Spanning-forest cluster linearization

The analysis presented delves into the strengths and challenges of the SFL algorithm compared to other algorithms like GGT and CSS in optimizing linearization processes. One critical area of focus is the termination condition of the SFL algorithm. It's established that if the algorithm terminates, it guarantees an optimal linearization outcome. However, uncertainty looms over its ability to consistently reach termination. Fuzzing tests suggest that the heuristic of merging chunks based on the maximum feerate difference could prevent repetitive states, potentially ensuring termination due to the finite nature of possible states.

Another significant aspect discussed is the complexity bound of the SFL algorithm. While a basic upper limit on iterations can be deduced from the finite state space, this ceiling isn't practically insightful due to its vastness. A more nuanced approach suggests considering the active dependencies and their arrangement as a spanning forest, which still results in an exponential complexity bound but offers a slightly more constrained perspective.

The discussion further highlights a challenge with equal-feerate chunk splitting. The algorithm's current design requires careful balancing between when to split and merge chunks based on their feerate differences to avoid infinite loops or non-topological outcomes. Identifying an efficient method for splitting chunks into topologically valid, separate equal-feerate components remains an open question. This issue extends to the granularity within chunks themselves, where the current SFL framework does not provide a mechanism to order transactions, thus affecting block building processes that require sub-chunk granularity.

Additionally, the potential for LIMO-like improvements is considered valuable. Such enhancements would allow directed steps within an SFL state to achieve linearizations at least as beneficial as rearranging subsets. This opens possibilities for integrating ancestor sets into the state for improved linearization outcomes.

Finally, the possibility of merging different SFL states into a third that combines the optimality of both is explored. While achievable through a roundabout process of extracting and merging linearizations before reapplying SFL, this method is less efficient and loses information intrinsic to the SFL states. An optimal final SFL state provides clear indications of no further beneficial splits or merges, achievable in quadratic time, contrasting with the cubic time requirements of computing a single min-cut with advanced algorithms. This exploration underscores the need for further research and development to address these identified gaps and improve the SFL algorithm's efficiency and applicability.