From: shymaa arafat <shymaa.arafat@gmail•com>
To: Bitcoin Protocol Discussion
<bitcoin-dev@lists•linuxfoundation.org>,
lightning-dev <lightning-dev@lists•linuxfoundation.org>
Subject: [bitcoin-dev] Storing the Merkle Tree in a compact way
Date: Sat, 11 Sep 2021 05:00:12 +0200 [thread overview]
Message-ID: <CAM98U8=r+DGW46O5Srp5SzqB38suYnZY8DR06dqx-_gdB5Ruxw@mail.gmail.com> (raw)
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Allow me to introduce this simple idea that could be useful ...
-The Intuition was some discussion on Utreexo project about storage saving
and some traversing issues in handling the UTXOS Merkle Tree/ forest; that
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 traverse
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=8 nodes
R[0]=0,1,2,...,7
R[1]=8,9,10,11
R[2]=12,13
R[3]=14
.
-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)==0) drct=1;
else drct=-1;
// first, the sibling node
proof[i]=R[0,i+drct]
//add the rest thru loop
For(j=1; j≤logN; j++)
{ index= i/(2^j)+drct;
proof[i]=Add(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 Tree
.
Thanks for your time,
Shymaa M Arafat
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next reply other threads:[~2021-09-11 3:00 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2021-09-11 3:00 shymaa arafat [this message]
[not found] ` <f6RaXDTOElzKjWTLDhUPFKXs1AeJnaxdC2HGbaO8NponuccadSaInyzyBNIoH-Wa3_cyv4SKOoWNx2gTj1jdhyGLwFExyGF4q1d9UJ68skI=@protonmail.com>
2021-09-16 15:05 ` [bitcoin-dev] [Lightning-dev] " shymaa arafat
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