# The number of trimming rounds estimation

**URL:** <https://forum.grin.mw/t/the-number-of-trimming-rounds-estimation/6110>\
**Category:** Research\
**Created:** [September 19, 2019, 8:06pm UTC](https://forum.grin.mw/t/the-number-of-trimming-rounds-estimation/6110 "2019-09-19T20:06:49Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Jack](https://avatars.discourse-cdn.com/v4/letter/j/cc9497/32.png) [@Jack](https://forum.grin.mw/u/Jack)\
**Post date:** [September 19, 2019, 8:06pm UTC](https://forum.grin.mw/t/the-number-of-trimming-rounds-estimation/6110/1 "2019-09-19T20:06:49Z")

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Hello,

I’ve red the article “Cuckoo Cycle: a memory bound graph-theoretic proof-of-work” but haven’t understand sentence:“The number of trimming rounds, which can be set with option -n, defaults to 1+(B+3)\*(B+4)=2, which was determined empirically to achieve a load close to 50%.”

I think that it’s possible to estimate number of trimming rounds to achieve a (some) load using binomial distribution. And it should be more precious than empirically data.

Or may be I don’t understand something?

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**Author:** ![tromp](https://yyz2.discourse-cdn.com/flex036/user_avatar/forum.grin.mw/tromp/32/22_2.png) [@tromp](https://forum.grin.mw/u/tromp)\
**Post date:** [September 19, 2019, 10:19pm UTC](https://forum.grin.mw/t/the-number-of-trimming-rounds-estimation/6110/2 "2019-09-19T22:19:05Z")

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Apparently someone has proven the following Cuckoo Cycle Conjecture:

> <https://mathoverflow.net/questions/327172/seeking-proof-of-the-cuckoo-cycle-conjecture>

which allows us to compute exactly how many rounds are needed to reduce the number of remaining edges to any desired fraction.

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**Author:** ![Jack](https://avatars.discourse-cdn.com/v4/letter/j/cc9497/32.png) [@Jack](https://forum.grin.mw/u/Jack)\
**Post date:** [September 20, 2019, 1:40pm UTC](https://forum.grin.mw/t/the-number-of-trimming-rounds-estimation/6110/3 "2019-09-20T13:40:22Z")

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Oh, thx a lot. I should learn it…

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**Author:** ![BAssiboY](https://yyz2.discourse-cdn.com/flex036/user_avatar/forum.grin.mw/bassiboy/32/2551_2.png) [@BAssiboY](https://forum.grin.mw/u/BAssiboY)\
**Post date:** [September 22, 2019, 2:21pm UTC](https://forum.grin.mw/t/the-number-of-trimming-rounds-estimation/6110/4 "2019-09-22T14:21:14Z")

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I think that before your article you need to read thishttps://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC\_%D0%BA%D1%83%D0%BA%D1%83%D1%88%D0%BA%D0%B8,  
there is a foundation, and then you already have the analysis.

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**Author:** ![Jack](https://avatars.discourse-cdn.com/v4/letter/j/cc9497/32.png) [@Jack](https://forum.grin.mw/u/Jack)\
**Post date:** [October 7, 2019, 11:42am UTC](https://forum.grin.mw/t/the-number-of-trimming-rounds-estimation/6110/5 "2019-10-07T11:42:45Z")

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Yes. I’ve make a mistake.

Of course it’s possible use binomial distribution but just for the first trimming step. So the calculation gives us good estimation 63%. But a lot off different kind of graphs can lead to the same graph after the first step. These are dependent probability events.

Thx for attention