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https://issues.apache.org/jira/browse/LUCENE-2089?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12832150#action_12832150
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Robert Muir commented on LUCENE-2089:
-------------------------------------

bq. and we need to be able to compare old relevance with new one (with integer 
distance threshold it is not the same as with classic float-point...)

this is not true, we can determine for any word, and any floating point value, 
the maximum integer distance that equates.

This query will be completely backwards compatible, same results, same order, 
only faster.

bq. What if we can store some precounted values in the index... such as storing 
"similar terms" in additional field... or some pieces of DFA (which I still 
need to learn...)

This is not necessary for AutomatonQuery, and imposes too much of a space 
tradeoff. You can see an example of this in LUCENE-1513, where deletion 
neighborhoods are indexed. 

However, given the speedups to AutomatonQuery itself done in LUCENE-1606, it 
will actually surpass this approach, impose no index or storage requirements, 
scale to higher N, and allow for full back compat.  

The only "tradeoff" in this approach is the headache caused by the mathematics, 
and the majority of this is now solved... unlike approaches that require 
additional disk or memory or indexing changes, users are unaffected if we stay 
up too late staring at funky math.


> 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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