[轉]BloomFilter——大規模數據處理利器

時間 2019-11-12

原文原文鏈接

Bloom Filter是由Bloom在1970年提出的一種多哈希函數映射的快速查找算法。一般應用在一些須要快速判斷某個元素是否屬於集合，可是並不嚴格要求100%正確的場合。html

一. 實例java

　　爲了說明Bloom Filter存在的重要意義，舉一個實例：node

　　假設要你寫一個網絡蜘蛛（web crawler）。因爲網絡間的連接錯綜複雜，蜘蛛在網絡間爬行極可能會造成「環」。爲了不造成「環」，就須要知道蜘蛛已經訪問過那些URL。給一個URL，怎樣知道蜘蛛是否已經訪問過呢？稍微想一想，就會有以下幾種方案：git

　　1. 將訪問過的URL保存到數據庫。github

　　2. 用HashSet將訪問過的URL保存起來。那隻需接近O(1)的代價就能夠查到一個URL是否被訪問過了。web

　　3. URL通過MD5或SHA-1等單向哈希後再保存到HashSet或數據庫。算法

　　4. Bit-Map方法。創建一個BitSet，將每一個URL通過一個哈希函數映射到某一位。數據庫

　　方法1~3都是將訪問過的URL完整保存，方法4則只標記URL的一個映射位。express

　　以上方法在數據量較小的狀況下都能完美解決問題，可是當數據量變得很是龐大時問題就來了。apache

　　方法1的缺點：數據量變得很是龐大後關係型數據庫查詢的效率會變得很低。並且每來一個URL就啓動一次數據庫查詢是否是過小題大作了？

　　方法2的缺點：太消耗內存。隨着URL的增多，佔用的內存會愈來愈多。就算只有1億個URL，每一個URL只算50個字符，就須要5GB內存。

　　方法3：因爲字符串通過MD5處理後的信息摘要長度只有128Bit，SHA-1處理後也只有160Bit，所以方法3比方法2節省了好幾倍的內存。

　　方法4消耗內存是相對較少的，但缺點是單一哈希函數發生衝突的機率過高。還記得數據結構課上學過的Hash表衝突的各類解決方法麼？若要下降衝突發生的機率到1%，就要將BitSet的長度設置爲URL個數的100倍。

　　實質上上面的算法都忽略了一個重要的隱含條件：容許小几率的出錯，不必定要100%準確！也就是說少許url實際上沒有沒網絡蜘蛛訪問，而將它們錯判爲已訪問的代價是很小的——大不了少抓幾個網頁唄。

二. Bloom Filter的算法

　　廢話說到這裏，下面引入本篇的主角——Bloom Filter。其實上面方法4的思想已經很接近Bloom Filter了。方法四的致命缺點是衝突機率高，爲了下降衝突的概念，Bloom Filter使用了多個哈希函數，而不是一個。

　Bloom Filter算法以下：

　建立一個m位BitSet，先將全部位初始化爲0，而後選擇k個不一樣的哈希函數。第i個哈希函數對字符串str哈希的結果記爲h（i，str），且h（i，str）的範圍是0到m-1 。

(1) 加入字符串過程

　　下面是每一個字符串處理的過程，首先是將字符串str「記錄」到BitSet中的過程：

　　對於字符串str，分別計算h（1，str），h（2，str）…… h（k，str）。而後將BitSet的第h（1，str）、h（2，str）…… h（k，str）位設爲1。

　　圖1.Bloom Filter加入字符串過程

　　很簡單吧？這樣就將字符串str映射到BitSet中的k個二進制位了。

(2) 檢查字符串是否存在的過程

　　下面是檢查字符串str是否被BitSet記錄過的過程：

　　對於字符串str，分別計算h（1，str），h（2，str）…… h（k，str）。而後檢查BitSet的第h（1，str）、h（2，str）…… h（k，str）位是否爲1，若其中任何一位不爲1則能夠斷定str必定沒有被記錄過。若所有位都是1，則「認爲」字符串str存在。

　　若一個字符串對應的Bit不全爲1，則能夠確定該字符串必定沒有被Bloom Filter記錄過。（這是顯然的，由於字符串被記錄過，其對應的二進制位確定所有被設爲1了）

　　可是若一個字符串對應的Bit全爲1，其實是不能100%的確定該字符串被Bloom Filter記錄過的。（由於有可能該字符串的全部位都恰好是被其餘字符串所對應）這種將該字符串劃分錯的狀況，稱爲false positive 。

(3) 刪除字符串過程

字符串加入了就被不能刪除了，由於刪除會影響到其餘字符串。實在須要刪除字符串的可使用Counting bloomfilter(CBF)，這是一種基本Bloom Filter的變體，CBF將基本Bloom Filter每個Bit改成一個計數器，這樣就能夠實現刪除字符串的功能了。

　　Bloom Filter跟單哈希函數Bit-Map不一樣之處在於：Bloom Filter使用了k個哈希函數，每一個字符串跟k個bit對應。從而下降了衝突的機率。

三. Bloom Filter參數選擇

(1)哈希函數選擇

　　哈希函數的選擇對性能的影響應該是很大的，一個好的哈希函數要能近似等機率的將字符串映射到各個Bit。選擇k個不一樣的哈希函數比較麻煩，一種簡單的方法是選擇一個哈希函數，而後送入k個不一樣的參數。

(2)Bit數組大小選擇

　　哈希函數個數k、位數組大小m、加入的字符串數量n的關係能夠參考參考文獻1。該文獻證實了對於給定的m、n，當 k = ln(2)* m/n 時出錯的機率是最小的。

　　同時該文獻還給出特定的k，m，n的出錯機率。例如：根據參考文獻1，哈希函數個數k取10，位數組大小m設爲字符串個數n的20倍時，false positive發生的機率是0.0000889 ，這個機率基本能知足網絡爬蟲的需求了。

四. Bloom Filter實現代碼

　下面給出一個簡單的Bloom Filter的Java實現代碼：

import java.util.BitSet;
publicclass BloomFilter { /* BitSet初始分配2^24個bit */privatestaticfinalint DEFAULT_SIZE =1<<25; /* 不一樣哈希函數的種子，通常應取質數 */privatestaticfinalint[] seeds =newint[] { 5, 7, 11, 13, 31, 37, 61 }; private BitSet bits =new BitSet(DEFAULT_SIZE); /* 哈希函數對象 */private SimpleHash[] func =new SimpleHash[seeds.length];
public BloomFilter() { for (int i =0; i < seeds.length; i++) { func[i] =new SimpleHash(DEFAULT_SIZE, seeds[i]); } }
// 將字符串標記到bits中publicvoid add(String value) { for (SimpleHash f : func) { bits.set(f.hash(value), true); } }
//判斷字符串是否已經被bits標記publicboolean contains(String value) { if (value ==null) { returnfalse; } boolean ret =true; for (SimpleHash f : func) { ret = ret && bits.get(f.hash(value)); } return ret; }
/* 哈希函數類 */publicstaticclass SimpleHash { privateint cap; privateint seed;
public SimpleHash(int cap, int seed) { this.cap = cap; this.seed = seed; }
//hash函數，採用簡單的加權和hashpublicint hash(String value) { int result =0; int len = value.length(); for (int i =0; i < len; i++) { result = seed * result + value.charAt(i); } return (cap -1) & result; } } }

參考文獻：

[1]Pei Cao. Bloom Filters - the math.

http://pages.cs.wisc.edu/~cao/papers/summary-cache/node8.html

[2]Wikipedia. Bloom filter.

http://en.wikipedia.org/wiki/Bloom_filter

Google Guava的Bloom filter實現

/*
* Copyright (C) 2011 The Guava Authors
*
* Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
* in compliance with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software distributed under the License
* is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
* or implied. See the License for the specific language governing permissions and limitations under
* the License.
*/

package com.google.common.hash;

import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.base.Preconditions.checkNotNull;

import com.google.common.annotations.Beta;
import com.google.common.annotations.VisibleForTesting;
import com.google.common.base.Preconditions;
import com.google.common.hash.BloomFilterStrategies.BitArray;

import java.io.Serializable;

/**
* A Bloom filter for instances of {@code T}. A Bloom filter offers an approximate containment test
* with one-sided error: if it claims that an element is contained in it, this might be in error,
* but if it claims that an element is <i>not</i> contained in it, then this is definitely true.
*
* <p>If you are unfamiliar with Bloom filters, this nice
* <a href="http://llimllib.github.com/bloomfilter-tutorial/">tutorial</a> may help you understand
* how they work.
*
* @param <T> the type of instances that the {@code BloomFilter} accepts
* @author Kevin Bourrillion
* @author Dimitris Andreou
* @since 11.0
*/
@Beta
public final class BloomFilter<T> implements Serializable {
/**
* A strategy to translate T instances, to {@code numHashFunctions} bit indexes.
*/
interface Strategy extends java.io.Serializable {
/**
* Sets {@code numHashFunctions} bits of the given bit array, by hashing a user element.
*/
<T> void put(T object, Funnel<? super T> funnel, int numHashFunctions, BitArray bits);

/**
* Queries {@code numHashFunctions} bits of the given bit array, by hashing a user element;
* returns {@code true} if and only if all selected bits are set.
*/
<T> boolean mightContain(
T object, Funnel<? super T> funnel, int numHashFunctions, BitArray bits);
}

/** The bit set of the BloomFilter (not necessarily power of 2!)*/
private final BitArray bits;

/** Number of hashes per element */
private final int numHashFunctions;

/** The funnel to translate Ts to bytes */
private final Funnel<T> funnel;

/**
* The strategy we employ to map an element T to {@code numHashFunctions} bit indexes.
*/
private final Strategy strategy;

/**
* Creates a BloomFilter.
*/
private BloomFilter(BitArray bits, int numHashFunctions, Funnel<T> funnel,
Strategy strategy) {
Preconditions.checkArgument(numHashFunctions > 0, "numHashFunctions zero or negative");
this.bits = checkNotNull(bits);
this.numHashFunctions = numHashFunctions;
this.funnel = checkNotNull(funnel);
this.strategy = strategy;
}

/**
* Returns {@code true} if the element <i>might</i> have been put in this Bloom filter,
* {@code false} if this is <i>definitely</i> not the case.
*/
public boolean mightContain(T object) {
return strategy.mightContain(object, funnel, numHashFunctions, bits);
}

/**
* Puts an element into this {@code BloomFilter}. Ensures that subsequent invocations of
* {@link #mightContain(Object)} with the same element will always return {@code true}.
*/
public void put(T object) {
strategy.put(object, funnel, numHashFunctions, bits);
}

@VisibleForTesting int getHashCount() {
return numHashFunctions;
}

@VisibleForTesting double computeExpectedFalsePositiveRate(int insertions) {
return Math.pow(
1 - Math.exp(-numHashFunctions * ((double) insertions / (bits.size()))),
numHashFunctions);
}

/**
* Creates a {@code Builder} of a {@link BloomFilter BloomFilter<T>}, with the expected number
* of insertions and expected false positive probability.
*
* <p>Note that overflowing a {@code BloomFilter} with significantly more elements
* than specified, will result in its saturation, and a sharp deterioration of its
* false positive probability.
*
* <p>The constructed {@code BloomFilter<T>} will be serializable if the provided
* {@code Funnel<T>} is.
*
* @param funnel the funnel of T's that the constructed {@code BloomFilter<T>} will use
* @param expectedInsertions the number of expected insertions to the constructed
* {@code BloomFilter<T>}; must be positive
* @param falsePositiveProbability the desired false positive probability (must be positive and
* less than 1.0)
* @return a {@code Builder}
*/
public static <T> BloomFilter<T> create(Funnel<T> funnel, int expectedInsertions /* n */,
double falsePositiveProbability) {
checkNotNull(funnel);
checkArgument(expectedInsertions > 0, "Expected insertions must be positive");
checkArgument(falsePositiveProbability > 0.0 & falsePositiveProbability < 1.0,
"False positive probability in (0.0, 1.0)");
/*
* andreou: I wanted to put a warning in the javadoc about tiny fpp values,
* since the resulting size is proportional to -log(p), but there is not
* much of a point after all, e.g. optimalM(1000, 0.0000000000000001) = 76680
* which is less that 10kb. Who cares!
*/
int numBits = optimalNumOfBits(expectedInsertions, falsePositiveProbability);
int numHashFunctions = optimalNumOfHashFunctions(expectedInsertions, numBits);
return new BloomFilter<T>(new BitArray(numBits), numHashFunctions, funnel,
BloomFilterStrategies.MURMUR128_MITZ_32);
}

/**
* Creates a {@code Builder} of a {@link BloomFilter BloomFilter<T>}, with the expected number
* of insertions, and a default expected false positive probability of 3%.
*
* <p>Note that overflowing a {@code BloomFilter} with significantly more elements
* than specified, will result in its saturation, and a sharp deterioration of its
* false positive probability.
*
* <p>The constructed {@code BloomFilter<T>} will be serializable if the provided
* {@code Funnel<T>} is.
*
* @param funnel the funnel of T's that the constructed {@code BloomFilter<T>} will use
* @param expectedInsertions the number of expected insertions to the constructed
* {@code BloomFilter<T>}; must be positive
* @return a {@code Builder}
*/
public static <T> BloomFilter<T> create(Funnel<T> funnel, int expectedInsertions /* n */) {
return create(funnel, expectedInsertions, 0.03); // FYI, for 3%, we always get 5 hash functions
}

/*
* Cheat sheet:
*
* m: total bits
* n: expected insertions
* b: m/n, bits per insertion

* p: expected false positive probability
*
* 1) Optimal k = b * ln2
* 2) p = (1 - e ^ (-kn/m))^k
* 3) For optimal k: p = 2 ^ (-k) ~= 0.6185^b
* 4) For optimal k: m = -nlnp / ((ln2) ^ 2)
*/

private static final double LN2 = Math.log(2);
private static final double LN2_SQUARED = LN2 * LN2;

/**
* Computes the optimal k (number of hashes per element inserted in Bloom filter), given the
* expected insertions and total number of bits in the Bloom filter.
*
* See http://en.wikipedia.org/wiki/File:Bloom_filter_fp_probability.svg for the formula.
*
* @param n expected insertions (must be positive)
* @param m total number of bits in Bloom filter (must be positive)
*/
@VisibleForTesting static int optimalNumOfHashFunctions(int n, int m) {
return Math.max(1, (int) Math.round(m / n * LN2));
}

/**
* Computes m (total bits of Bloom filter) which is expected to achieve, for the specified
* expected insertions, the required false positive probability.
*
* See http://en.wikipedia.org/wiki/Bloom_filter#Probability_of_false_positives for the formula.
*
* @param n expected insertions (must be positive)
* @param p false positive rate (must be 0 < p < 1)
*/
@VisibleForTesting static int optimalNumOfBits(int n, double p) {
return (int) (-n * Math.log(p) / LN2_SQUARED);
}

private Object writeReplace() {
return new SerialForm<T>(this);
}

private static class SerialForm<T> implements Serializable {
final long[] data;
final int numHashFunctions;
final Funnel<T> funnel;
final Strategy strategy;

SerialForm(BloomFilter<T> bf) {
this.data = bf.bits.data;
this.numHashFunctions = bf.numHashFunctions;
this.funnel = bf.funnel;
this.strategy = bf.strategy;
}
Object readResolve() {
return new BloomFilter<T>(new BitArray(data), numHashFunctions, funnel, strategy);
}
private static final long serialVersionUID = 1;
}
}

本質是BitSet，適用可容忍必定錯誤的場景，優點是高效、佔用空間小；

3億個KEY，每一個實例映射1W KEY，須要3W個實例，佔用空間約600M。