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https://issues.apache.org/jira/browse/LUCENE-2089?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12781157#action_12781157
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Mark Miller commented on LUCENE-2089:
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bq. Mark, they would get large fast, but i think we only need say 1,2,3.
Ah, right - you mention that above in the summary.
bq. Another twist, is that we have to support the 'constant prefix' as well.
Generally, if you have any kind of length to the prefix, linear wouldn't be so
bad either though right? Guess it depends on your terms though.
> 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
>
> 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 AutomatonTermEnum, here is my idea
> * up front, calculate the maximum required K edits needed to match the users
> supplied float threshold.
> * for at least common K (1,2,3, etc) we should use automatontermenum. if its
> outside of that, maybe use the existing slow logic. At high K, it will seek
> too much to be helpful anyway.
> 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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