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https://issues.apache.org/jira/browse/LUCENE-2089?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12836372#action_12836372
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Robert Muir commented on LUCENE-2089:
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Mike, this is awesome!
We can use the junit test case to test N=1 once we get to a nice place with
this.
The way it works is, it builds an NFA for N=1, and compares it with the results
of this with Automaton.equals, which ensures they accept the same language.
The test already checks this for all possible characteristic vectors, so if you
believe the paper, and the tests pass, then its correct for all strings.
Testing the correctness of N=2 is harder, we can use the same principles I
think, but no automaton.equals as I don't know how to generate an NFA for N=2,
even slowly.
instead I think we will have to verify against the actual levenshtein distance
formula, but i think that verifying for all permutations of an alphabet of size
2n+1, for a string of length at least 2n+1 should be sufficient.
(i plan to also randomly brute-force test the new query against the old fuzzy
query at some point, in any case)
in my opinion we should take the lessons learned from N=2 and if successful,
regenerate N=1 too, as the way I "keyed it in" is likely not the best or most
compact.
> explore using automaton for fuzzyquery
> --------------------------------------
>
> Key: LUCENE-2089
> URL: https://issues.apache.org/jira/browse/LUCENE-2089
> Project: Lucene - Java
> Issue Type: Improvement
> Components: Search
> Affects Versions: Flex Branch
> Reporter: Robert Muir
> Assignee: Mark Miller
> Priority: Minor
> Fix For: Flex Branch
>
> Attachments: ContrivedFuzzyBenchmark.java, gen.py,
> Lev2ParametricDescription.java, LUCENE-2089.patch, LUCENE-2089.patch,
> LUCENE-2089.patch, LUCENE-2089.patch, LUCENE-2089.patch,
> LUCENE-2089_concat.patch, Moman-0.2.1.tar.gz, TestFuzzy.java
>
>
> we can optimize fuzzyquery by using AutomatonTermsEnum. The idea is to speed
> up the core FuzzyQuery in similar fashion to Wildcard and Regex speedups,
> maintaining all backwards compatibility.
> The advantages are:
> * we can seek to terms that are useful, instead of brute-forcing the entire
> terms dict
> * we can determine matches faster, as true/false from a DFA is array lookup,
> don't even need to run levenshtein.
> We build Levenshtein DFAs in linear time with respect to the length of the
> word: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.652
> To implement support for 'prefix' length, we simply concatenate two DFAs,
> which doesn't require us to do NFA->DFA conversion, as the prefix portion is
> a singleton. the concatenation is also constant time with respect to the size
> of the fuzzy DFA, it only need examine its start state.
> with this algorithm, parametric tables are precomputed so that DFAs can be
> constructed very quickly.
> if the required number of edits is too large (we don't have a table for it),
> we use "dumb mode" at first (no seeking, no DFA, just brute force like now).
> As the priority queue fills up during enumeration, the similarity score
> required to be a competitive term increases, so, the enum gets faster and
> faster as this happens. This is because terms in core FuzzyQuery are sorted
> by boost value, then by term (in lexicographic order).
> For a large term dictionary with a low minimal similarity, you will fill the
> pq very quickly since you will match many terms.
> This not only provides a mechanism to switch to more efficient DFAs (edit
> distance of 2 -> edit distance of 1 -> edit distance of 0) during
> enumeration, but also to switch from "dumb mode" to "smart mode".
> With this design, we can add more DFAs at any time by adding additional
> tables. The tradeoff is the tables get rather large, so for very high K, we
> would start to increase the size of Lucene's jar file. The idea is we don't
> have include large tables for very high K, by using the 'competitive boost'
> attribute of the priority queue.
> For more information, see http://en.wikipedia.org/wiki/Levenshtein_automaton
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