Return-Path: Received: from smtp3.osuosl.org (smtp3.osuosl.org [IPv6:2605:bc80:3010::136]) by lists.linuxfoundation.org (Postfix) with ESMTP id 65321C000D; Thu, 16 Sep 2021 15:05:39 +0000 (UTC) Received: from localhost (localhost [127.0.0.1]) by smtp3.osuosl.org (Postfix) with ESMTP id 3425A60638; Thu, 16 Sep 2021 15:05:39 +0000 (UTC) X-Virus-Scanned: amavisd-new at osuosl.org X-Spam-Flag: NO X-Spam-Score: 0.334 X-Spam-Level: X-Spam-Status: No, score=0.334 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, DKIM_VALID_EF=-0.1, FREEMAIL_FROM=0.001, FREEMAIL_REPLY=1, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_HELO_NONE=0.001, SPF_PASS=-0.001, URI_DOTEDU=1.432] autolearn=no autolearn_force=no Authentication-Results: smtp3.osuosl.org (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com Received: from smtp3.osuosl.org ([127.0.0.1]) by localhost (smtp3.osuosl.org [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id DPffzztO7Y4l; Thu, 16 Sep 2021 15:05:38 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.8.0 X-Greylist: whitelisted by SQLgrey-1.8.0 Received: from mail-pj1-x102d.google.com (mail-pj1-x102d.google.com [IPv6:2607:f8b0:4864:20::102d]) by smtp3.osuosl.org (Postfix) with ESMTPS id F23CF6062E; Thu, 16 Sep 2021 15:05:37 +0000 (UTC) Received: by mail-pj1-x102d.google.com with SMTP id i19so4750744pjv.4; Thu, 16 Sep 2021 08:05:37 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20210112; h=mime-version:references:in-reply-to:from:date:message-id:subject:to :cc; bh=RtdKAwEnirXBv12yP5TfMkjLaRTjWKuC0Iv/dM7E1Qw=; b=WPZSP5piwvnAcSsRYJiIIfPsN4YpRMleY9yt17PxBv2u/3gi4V7Xn0uzUvPzu5rQv7 aZg1+vC8jUPsFzn8P8+82UDC+9fqKWHmGHlutpS2DbE2AjhDYGxSoVNCW3n5QnvUa5uv AkHyVr5hRi4XFBVtpGsZsTfqoA1Xew+HwzseRQTG4fx1xfwuQ00mJ+cuUZSVjf9jlIIu NDCp4ktx4WsNzMfV8gwqHUB4NAjGB6WEnAhCiQst2SVZN3xTtzNLkkYAf8tyk+3Msr2j KM8oCx6Wky4ho6qLPtkE/XKjYKdViqzGMuoedGc/Fj3HFe9ySrN6EoZuExLFEt5rmfa7 yXZA== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20210112; h=x-gm-message-state:mime-version:references:in-reply-to:from:date :message-id:subject:to:cc; bh=RtdKAwEnirXBv12yP5TfMkjLaRTjWKuC0Iv/dM7E1Qw=; b=pp9fU2+WoRixqIE7eVHY5ggM9LddPdjPnzW3iY90k5Iks/oOjKib1FH21XFBmEGm79 k8f5xrlfflQSOEn6q6nhQoMpGupBLPaj7OMsyuL0uKqJkL0HvWkqdj+0nZ5ZuLIOHXh2 pq7eSc3d0NoGdma4LDWIEZJ0bhlZbeRj/hhVK/xUmoT3izGc+RElPW0fV3Chd7ZA0ag9 FN9wlWeIC1u6BtadshuwqV+ADfHCXRTTMMm4kOMh4p+5iwhSv0uhyrqtROKiJoXivWSS ZeXyopRdQw5U32BMaS+vIsZiCjQJ2+RAXNyO91NUYe+Q4vQi99osTdjxn4zP78H7tQZC Izgg== X-Gm-Message-State: AOAM531ZVOxEdax83XGv8+EySAfRbW8XkebWnNltC2MRPRcBu7nNpsD9 iAKIV1PH5+nQoZ/EhZAkEbNDGv+O9fuDGC3x8pfi4JUF X-Google-Smtp-Source: ABdhPJw/M+5E39g81g+JvKMJlcpnQWBty+sNI+1YIsntIxjBKTYCUitfv1Zs92O7J6uOE6oj/CNTOh3QdtSO5iyYqK8= X-Received: by 2002:a17:90a:be06:: with SMTP id a6mr15472459pjs.60.1631804736627; Thu, 16 Sep 2021 08:05:36 -0700 (PDT) MIME-Version: 1.0 References: In-Reply-To: From: shymaa arafat Date: Thu, 16 Sep 2021 17:05:24 +0200 Message-ID: To: Vincent Content-Type: multipart/mixed; boundary="000000000000ac35a005cc1e2556" X-Mailman-Approved-At: Thu, 16 Sep 2021 15:18:42 +0000 Cc: Bitcoin Protocol Discussion , lightning-dev Subject: Re: [bitcoin-dev] [Lightning-dev] Storing the Merkle Tree in a compact way X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.15 Precedence: list List-Id: Bitcoin Protocol Discussion List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Thu, 16 Sep 2021 15:05:39 -0000 --000000000000ac35a005cc1e2556 Content-Type: multipart/alternative; boundary="000000000000ac359e05cc1e2554" --000000000000ac359e05cc1e2554 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable It could be viewed as the simple complete tree to 1D array with no pointers described in lecture 8 here https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-0= 06-introduction-to-algorithms-spring-2020/lecture-notes/index.htm starting from min 15 in this video https://youtu.be/Xnpo1atN-Iw Since all trees in Utreexo forest are full binary trees, this is perfect to use, and we can save *76*10=E2=81=B6*2*size of pointer(probably4bytes)* *~600MB *with almost no effort. However, I suggest to put it in a 2D array to make it more easy to handle (the indexing math) as we, different than the lecture, traverse in many ways ( normally to delete or insert, and the parent siblings for the proofs= ) I wrote more details here https://bitcointalk.org/index.php?topic=3D5360009.0 On Thu, Sep 16, 2021, 14:37 Vincent wrote: > Hi. > > Thanks for the reference, but I missed where you want save space with thi= s > compression on the Merkle Tree. > > Regards. > > Vincent. > vincenzo.palazzo@protonmail.com > https://github.com/vincenzopalazzo > =E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90 Original = Message =E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90 > On Thursday, September 16th, 2021 at 5:15 AM, shymaa arafat < > shymaa.arafat@gmail.com> wrote: > > Allow me to introduce this simple idea that could be useful ... > > -The Intuition was some discussion on Utreexo project about storage savin= g > and some traversing issues in handling the UTXOS Merkle Tree/ forest; tha= t > is N internal nodes need to be stored along with 2N pointers (left&right= ), > + maybe 1 more pointer in the leaves special nodes to handle different > traversing options (insert, delete, & differently proof fetch that traver= se > aunt or niece node according to your implementation > https://github.com/mit-dci/utreexo/discussions/316) > . > Then, I thought of a simple idea that gets rid of all the pointers; > specially appealing when we have all trees are full (complete) in the > forest, but can work for any Merkle Tree: > > - 2D array with variable row size; R[j] is of length (N/2^j) > -For example when N=3D8 nodes > R[0]=3D0,1,2,...,7 > R[1]=3D8,9,10,11 > R[2]=3D12,13 > R[3]=3D14 > . > -We can see that total storage is just 2N-1 nodes, > no need for pointers, and traversing could be neat in any direction with > the right formula: > > -Pseudo code to fetch proof[i] ... > > //direction to know + or - > If ((i mod 2)=3D=3D0) drct=3D1; > else drct=3D-1; > // first, the sibling node > proof[i]=3DR[0,i+drct] > > //add the rest thru loop > For(j=3D1; j=E2=89=A4logN; j++) > { index=3D i/(2^j)+drct; > proof[i]=3DAdd(R[j,index]); > } > > -In fact it's just the simple primitive approach of transforming a > recursion to an iteration, and even if Utreexo team solved their problem > differently I thought it is worth telling as it can work for any Merkle T= ree > . > Thanks for your time, > Shymaa M Arafat > > > --000000000000ac359e05cc1e2554 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
It could be viewed as the simple complete tree to 1D= array=C2=A0 with no pointers described in lecture 8 here
starting from min 15 in this video
https://youtu.be/Xnpo1atN-Iw

Since all trees in Utreexo forest are full binary trees, this is = perfect to use, and we can save 76*10=E2=81=B6*2*size of pointer(probabl= y4bytes)
~600MB=C2=A0with almost n= o effort.

However, I sug= gest to put it in a 2D array to make it more easy to handle (the indexing m= ath) as we, different than the lecture, traverse in many ways ( normally to= delete or insert, and the parent siblings for the proofs)

I wrote more details here

On= Thu, Sep 16, 2021, 14:37 Vincent <vin= cent.palazzo@protonmail.com> wrote:
Hi.

Thanks for the reference, but= I missed where you want save space with this compression on the Merkle Tre= e.

Regards.

Vince= nt.
=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90 Ori= ginal Message =E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80=90=E2=80= =90
On Thursday, September 16th, 2021 at 5:15 AM, shymaa arafat <shymaa.arafat@gmail.com> wrote:
Allow me to introduce this = simple idea that could be useful ...

-The = Intuition was some discussion on Utreexo project about storage saving and s= ome traversing issues in handling the UTXOS Merkle Tree/ forest; that is=C2= =A0 N internal nodes need to be stored along with 2N pointers (left&rig= ht), + maybe 1 more pointer in the leaves special nodes to handle different= traversing options (insert, delete, & differently proof fetch that tra= verse aunt or niece node according to your implementation
= https://github.com/mit-dci/utreexo/discussions/316)
.
Then, I thought of a simple idea that gets= rid of all the pointers; specially appealing when we have all trees are fu= ll (complete) in the forest, but can work for any Merkle Tree:

- 2D array with variable row size; R= [j] is of length (N/2^j)
-For example when N=3D8 nod= es
R[0]=3D0,1,2,...,7
R[1]=3D= 8,9,10,11
R[2]=3D12,13
R[3]= =3D14
.
-We can see that tota= l storage is just 2N-1 nodes,
no need for pointers, = and traversing could be neat in any direction with the right formula:
=

-Pseudo code to fetch proof[i= ] ...

//direction to kno= w + or -
If ((i mod 2)=3D=3D0) drct=3D1;=C2=A0
=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 else drct=3D-1;=
// first, the sibling node
p= roof[i]=3DR[0,i+drct]
=C2=A0 =C2=A0 =C2=A0
//add the rest thru loop
For(j=3D1; j= =E2=89=A4logN; j++)
=C2=A0{ index=3D i/(2^j)+drct;
=C2=A0 =C2=A0 proof[i]=3DAdd(R[j,index]);
=C2=A0}

-In = fact it's just the simple primitive approach of transforming a recursio= n to an iteration, and even if Utreexo team solved their problem differentl= y I thought it is worth telling as it can work for any Merkle Tree
.
Thanks for your time,
Shymaa M Arafat


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