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https://issues.apache.org/jira/browse/CASSANDRA-8915?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14570981#comment-14570981
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Branimir Lambov commented on CASSANDRA-8915:
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Updated above with some of your suggestions.

bq. Perhaps clarify, that σ(P) => σ(R), so already correct.

This is not entirely true, {{(σ(P) & P = R) => σ(R)}}. I would find it 
confusing to put that info there, though, I prefer to split actions from proof.

bq. It would help to state {{P ≙ ep-heap(M,N)}} ... and more.

I hesitate to add this; I think the way it is now is enough to convince people 
that it is sound even if it is not very precise (esp wrt bottom).

> Improve MergeIterator performance
> ---------------------------------
>
>                 Key: CASSANDRA-8915
>                 URL: https://issues.apache.org/jira/browse/CASSANDRA-8915
>             Project: Cassandra
>          Issue Type: Improvement
>            Reporter: Branimir Lambov
>            Assignee: Branimir Lambov
>            Priority: Minor
>              Labels: compaction, performance
>             Fix For: 3.x
>
>
> The implementation of {{MergeIterator}} uses a priority queue and applies a 
> pair of {{poll}}+{{add}} operations for every item in the resulting sequence. 
> This is quite inefficient as {{poll}} necessarily applies at least {{log N}} 
> comparisons (up to {{2log N}}), and {{add}} often requires another {{log N}}, 
> for example in the case where the inputs largely don't overlap (where {{N}} 
> is the number of iterators being merged).
> This can easily be replaced with a simple custom structure that can perform 
> replacement of the top of the queue in a single step, which will very often 
> complete after a couple of comparisons and in the worst case scenarios will 
> match the complexity of the current implementation.
> This should significantly improve merge performance for iterators with 
> limited overlap (e.g. levelled compaction).



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