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https://issues.apache.org/jira/browse/LUCENE-8920?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16923428#comment-16923428
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Bruno Roustant edited comment on LUCENE-8920 at 9/5/19 8:46 PM:
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[~sokolov] There may be another option to speed-up FST arc lookup while
limiting the memory increase.
Direct-Addressing option looks up by accessing directly 1 label, and costs up
to (num labels x 4 x num bytes to encode) bytes.
Label-List option is the opposite, look up needs on average N/2 label
comparisons, and costs (num labels x var bytes to encode) bytes.
Another option is to use open-addressing. Look up would be <= L comparisons
where we can fix L < log(N)/2 (to be faster than binary search), and would cost
< (num labels x 2 x num bytes to encode).
The idea is to have an array of size 2^p such as 2^(p-1) < N < 2^p. We hash the
labels and store them in the array using the open-addressing idea: if a slot is
occupied, try with the next block. If we can’t store a label in less than L
tries, then abort and fallback to Label-List or Binary-Search option. At lookup
we hash the input label and know that we have less than L tries to compare.
This is another compromise speed/memory: faster than binary search (constant
L), with at least 2x less memory than Direct-Addressing.
On the Binary-Search side, it could be possible to support variable length
encoding, by finding the first byte starting a label based on the bit used to
encode the var length additional bytes.
was (Author: bruno.roustant):
[~sokolov] There may be another option to speed-up FST arc lookup while
limiting the memory increase.
Direct-Addressing option looks up by accessing directly 1 label, and costs up
to (num labels x 4 x num bytes to encode) bytes.
Label-List option is the opposite, look up needs on average N/2 label
comparisons, and costs (num labels x var bytes to encode) bytes.
Another option is to use open-addressing. Look up would be <= L comparisons
where we can fix L < log(N)/2 (to be faster than binary search), and would cost
< (num labels x 2 x num bytes to encode).
The idea is to have an array of size 2^p such as 2^(p-1) < N < 2^p. We hash the
labels and store them in the array using the open-addressing idea: if a slot is
occupied, try with the next block. If we can’t store a label in less than L
tries, then abort and fallback to Label-List or Binary-Search option. At lookup
we hash the input label and know that we have less than L tries to compare.
This is another compromise speed/memory: faster than binary search (constant
L), with at least 2x less memory than Direct-Addressing.
It is also possible to combine open-addressing and variable length encoding, by
finding the first byte starting a label based on the bit used to encode the var
length additional bytes.
> Reduce size of FSTs due to use of direct-addressing encoding
> -------------------------------------------------------------
>
> Key: LUCENE-8920
> URL: https://issues.apache.org/jira/browse/LUCENE-8920
> Project: Lucene - Core
> Issue Type: Improvement
> Reporter: Mike Sokolov
> Priority: Blocker
> Fix For: 8.3
>
> Time Spent: 1h 10m
> Remaining Estimate: 0h
>
> Some data can lead to worst-case ~4x RAM usage due to this optimization.
> Several ideas were suggested to combat this on the mailing list:
> bq. I think we can improve thesituation here by tracking, per-FST instance,
> the size increase we're seeing while building (or perhaps do a preliminary
> pass before building) in order to decide whether to apply the encoding.
> bq. we could also make the encoding a bit more efficient. For instance I
> noticed that arc metadata is pretty large in some cases (in the 10-20 bytes)
> which make gaps very costly. Associating each label with a dense id and
> having an intermediate lookup, ie. lookup label -> id and then id->arc offset
> instead of doing label->arc directly could save a lot of space in some cases?
> Also it seems that we are repeating the label in the arc metadata when
> array-with-gaps is used, even though it shouldn't be necessary since the
> label is implicit from the address?
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