How Aspell Works: 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.

In order two find all possible soundslike within a fixed edit distance one 
of two things can be tried.  1) Use trial an error by trying all possible 
edits and then seeing if they are in the dictionary, and 2) Scan the 
dictionary for possible soundslikes.  Before Aspell 0.60 Aspell used the 
first method when the edit distance was one and the second otherwise.
Aspell now uses the second method for both methods as I was able to make 
the scan very efficient, therefore saving the space of having to store a 
separate hash table for the soundslike.

The naive way to scan the list for all possible soundslike is to compute 
the edit-distance of every soundslike in the dictionary and keep the ones 
within the threshold.  This is exactly what Aspell did prior to 0.60. 
When a fast enough edit distance function is used this method turns out 
not to be unbearably slow, at least for English.  For other languages, 
with large word lists and no soundslike, it can be slow due to the number 
of items 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 version 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 my informal 
tests, however, 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.

By exploiting the properties of limit_edit_distance is possible to avoid 
having to look many of the soundslike in the dictionary. 
Limit_edit_distance is effecent because in many cases it doesn't have to 
look at the entire word before determine that it isn't within the given 
threshold.  By having it return the last position looked at, "p", it is 
possible to avoid having to look ta similar soundslike which are not 
within in threshold.  That is if two soundslike are the same up to the 
position "p" than nether 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 one 
contains the first 2 letter of a soundslike and the offset points into the 
second jump table.  The second one 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 
limit_edit_distance stops before reaching the end of a "soundslike" in the 
one of the jump tables than 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 limit_edit_distance scanned passed the end of the word than go 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 limit_edit_distance
      passed the end of the word than go 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 it and repeat.  If the
      first two letters are not the same than 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 add 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 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 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 was added in Aspell 0.60.3.  The function responsible for most of this 
is ReadOnlyDict::SoundslikeElements::next found in readonly_ws.cpp

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