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https://issues.apache.org/jira/browse/LUCENE-2089?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12832058#action_12832058
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Robert Muir commented on LUCENE-2089:
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Fuad yes, this is the problem with the paper you listed. in my opinion the
paper you mentioned is actually better/simpler in some ways than what we are
using, but the problem is the term dictionary would have to be restructured for
this, or we would have to keep all terms in RAM or something worse.
the advantage of the (more complex) 2002 paper is that we can run it on
lucene's existing term dictionary, and it will seek to the right spots (i.e.
you can take the code i attached here, and pass it to automatonquery and it
executes efficiently).
its also extremely fast algorithm, the construction of the DFA itself is O(n)
where n is the length of the word.
i tried to make a visual description of how Automaton works for regexp,
wildcard, and fuzzy here if you are interested:
http://rcmuir.wordpress.com/2009/12/04/finite-state-queries-for-lucene/
in short, AutomatonQuery can be viewed as a simplified form of the DFA
intersection presented in the paper you linked to (section 5.1). The lucene
term dictionary itself is a trie of terms in sorted order, therefore it is also
a DFA in the mathematical sense.
> explore using automaton for fuzzyquery
> --------------------------------------
>
> Key: LUCENE-2089
> URL: https://issues.apache.org/jira/browse/LUCENE-2089
> Project: Lucene - Java
> Issue Type: Wish
> Components: Search
> Reporter: Robert Muir
> Assignee: Mark Miller
> Priority: Minor
> Attachments: LUCENE-2089.patch, Moman-0.2.1.tar.gz, TestFuzzy.java
>
>
> Mark brought this up on LUCENE-1606 (i will assign this to him, I know he is
> itching to write that nasty algorithm)
> we can optimize fuzzyquery by using AutomatonTermsEnum, here is my idea
> * up front, calculate the maximum required K edits needed to match the users
> supplied float threshold.
> * for at least small common E up to some max K (1,2,3, etc) we should create
> a DFA for each E.
> if the required E is above our supported max, we use "dumb mode" at first (no
> seeking, no DFA, just brute force like now).
> As the pq fills, we swap progressively lower DFAs into the enum, based upon
> the lowest score in the pq.
> This should work well on avg, at high E, you will typically fill the pq very
> quickly since you will match many terms.
> This not only provides a mechanism to switch to more efficient DFAs during
> enumeration, but also to switch from "dumb mode" to "smart mode".
> i modified my wildcard benchmark to generate random fuzzy queries.
> * Pattern: 7N stands for NNNNNNN, etc.
> * AvgMS_DFA: this is the time spent creating the automaton (constructor)
> ||Pattern||Iter||AvgHits||AvgMS(old)||AvgMS (new,total)||AvgMS_DFA||
> |7N|10|64.0|4155.9|38.6|20.3|
> |14N|10|0.0|2511.6|46.0|37.9|
> |28N|10|0.0|2506.3|93.0|86.6|
> |56N|10|0.0|2524.5|304.4|298.5|
> as you can see, this prototype is no good yet, because it creates the DFA in
> a slow way. right now it creates an NFA, and all this wasted time is in
> NFA->DFA conversion.
> So, for a very long string, it just gets worse and worse. This has nothing to
> do with lucene, and here you can see, the TermEnum is fast (AvgMS -
> AvgMS_DFA), there is no problem there.
> instead we should just build a DFA to begin with, maybe with this paper:
> http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.652
> we can precompute the tables with that algorithm up to some reasonable K, and
> then I think we are ok.
> the paper references using http://portal.acm.org/citation.cfm?id=135907 for
> linear minimization, if someone wants to implement this they should not worry
> about minimization.
> in fact, we need to at some point determine if AutomatonQuery should even
> minimize FSM's at all, or if it is simply enough for them to be deterministic
> with no transitions to dead states. (The only code that actually assumes
> minimal DFA is the "Dumb" vs "Smart" heuristic and this can be rewritten as a
> summation easily). we need to benchmark really complex DFAs (i.e. write a
> regex benchmark) to figure out if minimization is even helping right now.
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