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From: Jim Posen <jim.posen@gmail.com>
Date: Tue, 29 May 2018 15:38:01 -0700
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	Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Subject: Re: [bitcoin-dev] Minimizing the redundancy in Golomb Coded Sets
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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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<div dir=3D"ltr">This is a really cool finding, thanks Pieter!<div><br></di=
v><div>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 minimi=
zes is:</div><div><br></div><div>filter_size(N, B)=C2=A0+ block_size * fals=
e_positive_probability(C, N, B)</div><div><br></div><div>N is the number of=
 filter elements per block</div><div>B is the Golomb-Rice coding parameter<=
/div><div>C is the number of filter elements watched by the client</div><di=
v><br></div><div>The main result is that:</div><div><br></div><div>For C =
=3D 10, B =3D 13 is optimal</div><div>For C =3D 100, B =3D 16 is optimal</d=
iv><div>For C =3D 1,000, B =3D 20 is optimal</div><div>For C =3D 10,000, B =
=3D 23 is optimal</div><div><br></div><div>So any value of B in the range 1=
6 to 20 seems reasonable, with M =3D=C2=A0<span style=3D"color:rgb(34,34,34=
);font-family:sans-serif;font-size:13px;font-style:normal;font-variant-liga=
tures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal=
;text-align:start;text-indent:0px;text-transform:none;white-space:normal;wo=
rd-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:init=
ial;text-decoration-color:initial;float:none;display:inline">1.4971 * 2^B f=
or optimal compression, as Pieter derived. The selection of the parameter d=
epends on the target number of elements that a client may watch.</span></di=
v><div><span style=3D"color:rgb(34,34,34);font-family:sans-serif;font-size:=
13px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:norm=
al;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;t=
ext-transform:none;white-space:normal;word-spacing:0px;background-color:rgb=
(255,255,255);text-decoration-style:initial;text-decoration-color:initial;f=
loat:none;display:inline"><br></span></div><div><span style=3D"color:rgb(34=
,34,34);font-family:sans-serif;font-size:13px;font-style:normal;font-varian=
t-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:=
normal;text-align:start;text-indent:0px;text-transform:none;white-space:nor=
mal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-styl=
e:initial;text-decoration-color:initial;float:none;display:inline">I attach=
ed some of the results, and would be happy to share the CSV and raw noteboo=
k if people are interested.</span></div><div><br></div></div><br><div class=
=3D"gmail_quote"><div dir=3D"ltr">On Fri, May 25, 2018 at 2:14 PM Gregory M=
axwell via bitcoin-dev &lt;<a href=3D"mailto:bitcoin-dev@lists.linuxfoundat=
ion.org" target=3D"_blank">bitcoin-dev@lists.linuxfoundation.org</a>&gt; wr=
ote:<br></div><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;=
border-left:1px #ccc solid;padding-left:1ex">On Fri, May 25, 2018 at 6:42 P=
M, Gregory Maxwell &lt;<a href=3D"mailto:greg@xiph.org" target=3D"_blank">g=
reg@xiph.org</a>&gt; wrote:<br>
&gt; configuration is roughly right, then M=3D1569861 and rice parameter 19=
<br>
&gt; should be used.<br>
<br>
That should have been M=3D784931 B=3D19=C2=A0 ... paste error.<br>
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bitcoin-dev@lists.linuxfoundation.org</a><br>
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man/listinfo/bitcoin-dev</a><br>
</blockquote></div>

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