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### 15.2 Part 2 - Quickly Finding Similar Soundslike

In order for Aspell to find suggestions for a misspelled word Aspell 1) creates a list of candidate words, 2) scores them, and 3) returns the most likely candidates. One of the ways Aspell finds candidate words is to look for all words with a soundslike which is of a small edit distance from the soundslike of the original word. The edit distance is the total number of deletions, insertions, exchanges, or adjacent swaps needed to make one string equivalent to the other. The exact distance chosen is either 1 or 2 depending on a number of factors. In this part I will focus on how Aspell find all such soundslike efficiently and how the jump tables play a key role.

This section will focus on how Aspell finds all such soundslike efficiently and how the jump tables play a key role.

The naive way to scan the list for all possible soundslike is to compute the edit-distance of every soundslike in the dictionary and then keep the ones within the threshold. This is exactly what Aspell did prior to 0.60. before a faster method was created. When a fast enough edit distance function is used this method turns out not to be unbearably slow, at least for English, but for other languages, with large word lists and no soundslike, this can be slow due to the number of items that need to be scanned.

Aspell uses a special edit distance function which gives up if the distance is larger than the threshold, thus making it very fast. The basic algorithm is as follows:

    limit_edit_distance(A,B,limit) = ed(A,B,0)
      where ed(A,B,d) = d                              if A & B is empty.
                      = infinity                       if d > limit
                      = ed(A[2..],B[2..], d)           if A[1] == B[1]
                      = min ( ed(A[2..],B[2..], d+1),
                              ed(A,     B[2..], d+1),
                              ed(A[2..],B,      d+1) ) otherwise

However the algorithm used also allows for swaps and is not recursive. Specialized versions are provided for an edit distance of one and two. The running time is asymptotically bounded above by `(3^l)*n` where `l` is the limit and `n` is the maximum of `strlen(A),strlen(B)`. Based on informal tests, the `n` does not really matter and the running time is more like `(3^l)`.

For complete details on this algorithm see the files `leditdist.hpp` and `leditdist.cpp` in the source distribution under `modules/speller/default`.

So, by exploiting the properties of `limit_edit_distance` it is possible to avoid having to look at many of the soundslikes in the dictionary. `Limit_edit_distance` is efficient because in many cases, it does not have to look at the entire word before it can determine that it isn’t within the given threshold, and then by having it return the last position looked at, p, it is possible to avoid having to look at similar soundslike which are not within the threshold. That is, if two soundslike are the same up to the position `p`, then neither of them are within the given threshold.

Aspell 0.60 exploits this property by using jump tables. Each entry in the jump table contains two fields: the first `N` letters of a soundslike, and an offset. The entries are sorted in lexicographic order based on the raw byte value. Aspell maintains two jump tables.

The first table contains the first 2 letters of a soundslike and the offset points into the second jump table.

The second table contains the first 3 letters of a soundslike where the offset points to the location of the soundslike in the data block. The soundslike in the datablock are sorted so that a linear scan can be used to find all soundslike with the same prefix. If the `limit_edit_distance` stops before reaching the end of a "soundslike" in one of the jump tables then it is possible to skip all the soundslike in the data block with the same prefix.

Thus, the scan for all soundslike within a given edit distance goes something like this:

1. Compare the entry in the first jump table using `limit_edit_distance`. If the `limit_edit_distance` scanned passed the end of the word, then go to the first entry in the second jump table with the same prefix, otherwise go to the next entry in the first jump table and repeat.
2. Compare the entry in the second jump table. If the `limit_edit_distance` passed the end of the word, then go to the first soundslike in the data block with this prefix, otherwise if the first two letters of the next entry are the same as the current one go to it and repeat. If the first two letters are not the same then go to the next entry in the first jump table and repeat step 1.
3. Compare the soundslike in the data block. If the edit distance is within the target distance, then add the word to the candidate list, otherwise don’t. Let `N` be the position where `limit_edit_distance` stopped, (starting at 0). If `N` is less than 6, then skip over any soundslike that have the same first `N + 1` letters. If after skipping over any similar soundslike the next soundslike does not have the same first three letters, then go to the next entry in the second jump table and repeat step 2, otherwise repeat this step with the next soundslike.

The part of skipping over soundslike with the first `N + 1` letters in step 3 were added in Aspell 0.60.3. The function responsible for most of this is found in function `ReadOnlyDict::SoundslikeElements::next` which is found in file `readonly_ws.cpp`.

The next part will describe how Aspell deals with soundslike lookup when affix compression is involved.

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