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https://issues.apache.org/jira/browse/LUCENE-2089?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12834695#action_12834695
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Uwe Schindler commented on LUCENE-2089:
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Hi Robert,
I reviewed you latest patch and was a little bit irritated, but then everything 
explained when also looking into AutomatonTermsEnum and understanding what 
happes. But there is still some "code duplication" (not really duplication, but 
functionality duplication):

- If a constant prefix is used, the generated Automatons are using a constant 
prefix + a Levenshtein Automaton (using concat)
- If you run such an automaton agains the TermIndex using the superclass, it 
will seek first to the prefix term (or some term starting with the prefix), 
thats ok. As soon as the prefix is no longer valid, the AutomatonTermsEnum 
stops processing (if running such an automaton using the standard 
AutomatonTermsEnum).
- The AutomatonFuzzyTermsEnum checks if the term starts with prefix and if not 
it exists ENDs (!) the automaton. The reason why this works is because 
nextString() in superclass returns automatically a string starting with the 
prefix, but this was the main fact that irritated me.
- The question is now, is this extra prefix check really needed? Running the 
automaton against the current term in accept would simply return no match and 
nextString() would stop further processing? Or is this because the accept 
method should not iterate through all distances once the prefix is not matched?

Maybe you should add some comments to the AutomatonFuzzyTermsEnum or some 
asserts to show whats happening.

> 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: LUCENE-2089.patch, LUCENE-2089.patch, LUCENE-2089.patch, 
> LUCENE-2089.patch, LUCENE-2089_concat.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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