数据相似性检测算法

1、引言
　　"数据同步算法研究"一文研究了在网络上高效同步数据的方法，其中有个前提是文件A和B非常相似，即两者之间存在大量相同的数据。如果两个文件相似性很低，虽然这种方法依然可以正常工作，但数据同步性能却不会得到提高，甚至会有所降低。因为会产生部分元数据和网络通信消耗，这在两个文件完全不相关时尤为明显。因此，同步数据前需要计算种子文件(seed file)与目标文件之间的相似性，如果相似性大于指定阈值(通常应大于50%)则应用该数据同步算法，否则接传输文件即可。如此，可使得数据同步算法则具有较好的自适应性，在数据具有不同相似性的情形下均可进行高性能的数据同步。另外，在数据相似性检测的基础之上，可对于相似性高的数据进行数据编码处理(如Delta编码)，通过一个文件给另一个文件编码的方式进行数据压缩，这是一种基于相似数据检测与编码的重复数据删除技术。
2、相似性计算
　　Unix diff对文档进行逐行对比来检测相似文件，它采用经典的LCS(Longest Common Subsequence，最长公共子串)算法，运用动态规划方法来计算相似性。LCS的含义是同时包含在字符串里的一个最长字符序列，LCS的长度作为这两个字符串相似性的度量。Diff算法以整行作为"字符"来计算最长公共子串，性能上比字符级的LCS算法快很多。这种方法效率很低，而且只适用文本文件的相似比较，不能直接适用于二进制文件。

　　目前通常的做法是将文件相似性问题转换为集合相似性问题，如基于shingle的计算方法和基于bloom filter的计算方法，这两种方法都可适用于任何格式的数据文件。这种方式的核心思想是为每个文件提取组特征值，以特征值集合来计算相似性，从而降低计算复杂性来提高性能。shingle用特征值交集来计算相似性会导致高计算和空间开销，bloom filter技术在计算开销和匹配精度上更具势。Bloom filter所定义的集合元素是文件按照CDC(content-defined chunking)算法所切分数据块的指纹值，其相似性定义如下：
                            |fingerprints(f1) ∩ fingerprints(f2)|
　　Sim(f1, f2) = ---------------------------------------------   (公式1)
                            |fingerprints(f1) ∪ fingerprints(f2)|

　　另外一种方法，是将二进制文件进行切块，使用数据块指纹来表示数据块，然后将数据块映射为"字符"，再应用LCS算法寻找最大公共子串并计算出相似度。其相似性定义如下：
　　                      2 * length(LCS(fingerprints(f1), fingerprints(f2)))
    Sim(f1, f2) = ------------------------------------------------------------------　(公式2)
                           length(fingerprints(f1)) + length(fingerprints(f2))

　　上面两种相似性算法中均采用数据切分技术，数据块可以是定长或变长。为了相似性计算的精确性，实现中采用以数据块长度作为权的加权计算方法。

3、Bloom filter算法
　　该文件相似性计算流程如下：
      (1) 采用CDC算法将文件切分成数据块集，并为每个数据块计算MD5指纹；
      (2) 计算两个指纹集合的交集和并集，通过hashtable来实现；
      (3) 按照公式1计算文件相似性，考虑重复数据块和数据块长度来提高计算精确度。
      详细参见附录bsim源码中的file_chunk，chunk_file_process和similarity_detect函数实现。

4、LCS算法
　　该文件相似性计算流程如下：
    (1) 采用CDC算法将文件切分成数据块集，并为每个数据块计算MD5指纹；
    (2) 将MD5指纹串映射为"字符"，则文件转换为"字符串"表示；
    (3) 应用LCS算法计算出最长公共子串，并计算其加权长度；
    (4) 按照公式2计算文件相似性，考虑重复数据块和数据块长度来提高计算精确度。
    详细参见附录bsim源码中的file_chunk，chunk_file_process，LCS和similarity_detect函数实现。

5、算法分析比较
　两种算法都对文件进行切分操作，假设文件f1切为m个块，文件f2切分成n个块。Bloom filter算法没有考虑数据块顺序，因此在相似性精确度方面要低于LCS算法，其时间和空间复杂性都是O(m + n)。相反，LCS算法考虑了数据块顺序问题，相似性度量相对精确，然而其时间和空间复杂性是O(mn)，这个大大限制了应用规模。综合来看，Bloom filter算法精确度比LCS算法要低，但计算消耗要小很多，性能和适用性非常好。LCS比较适合精确的文件相似性计算，这些文件往往比较小，50MB以内比较合适。对于重复数据删除和网络数据同步来说，消重效果和性能与数据块顺序性无关，因此Bloom filter算法计算的数据相似性更适用，性能也更高。

附录：bsim.c源码
(完整源码请参见deduputil源码)
/* Copyright (C) 2010 Aigui Liu * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License along * with this program; if not, visit the http://fsf.org website. */#include <stdio.h>#include <stdlib.h>#include <string.h>#include <sys/types.h>#include <sys/stat.h>#include <fcntl.h>#include <unistd.h>#include "hashtable.h"#include "sync.h"#define NEITHER 0#define UP 1#define LEFT 2#define UP_AND_LEFT 3#define MAX(x, y) (((x) > (y)) ? (x) : (y))#define MIN(x, y) (((x) < (y)) ? (x) : (y))#define MD5_LEN17enum {FILE1 = 0,FILE2};enum {LCS_NOT = 0,LCS_YES};typedef struct {uint32_t nr1;uint32_t nr2;uint32_t len;} hash_entry;typedef struct {char **str;uint32_t len;} lcs_entry;static uint32_t sim_union = 0;static uint32_t sim_intersect = 0;static void usage(){fprintf(stderr, "Usage: bsim FILE1 FILE2 CHUNK_ALGO LCS/n/n");fprintf(stderr, "Similarity detect between FILE1 and FILE2 based on block level./n");fprintf(stderr, "CHUNK_ALGO:/n");fprintf(stderr, " FSP - fixed-size partition/n");fprintf(stderr, " CDC - content-defined chunking/n");fprintf(stderr, " SBC - slide block chunking/n/n");fprintf(stderr, "LCS:/n");fprintf(stderr, " LCS_NOT - do not use LCS(longest lommon subsequence) algorithms/n");fprintf(stderr, " LCS_YES - use LCS algorithms/n/n");fprintf(stderr, "Report bugs to <[e-mail]>./n");}static int parse_arg(char *argname){if (0 == strcmp(argname, "FSP"))return CHUNK_FSP;else if (0 == strcmp(argname, "CDC"))return CHUNK_CDC;else if (0 == strcmp(argname, "SBC"))return CHUNK_SBC;else if (0 == strcmp(argname, "LCS_NOT"))return LCS_NOT;else if (0 == strcmp(argname, "LCS_YES"))return LCS_YES;elsereturn -1;}static char **alloc_2d_array(int row, int col){ int i; char *p, **pp; p = (char *)malloc(row * col * sizeof(char)); pp = (char **)malloc(row * sizeof(char *)); if (p == NULL || pp == NULL) return NULL; for (i = 0; i < row; i++) { pp[i] = p + col * i; } return pp;}static void free_2d_array(char **str){free(str[0]);free(str);}static void show_md5_hex(unsigned char md5_checksum[16]){ int i; for (i = 0; i < 16; i++) { printf("%02x", md5_checksum[i]); } printf("/n");}static int chunk_file_process(char *chunk_file, hashtable *htab, int which, int sim_algo, lcs_entry *le){int fd, i, ret = 0;ssize_t rwsize;chunk_file_header chunk_file_hdr;chunk_block_entry chunk_bentry;hash_entry *he = NULL;/* parse chunk file */fd = open(chunk_file, O_RDONLY);if (-1 == fd) {return -1;}rwsize = read(fd, &chunk_file_hdr, CHUNK_FILE_HEADER_SZ);if (rwsize != CHUNK_FILE_HEADER_SZ) {ret = -1;goto _CHUNK_FILE_PROCESS_EXIT;}if (sim_algo == LCS_YES) {le->str = alloc_2d_array(chunk_file_hdr.block_nr, MD5_LEN);if (le->str == NULL) {ret = -1;goto _CHUNK_FILE_PROCESS_EXIT;}le->len = chunk_file_hdr.block_nr;}for(i = 0; i < chunk_file_hdr.block_nr; i++) {rwsize = read(fd, &chunk_bentry, CHUNK_BLOCK_ENTRY_SZ);if (rwsize != CHUNK_BLOCK_ENTRY_SZ) {ret = -1;goto _CHUNK_FILE_PROCESS_EXIT;}he = (hash_entry *)hash_value((void *)chunk_bentry.md5, htab);if (he == NULL) {he = (hash_entry *)malloc(sizeof(hash_entry));he->nr1 = he->nr2 = 0;he->len = chunk_bentry.len;}(which == FILE1) ? he->nr1++ : he->nr2++;/* insert or update hash entry */hash_insert((void *)strdup(chunk_bentry.md5), (void *)he, htab);if (sim_algo == LCS_YES) {memcpy(le->str[i], chunk_bentry.md5, MD5_LEN);}}_CHUNK_FILE_PROCESS_EXIT:close(fd);return ret;}uint32_t LCS(char** a, int n, char** b, int m, hashtable *htab) { int** S; int** R; int ii; int jj; int pos; uint32_t len = 0;hash_entry *he = NULL;/* Memory allocation */ S = (int **)malloc( (n+1) * sizeof(int *) ); R = (int **)malloc( (n+1) * sizeof(int *) );if (S == NULL || R == NULL) {perror("malloc for S and R in LCS");exit(0);} for(ii = 0; ii <= n; ++ii) { S[ii] = (int*) malloc( (m+1) * sizeof(int) ); R[ii] = (int*) malloc( (m+1) * sizeof(int) );if (S[ii] == NULL || R[ii] == NULL) {perror("malloc for S[ii] and R[ii] in LCS");exit(0);} } /* It is important to use <=, not <. The next two for-loops are initialization */ for(ii = 0; ii <= n; ++ii) { S[ii][0] = 0; R[ii][0] = UP; } for(jj = 0; jj <= m; ++jj) { S[0][jj] = 0; R[0][jj] = LEFT; } /* This is the main dynamic programming loop that computes the score and */ /* backtracking arrays. */ for(ii = 1; ii <= n; ++ii) { for(jj = 1; jj <= m; ++jj) { if (strcmp(a[ii-1], b[jj-1]) == 0) { S[ii][jj] = S[ii-1][jj-1] + 1; R[ii][jj] = UP_AND_LEFT; } else { S[ii][jj] = S[ii-1][jj-1] + 0; R[ii][jj] = NEITHER; } if( S[ii-1][jj] >= S[ii][jj] ) { S[ii][jj] = S[ii-1][jj]; R[ii][jj] = UP; } if( S[ii][jj-1] >= S[ii][jj] ) { S[ii][jj] = S[ii][jj-1]; R[ii][jj] = LEFT; } } } /* The length of the longest substring is S[n][m] */ ii = n; jj = m; pos = S[ii][jj]; /* Trace the backtracking matrix. */ while( ii > 0 || jj > 0 ) { if( R[ii][jj] == UP_AND_LEFT ) { ii--; jj--; //lcs[pos--] = a[ii];he = (hash_entry *)hash_value((void *)a[ii], htab);len += ((he == NULL) ? 0: he->len); } else if( R[ii][jj] == UP ) { ii--; } else if( R[ii][jj] == LEFT ) { jj--; } } for(ii = 0; ii <= n; ++ii ) { free(S[ii]); free(R[ii]); } free(S); free(R);return len;}int hash_callback(void *key, void *data){hash_entry *he = (hash_entry *)data;sim_union += (he->len * (he->nr1 + he->nr2));sim_intersect += (he->len * MIN(he->nr1, he->nr2));}static float similarity_detect(hashtable *htab, char **str1, int n, char **str2, int m, int sim_algo){uint32_t lcs_len = 0;hash_for_each_do(htab, hash_callback);if (sim_algo == LCS_YES) {lcs_len = LCS(str1, n, str2, m, htab);return lcs_len * 2.0 / sim_union;} else { /* LCS_NOT */return sim_intersect * 2.0 / sim_union;}}int main(int argc, char *argv[]){int chunk_algo = CHUNK_CDC;int sim_algo = LCS_NOT;char *file1 = NULL;char *file2 = NULL;lcs_entry le1, le2;char tmpname[NAME_MAX_SZ] = {0};char template[] = "deduputil_bsim_XXXXXX";hashtable *htab = NULL;int ret = 0;if (argc < 5) {usage();return -1;}/* parse chunk algorithms */file1 = argv[1];file2 = argv[2];chunk_algo = parse_arg(argv[3]);sim_algo = parse_arg(argv[4]);if (chunk_algo == -1 || sim_algo == -1) {usage();return -1;}htab = create_hashtable(HASHTABLE_BUCKET_SZ);if (htab == NULL) {fprintf(stderr, "create hashtabke failed/n");return -1;}/* chunk file1 and file2 into blocks */sprintf(tmpname, "/tmp/%s_%d", mktemp(template), getpid());ret = file_chunk(file1, tmpname, chunk_algo);if (0 != ret) {fprintf(stderr, "chunk %s failed/n", file1);goto _BENCODE_EXIT;}le1.str = NULL;ret = chunk_file_process(tmpname, htab, FILE1, sim_algo, &le1);if (ret != 0) {fprintf(stderr, "pasre %s failed/n", file1);goto _BENCODE_EXIT;}ret = file_chunk(file2, tmpname, chunk_algo);if (0 != ret){fprintf(stderr, "chunk %s failed/n", file2);goto _BENCODE_EXIT;}le2.str = NULL;ret = chunk_file_process(tmpname, htab, FILE2, sim_algo, &le2);if (ret != 0) {fprintf(stderr, "pasre %s failed/n", file2);goto _BENCODE_EXIT;}fprintf(stderr, "similarity = %.4f/n", similarity_detect(htab, le1.str, le1.len, le2.str, le2.len, sim_algo));_BENCODE_EXIT:unlink(tmpname);hash_free(htab);if (le1.str) free_2d_array(le1.str);if (le2.str) free_2d_array(le2.str);return ret;}