Minimizing the redundancy in Golomb Coded Sets

Minimizing the redundancy in Golomb Coded Sets
2018-05-25 18:42 ` Gregory Maxwell
  
From: Pieter Wuille @ 2018-05-25 17:54 UTC (permalink / raw)
  To: Bitcoin Dev

Hi all,

I spent some time working out the optimal parameter selection for the
Golomb Coded Sets that are proposed in BIP158:
https://gist.github.com/sipa/576d5f09c3b86c3b1b75598d799fc845

TL;DR: if we really want an FP rate of exactly 1 in 2^20, the Rice
parameter should be 19, not 20. If we don't, we should pick an FP rate
of 1 in a 1.4971*2^B. So for example M=784931 B=19 or M=1569861 B=20.

Cheers,

-- 
Pieter


 permalink raw reply	[|nested]
2018-05-25 17:54 [bitcoin-dev] Minimizing the redundancy in Golomb Coded Sets Pieter Wuille

  2018-05-25 21:13   ` Gregory Maxwell
  
From: Gregory Maxwell @ 2018-05-25 18:42 UTC (permalink / raw)
  To: Pieter Wuille, Bitcoin Protocol Discussion

On Fri, May 25, 2018 at 5:54 PM, Pieter Wuille via bitcoin-dev
<bitcoin-dev@lists•linuxfoundation.org> wrote:
> Hi all,
>
> I spent some time working out the optimal parameter selection for the
> Golomb Coded Sets that are proposed in BIP158:
> https://gist.github.com/sipa/576d5f09c3b86c3b1b75598d799fc845
>
> TL;DR: if we really want an FP rate of exactly 1 in 2^20, the Rice
> parameter should be 19, not 20. If we don't, we should pick an FP rate
> of 1 in a 1.4971*2^B. So for example M=784931 B=19 or M=1569861 B=20.


I did a rough analysis using Pieter's approximations on what
parameters minimizes the total communications for a lite wallet
scanning the chain and fetching a witnessless block whenever they get
a filter hit. For a wallet with 1000 keys and blocks of 1MB if the
number of entries in the is at least 5096 then M=784931 results in a
lower total data rate rate (FP blocks + filters) than M=1569861.
M=392465 (the optimal value for the rice parameter 18) is
communications is better if at least 10192 entries are set, and
M=196233 (optimal FP for rice 17) is better if at least 20384 entries
are set.

The prior filter set proposal is setting roughly 13300 entries per
full block,  and I guestimate that the in+out scripts only ones are
setting about 7500 entries (if that actual number was in any of the
recent posts I missed it, I'm guessing based on jimpo's sizes graph).

The breakpoints are obviously different if the client is monitoring
for, say, 10,000 keys instead of 1000 but I think it generally makes
more sense to optimize for lower key counts since bigger users are
more likely to tolerate the additional bandwidth usage.

So I think that assuming that all-scripts inputs and outputs (but no
txids) are used and that my guess of 7500 bits set for that
configuration is roughly right, then M=1569861 and rice parameter 19
should be used.

The actual optimal FP rate for total data transferred won't be one
that gets the optimal rice coding efficiency, but since different
clients will be monitoring for different numbers of keys, it probably
makes sense to pick a parameter with optimal compression rather than
optimal-data-transfer-for-a-specific-key-count-- at least then we're
spending the least amount of filter bits per false positive rate,
whatever that rate is... if we can't be optimal at least we can be
efficient. :)


 permalink raw reply	[|nested]
2018-05-25 18:42 ` Gregory Maxwell

  2018-05-29 22:38     ` Jim Posen
  
From: Gregory Maxwell @ 2018-05-25 21:13 UTC (permalink / raw)
  To: Pieter Wuille, Bitcoin Protocol Discussion

On Fri, May 25, 2018 at 6:42 PM, Gregory Maxwell <greg@xiph•org> wrote:
> configuration is roughly right, then M=1569861 and rice parameter 19
> should be used.

That should have been M=784931 B=19  ... paste error.


 permalink raw reply	[|nested]
2018-05-25 21:13   ` Gregory Maxwell

  2018-05-30  3:10       ` Lucas Ontivero
  
From: Jim Posen @ 2018-05-29 22:38 UTC (permalink / raw)
  To: pieter.wuille, Bitcoin Protocol Discussion


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This is a really cool finding, thanks Pieter!

I did some more analysis on selecting a good P value to reduce total data
downloaded considering both filters themselves and blocks in the case of
false positive matches, using data from mainnet. The quantity it minimizes
is:

filter_size(N, B) + block_size * false_positive_probability(C, N, B)

N is the number of filter elements per block
B is the Golomb-Rice coding parameter
C is the number of filter elements watched by the client

The main result is that:

For C = 10, B = 13 is optimal
For C = 100, B = 16 is optimal
For C = 1,000, B = 20 is optimal
For C = 10,000, B = 23 is optimal

So any value of B in the range 16 to 20 seems reasonable, with M = 1.4971 *
2^B for optimal compression, as Pieter derived. The selection of the
parameter depends on the target number of elements that a client may watch.

I attached some of the results, and would be happy to share the CSV and raw
notebook if people are interested.


On Fri, May 25, 2018 at 2:14 PM Gregory Maxwell via bitcoin-dev <
bitcoin-dev@lists•linuxfoundation.org> wrote:

> On Fri, May 25, 2018 at 6:42 PM, Gregory Maxwell <greg@xiph•org> wrote:
> > configuration is roughly right, then M=1569861 and rice parameter 19
> > should be used.
>
> That should have been M=784931 B=19  ... paste error.
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists•linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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 permalink raw reply	[|nested]
2018-05-29 22:38     ` Jim Posen

  
From: Lucas Ontivero @ 2018-05-30  3:10 UTC ( / )
  To: Jim Posen, Bitcoin Protocol Discussion



Hi Jim,

Yes please, could you share CSV? We are developing a Wallet that uses
Golomb-Rice filters it would help a lot for determine the best P value
depending on the estimated number of elements the client needs to watch.

2018-05-29 19:38 GMT-03:00 Jim Posen via bitcoin-dev <
bitcoin-dev@lists•linuxfoundation.org>:

> This is a really cool finding, thanks Pieter!
>
> I did some more analysis on selecting a good P value to reduce total data
> downloaded considering both filters themselves and blocks in the case of
> false positive matches, using data from mainnet. The quantity it minimizes
> is:
>
> filter_size(N, B) + block_size * false_positive_probability(C, N, B)
>
> N is the number of filter elements per block
> B is the Golomb-Rice coding parameter
> C is the number of filter elements watched by the client
>
> The main result is that:
>
> For C = 10, B = 13 is optimal
> For C = 100, B = 16 is optimal
> For C = 1,000, B = 20 is optimal
> For C = 10,000, B = 23 is optimal
>
> So any value of B in the range 16 to 20 seems reasonable, with M = 1.4971
> * 2^B for optimal compression, as Pieter derived. The selection of the
> parameter depends on the target number of elements that a client may watch.
>
> I attached some of the results, and would be happy to share the CSV and
> raw notebook if people are interested.
>
>
> On Fri, May 25, 2018 at 2:14 PM Gregory Maxwell via bitcoin-dev <
> bitcoin-dev@lists•linuxfoundation.org> wrote:
>
>> On Fri, May 25, 2018 at 6:42 PM, Gregory Maxwell <greg@xiph•org> wrote:
>> > configuration is roughly right, then M=1569861 and rice parameter 19
>> > should be used.
>>
>> That should have been M=784931 B=19  ... paste error.
>> _______________________________________________
>> bitcoin-dev mailing list
>> bitcoin-dev@lists•linuxfoundation.org
>> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>>
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists•linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
>