Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Geometric Search Trees

g-trees.github.io

Post reply on HN
Print view View original

11–18 of 18 posts

Re: Geometric Search Trees

#11

Post by carsonfarmer »

yorwba wrote: post #7
bminor13 wrote: post #3

Earlier quoted context omitted.

In order to be in the same G-node, they'd need to have the same rank and be close in value (such that they were not "broken up" by a value in the next highest rank), right? Seems like brute-force search for adjacent values with the same rank is possible, but guaranteeing that intermediate higher-rank values dont also exist may not be (for an attacker). Maybe one mitigation on this sort of attack is to search for high…

Generating arbitrarily many values of the minimum rank is very easy for an attacker. Since the rank is geometrically distributed with parameter p = 1 - 1/ k and k ≥ 2, randomly sampling a value will give you one of minimum rank with probability p ≥ 1/2 and it only gets easier for larger k . If you want to break that up with dummy elements, you now have the problem of choosing those dummies in a history-independent ma…

Yes this exactly. Another really simple way to do this, is to use alternating leading and trailing zero counts in the hash in your nested G-trees. Simple, and pretty effective.

Re: Geometric Search Trees

#12

Post by carsonfarmer »

EdSchouten wrote: post #5
bminor13 wrote: post #3

Earlier quoted context omitted.

In order to be in the same G-node, they'd need to have the same rank and be close in value (such that they were not "broken up" by a value in the next highest rank), right? Seems like brute-force search for adjacent values with the same rank is possible, but guaranteeing that intermediate higher-rank values dont also exist may not be (for an attacker). Maybe one mitigation on this sort of attack is to search for high…

Exactly. But my concern is that this is not any stronger/better than what Prolly trees already offer, which is why I'm disappointed that they are mentioned under "related work", but not discussed/compared in more detail.

You're right, we should delve into a comparison more with respect to prolly trees. We actually have a lot of experience with prolly trees, and have found, in practice, that you need to do a lot of the things that folks like dolt have had to do to make them work nicely. Whereas with G-trees, the basic implementation turns out to be quite nice (and extremely easy to reason about).

One of the biggest benefits of G-trees in my mind, is their ease of implementation. Additionally, we did a lot of work to explore their statistical properties, which doesn't exist for prolly trees (though in hindsight, we have done this, so should probably write it up formally).

Re: Geometric Search Trees

#13

Post by hiimkeks »

zermelo44 wrote: post #4

The presentation of the webpage is really really nice. Especially the highlighting/linking of mathematical definitions and bound variables. How did you achieve this?

Aljoscha initially built the macro framework for the specs on willowprotocol.org

Re: Geometric Search Trees

#14

Post by carsonfarmer »

zermelo44 wrote: post #4

The presentation of the webpage is really really nice. Especially the highlighting/linking of mathematical definitions and bound variables. How did you achieve this?

Thanks, that's all due to my co-author. Here's what we used: https://news.ycombinator.com/item?id=41589728 (link is to a post from @msy)

Re: Geometric Search Trees

#16

Post by yorwba »

carsonfarmer wrote: post #11
yorwba wrote: post #7

Earlier quoted context omitted.

Generating arbitrarily many values of the minimum rank is very easy for an attacker. Since the rank is geometrically distributed with parameter p = 1 - 1/ k and k ≥ 2, randomly sampling a value will give you one of minimum rank with probability p ≥ 1/2 and it only gets easier for larger k . If you want to break that up with dummy elements, you now have the problem of choosing those dummies in a history-independent ma…

Yes this exactly. Another really simple way to do this, is to use alternating leading and trailing zero counts in the hash in your nested G-trees. Simple, and pretty effective.

Hmmm... if you need to go deeper (because 1/4 of all hashes have zero leading zeros and zero trailing zeros), you can generalize this by converting the hash into its run-length encoding to get a sequence of rank functions where finding values with the same rank for all rank functions is equivalent to finding hash collisions. Very nice.

Re: Geometric Search Trees

#17

Post by EdSchouten »

carsonfarmer wrote: post #12
EdSchouten wrote: post #5

Earlier quoted context omitted.

Exactly. But my concern is that this is not any stronger/better than what Prolly trees already offer, which is why I'm disappointed that they are mentioned under "related work", but not discussed/compared in more detail.

You're right, we should delve into a comparison more with respect to prolly trees. We actually have a lot of experience with prolly trees, and have found, in practice, that you need to do a lot of the things that folks like dolt have had to do to make them work nicely. Whereas with G-trees, the basic implementation turns out to be quite nice (and extremely easy to reason about). One of the biggest benefits of G-trees…

Another thing that's worth investigating:

As the name implies, the sizes of nodes of Prolly trees and geometric search trees are geometrically distributed. My question is: is this really the right distribution to use? The larger nodes get, the larger the probability is that they get mutated. This means that in a content addressed storage system, there will be more large objects than small ones. My gut feeling tells me that the distribution should be uniform, with the spread between min/max sizes bound by a small constant factor (2x? 4x?).

Some time ago I experimented with this, where I implemented a content defined chunking algorithm that chunks inputs at locations where the value of a rolling hash is maximal, as opposed to finding offsets at which the first/last n bits are zeros/ones. My observation was that this led to a 2-3% reduction in storage space usage. The source code for this can be found here:

https://github.com/buildbarn/go-cdc

Would it also be possible to model trees around this approach as well? If so, would this lead to better deduplication rates than Prolly/geometric search trees?

Re: Geometric Search Trees

#18

Post by carsonfarmer »

yorwba wrote: post #16
carsonfarmer wrote: post #11

Earlier quoted context omitted.

Yes this exactly. Another really simple way to do this, is to use alternating leading and trailing zero counts in the hash in your nested G-trees. Simple, and pretty effective.

Hmmm... if you need to go deeper (because 1/4 of all hashes have zero leading zeros and zero trailing zeros), you can generalize this by converting the hash into its run-length encoding to get a sequence of rank functions where finding values with the same rank for all rank functions is equivalent to finding hash collisions. Very nice.

Whoah, I totally hadn't taken the thought experiment this far. This is fantastic! I'd like to explore this further, interested in a quick research chat/sync some time? My email is linked from the paper.
Post reply on HN