# Spanning-forest cluster linearization

**URL:** <https://delvingbitcoin.org/t/spanning-forest-cluster-linearization/1419>\
**Category:** Implementation\
**Tags:** mempool\
**Created:** [February 4, 2025, 2:31pm UTC](https://delvingbitcoin.org/t/spanning-forest-cluster-linearization/1419 "2025-02-04T14:31:21Z")\
**Posts on this page:** 1\
**Showing post:** 11

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**Author:** ![blockchainhao](https://delvingbitcoin.org/user_avatar/delvingbitcoin.org/blockchainhao/32/1246_2.png) [@blockchainhao](https://delvingbitcoin.org/u/blockchainhao)\
**Post date:** [January 16, 2026, 3:21pm UTC](https://delvingbitcoin.org/t/spanning-forest-cluster-linearization/1419/11 "2026-01-16T15:21:23Z")

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> [@sipa](#):
>
> The simplex algorithm then maintains a set of n-1 **_free_ variables** , which are chosen to be zero. All other variables (the **_basic_ variables** ) can be computed from the free variables using the m+2 equations.

I think here g as the optimization target shouldn’t be seen as a variable and g = \sum\_i t\_i \mathrm{fee} as the goal function shouldn’t be seen as an equation. So it’s better to say: the m + 1 basic variables can be computed from the free variables using the m + 1 equations

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