# How to linearize your cluster

**URL:** <https://delvingbitcoin.org/t/how-to-linearize-your-cluster/303>\
**Category:** Implementation\
**Tags:** wg-cluster-mempool, mempool\
**Created:** [December 18, 2023, 8:55pm UTC](https://delvingbitcoin.org/t/how-to-linearize-your-cluster/303 "2023-12-18T20:55:14Z")\
**Posts on this page:** 1\
**Showing post:** 4

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**Author:** ![lorbax](https://delvingbitcoin.org/user_avatar/delvingbitcoin.org/lorbax/32/797_2.png) [@lorbax](https://delvingbitcoin.org/u/lorbax)\
**Post date:** [January 6, 2025, 5:28pm UTC](https://delvingbitcoin.org/t/how-to-linearize-your-cluster/303/4 "2025-01-06T17:28:43Z")

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Hi! First of all I give you my compliments for your work. It is very complete and comprehensive. I am struggling to understand the following statement:

> [@sipa](#):
>
> the transactions in pot that do not belong to inc must have a feerate at least as high as can be achieved by _any_ set that includes inc and excludes exc

I have the feeling that I am missing something. Consider this example: there are three transactions a,b and c, with equal size and fees respectively 2, 1000 and 1. Suppose that a has b as only parent, and b has c as only parent, so in the graph a \to b \to c. Suppose also that inc = \{a\} and pot = \{a,b,c\}. Then adding a to \{b,c\} actually decrease feerate.

BTW the same example seems to go against the following Proposition with best = \{b,c\} and pot as a topologically valid subset of itself.

> [@sipa](#):
>
> every highest-feerate topologically-valid set among those that include inc and exclude exc _must_ contain every topologically valid subset of pot

Can examples like the above appear?

Anyway, this is needed only for the jump ahead optimization, but seems that the heart of the algo is still pretty much effective!

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