, len);    rev &= checkBit(bitpos);    bitpos = ELFHash(str, len);    rev &= checkBit(bitpos);    bitpos = BKDRHash(str, len);    rev &= checkBit(bitpos);    bitpos = SDBMHash(str, len);    rev &= checkBit(bitpos);    bitpos = DJBHash(str, len);    rev &= checkBit(bitpos);    bitpos = DEKHash(str, len);    rev &= checkBit(bitpos);    bitpos = BPHash(str, len);    rev &= checkBit(bitpos);    bitpos = FNVHash(str, len);    rev &= checkBit(bitpos);    return rev;}void BloomFilter::setBit(unsigned int count){    count = count % (SIZE * 8);    vec[count / 8] |= (1 << (count % 8));}bool BloomFilter::checkBit(unsigned int count){    count = count % (SIZE * 8);    return vec[count / 8] &= (1 << (count % 8));}

hash.h

unsigned int RSHash(const char* str, unsigned int len);unsigned int JSHash(const char* str, unsigned int len);unsigned int PJWHash(const char* str, unsigned int len);unsigned int ELFHash(const char* str, unsigned int len);unsigned int BKDRHash(const char* str, unsigned int len);unsigned int SDBMHash(const char* str, unsigned int len);unsigned int DJBHash(const char* str, unsigned int len);unsigned int DEKHash(const char* str, unsigned int len);unsigned int BPHash(const char* str, unsigned int len);unsigned int FNVHash(const char* str, unsigned int len);

hash.cc

#include "hash.h"unsigned int RSHash(const char* str, unsigned int len){   unsigned int b = 378551;   unsigned int a = 63689;   unsigned int hash = 0;   unsigned int i = 0;   for(i=0; i<len; str++, i++)   {      hash = hash*a + (*str);      a = a*b;   }   return hash;}/* End Of RS Hash Function */unsigned int JSHash(const char* str, unsigned int len){   unsigned int hash = 1315423911;   unsigned int i    = 0;   for(i=0; i<len; str++, i++)   {      hash ^= ((hash<<5) + (*str) + (hash>>2));   }   return hash;}/* End Of JS Hash Function */unsigned int PJWHash(const char* str, unsigned int len){   const unsigned int BitsInUnsignedInt = (unsigned int)(sizeof(unsigned int) * 8);   const unsigned int ThreeQuarters = (unsigned int)((BitsInUnsignedInt  * 3) / 4);   const unsigned int OneEighth = (unsigned int)(BitsInUnsignedInt / 8);   const unsigned int HighBits = (unsigned int)(0xFFFFFFFF) << (BitsInUnsignedInt - OneEighth);   unsigned int hash = 0;   unsigned int test = 0;   unsigned int i = 0;   for(i=0;i<len; str++, i++)   {      hash = (hash<<OneEighth) + (*str);      if((test = hash & HighBits)  != 0)      {         hash = ((hash ^(test >> ThreeQuarters)) & (~HighBits));      }   }   return hash;}/* End Of  P. J. Weinberger Hash Function */unsigned int ELFHash(const char* str, unsigned int len){   unsigned int hash = 0;   unsigned int x    = 0;   unsigned int i    = 0;   for(i = 0; i < len; str++, i++)   {      hash = (hash << 4) + (*str);      if((x = hash & 0xF0000000L) != 0)      {         hash ^= (x >> 24);      }      hash &= ~x;   }   return hash;}/* End Of ELF Hash Function */unsigned int BKDRHash(const char* str, unsigned int len){   unsigned int seed = 131; /* 31 131 1313 13131 131313 etc.. */   unsigned int hash = 0;   unsigned int i    = 0;   for(i = 0; i < len; str++, i++)   {      hash = (hash * seed) + (*str);   }   return hash;}/* End Of BKDR Hash Function */unsigned int SDBMHash(const char* str, unsigned int len){   unsigned int hash = 0;   unsigned int i    = 0;   for(i = 0; i < len; str++, i++)   {      hash = (*str) + (hash << 6) + (hash << 16) - hash;   }   return hash;}/* End Of SDBM Hash Function */unsigned int DJBHash(const char* str, unsigned int len){   unsigned int hash = 5381;   unsigned int i    = 0;   for(i = 0; i < len; str++, i++)   {      hash = ((hash << 5) + hash) + (*str);   }   return hash;}/* End Of DJB Hash Function */unsigned int DEKHash(const char* str, unsigned int len){   unsigned int hash = len;   unsigned int i    = 0;   for(i = 0; i < len; str++, i++)   {      hash = ((hash << 5) ^ (hash >> 27)) ^ (*str);   }   return hash;}/* End Of DEK Hash Function */unsigned int BPHash(const char* str, unsigned int len){   unsigned int hash = 0;   unsigned int i    = 0;   for(i = 0; i < len; str++, i++)   {      hash = hash << 7 ^ (*str);   }   return hash;}/* End Of BP Hash Function */unsigned int FNVHash(const char* str, unsigned int len){   const unsigned int fnv_prime = 0x811C9DC5;   unsigned int hash      = 0;   unsigned int i         = 0;   for(i = 0; i < len; str++, i++)   {      hash *= fnv_prime;      hash ^= (*str);   }   return hash;}/* End Of FNV Hash Function */

数据下载：http://pan.baidu.com/s/1hqBTks0

Github 地址：https://github.com/jihite/Bloom-Filter

5. 扩展

如何删除存储数组中的元素？

思路：把存储数组的每一个元素扩展一下（原来是1b）用来存储该位置被置1的次数。存储是，计数次数加一；删除的时候，计数次数减一。

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