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https://issues.apache.org/jira/browse/LUCENE-8681?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16761583#comment-16761583
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Jim Ferenczi commented on LUCENE-8681:
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For the normal case where a single top docs collector is used and segments are 
consumed sequentially we can early terminate any segment on the first non 
competitive hits when the queue is already full.
So most of the time we don't need to collect N documents per segment in the 
index sorted case. I guess this optimization can be useful when each segment is 
consumed in a different thread and uses a different priority queue. 
However I wonder if this could be implemented directly in a custom 
CollectorManager, currently the CollectorManager creates a Collector for each 
leaf if the executor is not null and merge all the collectors at the end. Since 
each collector is independent you could set different topN size based on the 
segment statistics and the heuristic you described here. The only change that 
is missing to achieve this is to provide the reader context when the 
CollectorManager creates a collector (CollectorManager#newCollector), with this 
information you could create different top docs collector and merge them at the 
end with the expected topN size ? 


> Prorated early termination
> --------------------------
>
>                 Key: LUCENE-8681
>                 URL: https://issues.apache.org/jira/browse/LUCENE-8681
>             Project: Lucene - Core
>          Issue Type: Improvement
>          Components: core/search
>            Reporter: Mike Sokolov
>            Priority: Major
>
> In this issue we'll exploit the distribution of top K documents among 
> segments to extract performance gains when using early termination. The basic 
> idea is we do not need to collect K documents from every segment and then 
> merge. Rather we can collect a number of documents that is proportional to 
> the segment's size plus an error bound derived from the combinatorics seen as 
> a (multinomial) probability distribution.
> https://github.com/apache/lucene-solr/pull/564 has the proposed change.
> [~rcmuir] pointed out on the mailing list that this patch confounds two 
> settings: (1) whether to collect all hits, ensuring correct hit counts, and 
> (2) whether to guarantee that the top K hits are precisely the top K.
> The current patch treats this as the same thing. It takes the position that 
> if the user says it's OK to have approximate counts, then it's also OK to 
> introduce some small chance of ranking error; occasionally some of the top K 
> we return may draw from the top K + epsilon.
> Instead we could provide some additional knobs to the user. Currently the 
> public API is {{TopFieldCOllector.create(Sort, int, FieldDoc, int 
> threshold)}}. The threshold parameter controls when to apply early 
> termination; it allows the collector to terminate once the given number of 
> documents have been collected.
> Instead of using the same threshold to control leaf-level early termination, 
> we could provide an additional leaf-level parameter. For example, this could 
> be a scale factor on the error bound, eg a number of standard deviations to 
> apply. The patch uses 3, but a much more conservative bound would be 4 or 
> even 5. With these values, some speedup would still result, but with a much 
> lower level of ranking errors. A value of MAX_INT would ensure no leaf-level 
> termination would ever occur.
> We could also hide the precise numerical bound and offer users a three-way 
> enum (EXACT, APPROXIMATE_COUNT, APPROXIMATE_RANK) that controls whether to 
> apply this optimization, using some predetermined error bound.
> I posted the patch without any user-level tuning since I think the user has 
> already indicated a preference for speed over precision by specifying a 
> finite (global) threshold, but if we want to provide finer control, these two 
> options seem to make the most sense to me. Providing access to the number of 
> standard deviation to allow from the expected distribution gives the user the 
> finest control, but it could be hard to explain its proper use.



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