From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org [172.17.192.35]) by mail.linuxfoundation.org (Postfix) with ESMTPS id 64CDFD1E for ; Tue, 29 May 2018 22:38:16 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.7.6 Received: from mail-qt0-f179.google.com (mail-qt0-f179.google.com [209.85.216.179]) by smtp1.linuxfoundation.org (Postfix) with ESMTPS id 86649224 for ; Tue, 29 May 2018 22:38:14 +0000 (UTC) Received: by mail-qt0-f179.google.com with SMTP id h2-v6so20851384qtp.7 for ; Tue, 29 May 2018 15:38:14 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:references:in-reply-to:from:date:message-id:subject:to; bh=u+fLkNy55uE2PuIeFnl5u0tFQDewxK8XdoaiPyjf1fg=; b=nedKsk97lPcKqwujAMOC1NUJPaaarlojdXDDgwrpHbU/x/JTxM30qBrlQAnOlytIRM tvl3CehFJkgS4Sj6PvkA/v0k6O20YiUnxrzqI/kKkg9iKUqEgaxIQ6i2C3t8XXHSXVuF TOdBgT6pgtoclGxXDEavNxZc/9Apv+iyesOhj7kAMPIqF/Hjdnj4oJqFBGel+80d3Oxc 61mpMHrQHMMbS+ihQ7hTt3hASWHI+uhMm4b0Wu4VTxkNGRjIiz2zl/eaK0SkjDGm/lsI 8CkM58O2Nbycyc0/Sy9YXdQc7iWHpPp8qEQSrk0VdXcm/PBi0G00t91Wg2b1Z2eUgesm r97w== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:references:in-reply-to:from:date :message-id:subject:to; bh=u+fLkNy55uE2PuIeFnl5u0tFQDewxK8XdoaiPyjf1fg=; b=N/udSqg5VqLkMbr+kQMIYkWPRpYVlxdxqUjcOkSva8V20cqDFUXkiRi0p6E2qYu1Hq sngqJUqF4Cj8EXLVkGUV4RZro7rxr32HatMRoehGI+WAtMwh/UaHn3ecfC2RWgOdMgvC UnA/oV/sBQTfteIvrFZjkjA1sL+utzEUwsci92ffsFlByF1oMoIB+XM3XF/jnpp834Qq 2RQZa69gdIj1Afn4EW/9jqOuh585wHzs8L6KEw/MEQNr6Yp8TsO7NfOwjZv9rozkg16M TFKK22MT8Zy/OeC8aNT4O86auO08sN32CGGeWEYultKHZvq6C6TsgWHOx8YUZ5G9eq7f HycA== X-Gm-Message-State: APt69E2wAZbIvG/MELSIPk+5ukIHJoroms0MAuQwydsARrYxxDPy/alS Ey3+yh3B/TxMUtgJxyJ4tYoWylTqo+wBgHNtwUI= X-Google-Smtp-Source: ADUXVKJ09jOtp7UWpkBQIG1ttm2BB3D+n5QJ8nbeWMXqXaw/99LZW91oGr1cAk4HKJD4VT0KeeO88jyrc2YWoq7IVeo= X-Received: by 2002:a0c:e987:: with SMTP id z7-v6mr303044qvn.202.1527633493491; Tue, 29 May 2018 15:38:13 -0700 (PDT) MIME-Version: 1.0 References: In-Reply-To: From: Jim Posen Date: Tue, 29 May 2018 15:38:01 -0700 Message-ID: To: pieter.wuille@gmail.com, Bitcoin Protocol Discussion Content-Type: multipart/mixed; boundary="000000000000ba4249056d5fe395" X-Spam-Status: No, score=-2.0 required=5.0 tests=BAYES_00,DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, FREEMAIL_FROM, HTML_MESSAGE, RCVD_IN_DNSWL_NONE, T_HTML_ATTACH,URI_TRUNCATED autolearn=ham version=3.3.1 X-Spam-Checker-Version: SpamAssassin 3.3.1 (2010-03-16) on smtp1.linux-foundation.org X-Mailman-Approved-At: Tue, 29 May 2018 22:55:25 +0000 Subject: Re: [bitcoin-dev] Minimizing the redundancy in Golomb Coded Sets X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.12 Precedence: list List-Id: Bitcoin Protocol Discussion List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Tue, 29 May 2018 22:38:16 -0000 --000000000000ba4249056d5fe395 Content-Type: multipart/alternative; boundary="000000000000ba4246056d5fe393" --000000000000ba4246056d5fe393 Content-Type: text/plain; charset="UTF-8" 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 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 > --000000000000ba4246056d5fe393 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
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 minimi= zes is:

filter_size(N, B)=C2=A0+ block_size * fals= e_positive_probability(C, N, B)

N is the number of= filter elements per block
B is the Golomb-Rice coding parameter<= /div>
C is the number of filter elements watched by the client

The main result is that:

For C = =3D 10, B =3D 13 is optimal
For C =3D 100, B =3D 16 is optimal
For C =3D 1,000, B =3D 20 is optimal
For C =3D 10,000, B = =3D 23 is optimal

So any value of B in the range 1= 6 to 20 seems reasonable, with M =3D=C2=A01.4971 * 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.

I attach= ed some of the results, and would be happy to share the CSV and raw noteboo= k if people are interested.


On Fri, May 25, 2018 at 2:14 PM Gregory M= axwell via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wr= ote:
On Fri, May 25, 2018 at 6:42 P= M, Gregory Maxwell <g= reg@xiph.org> wrote:
> configuration is roughly right, then M=3D1569861 and rice parameter 19=
> should be used.

That should have been M=3D784931 B=3D19=C2=A0 ... paste error.
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https://lists.linuxfoundation.org/mail= man/listinfo/bitcoin-dev
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