Spanning-forest cluster linearization

The exploration of an algorithmic solution to effectively partition equal-feerate chunks within Bitcoin Core's transaction fee rate management strategy has led to a significant development. The challenge revolved around identifying and segregating transactions within a chunk that share the same fee rate but could be separated in a manner that is topologically valid. A practical solution has been found by leveraging a slight perturbation of the transactions' fee rates within the existing split/merge algorithm framework.

This innovative approach involves adjusting the fee rate of a selected transaction within a chunk either infinitesimally higher or lower than its actual value. Such adjustments enable the algorithm to identify potential splits where the adjusted transaction would either fall into the top or bottom part of the split, respectively. This is achieved without the need to actually alter the transaction fee rates but rather through simulating this change to influence the algorithm's decision-making process. For an increase in fee rate, the method looks for dependencies where the altered transaction appears in the upper segment, facilitated by specific dependency conditions. Conversely, for a decreased fee rate, the search targets dependencies placing the modified transaction at the bottom.

The procedure iterates through active and inactive dependencies to facilitate the splitting process, ensuring that if a split is feasible, it will be discovered by this bifurcation in treatment based on the transaction's hypothetical position in the chunk. It's important to note that this method requires the chunk to be otherwise optimized, as the newly generated split components are not intended to merge with others but rather to clarify the chunk's internal structure.

This algorithmic enhancement has been incorporated into Bitcoin Core through a pull request (Bitcoin Core PR #32545), marking a significant step forward in refining the split/merge strategy for transaction fee rate management. This addition promises to improve the efficiency and effectiveness of how transactions are grouped and processed based on their fee rates, offering a more nuanced approach to handling equal-feerate transactions within the network.