大数据量的过滤 (用于爬虫,蜘蛛) Bloom Filter 布隆过滤器
想像一下.如果你有一个非常大的无序的数据(url连接) 并且你要保证同样的一条连接不会在其它地方再次出现
你实时的收集哪些数据,你没有办法来预防两个相同的url出现,再不断增加的数据当中.
当这些数据是少的时候你可以轻松的创建一个list(dictonary or hashtable 或者你自已的数据结构)然后遍历它们,看它是不是已经存在在这个list当中,
遍历所花的时间是非常多的,
但是 当这些数据的长度超过可用的内存的时候? hashtable可以帮我加快速度,但是存...
上面的比较多的费话..看起来累 呦口继续不下去了.
得出的方案是用 bit数组来节省空间
a hash table capable of holding M items will take m/8 bytes of memory
接下来是实际的解决方法
net 里面有一个类 BitArray它可以帮我们很容易的创建出一个hashtable
创建一个简单的 HashingTable
public class SimpleHashTable
{
private BitArray hashbits = null; public SimpleHashTable(int tableSize)
{
hashbits = new BitArray(tableSize, false);
} public bool Test(string str) { int hash = Math.Abs(str.GetHashCode()) % hashbits.Count; return hashbits[hash]; } public bool Add(string str) { int hash = Math.Abs(str.GetHashCode()) % hashbits.Count; bool rslt = hashbits[hash]; if (!rslt) hashbits[hash] = true; return rslt; }
}
Add 里面没有这个值的时候是返回 false ,
Test 里面有值的话是返回 true;
class Program { static void Main(string[] args) { int urlsRead = 0; int collisions = 0; SimpleHashTable hashTable = new SimpleHashTable(1000000); using (StreamReader sr = new StreamReader("urls.txt")) { string url; while ((url = sr.ReadLine()) != null) { urlsRead++; bool rslt = hashTable.Add(url); if (rslt) collisions++; if ((urlsRead % 10000) == 0) { Console.WriteLine("{0} {1} {2}%", urlsRead, collisions, 100* (double)collisions / urlsRead); } } } Console.WriteLine("{0} urls read", urlsRead); Console.WriteLine("{0} collisions", collisions); Console.WriteLine("False positive rate = {0}%", 100*(double)collisions / urlsRead); } }The output from that program, run against the 100,000 unique URLs in my file, is:
10000 44 0.44%
20000 187 0.935%
30000 423 1.41%
40000 753 1.8825%
50000 1200 2.4%
60000 1753 2.92166666666667%
70000 2375 3.39285714285714%
80000 3123 3.90375%
90000 3946 4.38444444444444%
100000 4834 4.834%
100000 urls read
4834 collisions
False positive rate = 4.834%
然后写了一个简单的测试类,我们可以看到它的碰撞(冲突)还是比较明显的
接下来就是如何继续去解决这样的问题
创建一个新的 Hash算法函数 HashString
hi(x) = (f1(x) + if2(x)) mod m
然后提供了一个 防止碰撞的结构. hashkeys 保存这个hash的三个位置
public class BloomFilter { private BitArray hashbits; private int numKeys; private int[] hashKeys; public BloomFilter(int tableSize, int nKeys) { numKeys = nKeys; hashKeys = new int[numKeys]; hashbits = new BitArray(tableSize); } private int HashString(string s) { int hash = 0; for (int i = 0; i < s.Length; i++) { hash += s[i]; hash += (hash << 10); hash ^= (hash >> 6); } hash += (hash << 3); hash ^= (hash >> 11); hash += (hash << 15); return hash; } private void CreateHashes(string str) { int hash1 = str.GetHashCode(); int hash2 = HashString(str); hashKeys[0] = Math.Abs(hash1 % hashbits.Count); if (numKeys > 1) { for (int i = 1; i < numKeys; i++) { hashKeys[i] = Math.Abs((hash1 + (i * hash2)) % hashbits.Count); } } } public bool Test(string str) { CreateHashes(str); // Test each hash key. Return false if any // one of the bits is not set. foreach (int hash in hashKeys) { if (!hashbits[hash]) return false; } // All bits set. The item is there. return true; } public bool Add(string str) { // Initially assume that the item is in the table bool rslt = true; CreateHashes(str); foreach (int hash in hashKeys) { if (!hashbits[hash]) { // One of the bits wasn't set, so show that // the item wasn't in the table, and set that bit. rslt = false; hashbits[hash] = true; } } return rslt; } }测试:
class Program { static void Main(string[] args) { int urlsRead = 0; int hashCollisions = 0; int bloomCollisions = 0; SimpleHashTable hashTable = new SimpleHashTable(1000000); BloomFilter bloom = new BloomFilter(480833, 3); using (StreamReader sr = new StreamReader("urls.txt")) { string url; while ((url = sr.ReadLine()) != null) { urlsRead++; bool rslt = hashTable.Add(url); if (rslt) hashCollisions++; rslt = bloom.Add(url); if (rslt) bloomCollisions++; if ((urlsRead % 10000) == 0) { Console.WriteLine("{0} {1} {2}% {3} {4}%", urlsRead, hashCollisions, 100*(double)hashCollisions / urlsRead, bloomCollisions, 100*(double)bloomCollisions / urlsRead); } } } Console.WriteLine("{0} urls read", urlsRead); Console.WriteLine("{0} hash collisions", hashCollisions); Console.WriteLine("False positive rate (hash) = {0}%", 100*(double)hashCollisions / urlsRead); Console.WriteLine("{0} Bloom collisions", bloomCollisions); Console.WriteLine("False positive rate (Bloom) = {0}%", 100*(double)bloomCollisions / urlsRead); } }10000 44 0.44% 1 0.01%
20000 187 0.935% 10 0.05%
30000 423 1.41% 38 0.126666666666667%
40000 753 1.8825% 118 0.295%
50000 1200 2.4% 262 0.524%
60000 1753 2.92166666666667% 517 0.861666666666667%
70000 2375 3.39285714285714% 866 1.23714285714286%
80000 3123 3.90375% 1352 1.69%
90000 3946 4.38444444444444% 2118 2.35333333333333%
100000 4834 4.834% 2966 2.966%
100000 urls read
4834 hash collisions
False positive rate (hash) = 4.834%
2966 Bloom collisions
False positive rate (Bloom) = 2.966%
在添加数据的时候.他会判断前面这个位置是否有一个地址存了.如果有的话.它就存第二个. 如果都被存光了..哪就发生碰撞了
实际总的容量是有限的.
还有泛型和它的例子
public abstract class BloomFilter{ private BitArray hashbits; private int numKeys; protected int[] hashKeys; public BloomFilter(int tableSize, int nKeys) { numKeys = nKeys; hashKeys = new int[numKeys]; hashbits = new BitArray(tableSize); } public bool Test(TValue val) { CreateHashes(val); // Test each hash key. Return false // if any one of the bits is not set. foreach (int hash in hashKeys) { if (!hashbits[hash]) return false; } // All bits set. The item is there. return true; } public bool Add(TValue val) { // Initially assume that the item is in the table bool rslt = true; CreateHashes(val); foreach (int hash in hashKeys) { if (!hashbits[hash]) { // One of the bits wasn't set, so show that // the item wasn't in the table, and set that bit. rslt = false; hashbits[hash] = true; } } return rslt; } protected virtual void CreateHashes(TValue val) { int hash1 = CreateHash1(val); int hash2 = CreateHash2(val); hashKeys[0] = Math.Abs(hash1 % hashbits.Count); if (numKeys > 1) { for (int i = 1; i < numKeys; i++) { hashKeys[i] = Math.Abs((hash1 + (i * hash2)) % hashbits.Count); } } } protected abstract int CreateHash1(TValue val); protected abstract int CreateHash2(TValue val);}class StringBloomFilter : BloomFilter{ public StringBloomFilter(int tableSize, int nKeys) : base(tableSize, nKeys) { } protected override int CreateHash1(string val) { return val.GetHashCode(); } protected override int CreateHash2(string val) { int hash = 0; for (int i = 0; i < val.Length; i++) { hash += val[i]; hash += (hash << 10); hash ^= (hash >> 6); } hash += (hash << 3); hash ^= (hash >> 11); hash += (hash << 15); return hash; }}Google 数学之美哪边也介绍到了.
http://googlechinablog.com/2007/07/bloom-filter.html