如何加快Levenshtein距离计算

Question

我正在尝试运行模拟来测试随机二进制字符串之间的平均Levenshtein距离.

我的程序是在python中,但我正在使用此C扩展.大部分时间相关的函数计算两个字符串之间的Levenshtein距离,就是这个.

lev_edit_distance(size_t len1, const lev_byte *string1,
                  size_t len2, const lev_byte *string2,
                  int xcost)
{
  size_t i;
  size_t *row;  /* we only need to keep one row of costs */
  size_t *end;
  size_t half;

  /* strip common prefix */
  while (len1 > 0 && len2 > 0 && *string1 == *string2) {
    len1--;
    len2--;
    string1++;
    string2++;
  }

  /* strip common suffix */
  while (len1 > 0 && len2 > 0 && string1[len1-1] == string2[len2-1]) {
    len1--;
    len2--;
  }

  /* catch trivial cases */
  if (len1 == 0)
    return len2;
  if (len2 == 0)
    return len1;

  /* make the inner cycle (i.e. string2) the longer one */
  if (len1 > len2) {
    size_t nx = len1;
    const lev_byte *sx = string1;
    len1 = len2;
    len2 = nx;
    string1 = string2;
    string2 = sx;
  }
  /* check len1 == 1 separately */
  if (len1 == 1) {
    if (xcost)
      return len2 + 1 - 2*(memchr(string2, *string1, len2) != NULL);
    else
      return len2 - (memchr(string2, *string1, len2) != NULL);
  }
  len1++;
  len2++;
  half = len1 >> 1;
  /* initalize first row */
  row = (size_t*)malloc(len2*sizeof(size_t));
  if (!row)
    return (size_t)(-1);
  end = row + len2 - 1;
  for (i = 0; i < len2 - (xcost ? 0 : half); i++)
    row[i] = i;

  /* go through the matrix and compute the costs.  yes, this is an extremely
   * obfuscated version, but also extremely memory-conservative and relatively
   * fast.  */
  if (xcost) {
    for (i = 1; i < len1; i++) {
      size_t *p = row + 1;
      const lev_byte char1 = string1[i - 1];
      const lev_byte *char2p = string2;
      size_t D = i;
      size_t x = i;
      while (p <= end) {
        if (char1 == *(char2p++))
          x = --D;
        else
          x++;
        D = *p;
        D++;
        if (x > D)
          x = D;
        *(p++) = x;
      }
    }
  }
  else {
    /* in this case we don't have to scan two corner triangles (of size len1/2)
     * in the matrix because no best path can go throught them. note this
     * breaks when len1 == len2 == 2 so the memchr() special case above is
     * necessary */
    row[0] = len1 - half - 1;
    for (i = 1; i < len1; i++) {
      size_t *p;
      const lev_byte char1 = string1[i - 1];
      const lev_byte *char2p;
      size_t D, x;
      /* skip the upper triangle */
      if (i >= len1 - half) {
        size_t offset = i - (len1 - half);
        size_t c3;

        char2p = string2 + offset;
        p = row + offset;
        c3 = *(p++) + (char1 != *(char2p++));
        x = *p;
        x++;
        D = x;
        if (x > c3)
          x = c3;
        *(p++) = x;
      }
      else {
        p = row + 1;
        char2p = string2;
        D = x = i;
      }
      /* skip the lower triangle */
      if (i <= half + 1)
        end = row + len2 + i - half - 2;
      /* main */
      while (p <= end) {
        size_t c3 = --D + (char1 != *(char2p++));
        x++;
        if (x > c3)
          x = c3;
        D = *p;
        D++;
        if (x > D)
          x = D;
        *(p++) = x;
      }
      /* lower triangle sentinel */
      if (i <= half) {
        size_t c3 = --D + (char1 != *char2p);
        x++;
        if (x > c3)
          x = c3;
        *p = x;
      }
    }
  }

  i = *end;
  free(row);
  return i;
}

这可以加快吗？

我将在AMD FX(tm)-8350八核处理器上运行32位ubuntu代码.

这是调用它的python代码.

from Levenshtein import distance
import random
for i in xrange(16):
    sum = 0
    for j in xrange(1000):
        str1 = bin(random.getrandbits(2**i))[2:].zfill(2**i)
        str2 = bin(random.getrandbits(2**i))[2:].zfill(2**i)
        sum += distance(str1,str2)
    print i,sum/(1000*2**i)

Answer 1

您可以首先从以下站点学习一些 OpenMP 概念和指令：A初学者的 OpenMP 入门

您需要一个与 OpenMP 兼容的编译器。这里是一个可以工作的编译器的列表。-fopenmp您将需要在编译代码时使用该选项。

我只是将编译器指令添加#pragma omp parallel for到您的代码中，以告诉编译器以下代码块可以并行运行。通过将 while 循环更改为 for 循环，或者在整个函数中应用 OpenMP 模式，您可以看到性能的额外提升。您可以通过在这些块之前使用函数来调整用于执行 for 循环的线程数来调整性能omp_set_num_threads()。最好从 8 开始，因为您将在 8 核处理器上运行。

lev_edit_distance(size_t len1, const lev_byte *string1,
              size_t len2, const lev_byte *string2,
              int xcost)
{
  size_t i;
  size_t *row;  /* we only need to keep one row of costs */
  size_t *end;
  size_t half;

 // Set the number of threads the OpenMP framework will use to parallelize the for loops
 omp_set_num_threads(8);

  /* strip common prefix */
  while (len1 > 0 && len2 > 0 && *string1 == *string2) {
    len1--;
    len2--;
    string1++;
    string2++;
  }

  /* strip common suffix */
  while (len1 > 0 && len2 > 0 && string1[len1-1] == string2[len2-1]) {
    len1--;
    len2--;
  }

  /* catch trivial cases */
  if (len1 == 0)
    return len2;
  if (len2 == 0)
    return len1;

  /* make the inner cycle (i.e. string2) the longer one */
  if (len1 > len2) {
    size_t nx = len1;
    const lev_byte *sx = string1;
    len1 = len2;
    len2 = nx;
    string1 = string2;
    string2 = sx;
  }
  /* check len1 == 1 separately */
  if (len1 == 1) {
    if (xcost)
      return len2 + 1 - 2*(memchr(string2, *string1, len2) != NULL);
    else
      return len2 - (memchr(string2, *string1, len2) != NULL);
  }
  len1++;
  len2++;
  half = len1 >> 1;
  /* initalize first row */
  row = (size_t*)malloc(len2*sizeof(size_t));
  if (!row)
    return (size_t)(-1);
  end = row + len2 - 1;

  #pragma omp parallel for
  for (i = 0; i < len2 - (xcost ? 0 : half); i++)
    row[i] = i;

  /* go through the matrix and compute the costs.  yes, this is an extremely
   * obfuscated version, but also extremely memory-conservative and relatively
   * fast.  */
  if (xcost) {
   #pragma omp parallel for
   for (i = 1; i < len1; i++) {
      size_t *p = row + 1;
      const lev_byte char1 = string1[i - 1];
      const lev_byte *char2p = string2;
      size_t D = i;
      size_t x = i;
      while (p <= end) {
        if (char1 == *(char2p++))
          x = --D;
        else
          x++;
        D = *p;
        D++;
        if (x > D)
          x = D;
        *(p++) = x;
      }
    }
  }
  else {
    /* in this case we don't have to scan two corner triangles (of size len1/2)
     * in the matrix because no best path can go throught them. note this
     * breaks when len1 == len2 == 2 so the memchr() special case above is
     * necessary */
    row[0] = len1 - half - 1;
    #pragma omp parallel for
    for (i = 1; i < len1; i++) {
      size_t *p;
      const lev_byte char1 = string1[i - 1];
      const lev_byte *char2p;
      size_t D, x;
      /* skip the upper triangle */
      if (i >= len1 - half) {
        size_t offset = i - (len1 - half);
        size_t c3;

        char2p = string2 + offset;
        p = row + offset;
        c3 = *(p++) + (char1 != *(char2p++));
        x = *p;
        x++;
        D = x;
        if (x > c3)
          x = c3;
        *(p++) = x;
      }
      else {
        p = row + 1;
        char2p = string2;
        D = x = i;
      }
      /* skip the lower triangle */
      if (i <= half + 1)
        end = row + len2 + i - half - 2;
      /* main */
      while (p <= end) {
        size_t c3 = --D + (char1 != *(char2p++));
        x++;
        if (x > c3)
          x = c3;
        D = *p;
        D++;
        if (x > D)
          x = D;
        *(p++) = x;
      }
      /* lower triangle sentinel */
       if (i <= half) {
        size_t c3 = --D + (char1 != *char2p);
        x++;
        if (x > c3)
          x = c3;
        *p = x;
      }
    }
  }

  i = *end;
  free(row);
  return i;
}

您还可以对 for 循环中正在操作的变量进行归约运算，以提供简单的并行计算，例如求和、乘法等。

int main()
{
    int i = 0,
        j = 0,
        sum = 0;
    char str1[30]; // Change size to fit your specifications
    char str2[30];

    #pragma omp parallel for
    for(i=0;i<16;i++)
    {
        sum = 0;
            // Could do a reduction on sum across all threads
        for(j=0;j<1000;j++)
        {
            // Calls will have to be changed
            // I don't know much Python so I'll leave that to the experts 
            str1 = bin(random.getrandbits(2**i))[2:].zfill(2**i)
            str2 = bin(random.getrandbits(2**i))[2:].zfill(2**i)
            sum += distance(str1,str2)
        }
        printf("%d %d",i,(sum/(1000*2*i)));
    }
}