How to linearize your cluster

The Spanning-Forest Linearization (SFL) algorithm is emerging as a preferable choice over the min-cut GGT algorithm for transaction clustering linearization, despite its potentially worse asymptotic complexity and lack of termination proof. SFL's practical advantages stem from several key features that align well with real-world application requirements. One significant advantage is its status as an anytime algorithm, allowing interruption at any stage while still providing useful linearization output. This contrasts with GGT, where incomplete min-cuts may not offer any improvement. Additionally, SFL can enhance existing linearizations, making it possible to initiate the algorithm with a pre-existing linearization and guarantee an output that is either an improvement or at least equal in quality.

Another point in favor of SFL over both GGT and CSS (candidate set search) involves load balancing and fairness during operation. Unlike GGT and CSS, which require subdividing the problem into various subproblems, potentially complicating computation budget allocation, SFL operates on a single state, simplifying budgeting decisions. Furthermore, SFL ensures a more equitable distribution of computational effort across all transactions within a cluster by employing a round-robin approach to dependency improvement. This aspect is particularly advantageous in preventing attackers from disproportionately affecting the algorithm's focus through complex transaction sets.

Performance metrics also support the selection of SFL; preliminary benchmarks indicate that SFL is approximately twice as fast as GGT when analyzing replayed mempool data. Moreover, the algorithm's reliance on integer arithmetic is less demanding in terms of the precision required compared to GGT, needing integers large enough to represent only $2SF$ rather than $2S^3R$, thereby simplifying implementation.

Despite its benefits, SFL is not without drawbacks, especially when compared to CSS and GGT. The absence of complexity bounds for SFL, suggesting a potential worst-case runtime of $\mathcal{O}(n^5)$, raises concerns about predictability and efficiency in extreme cases. Unlike CSS, which can incorporate optimal ancestor sets for improved topological ordering, SFL lacks a mechanism for integrating such criteria, possibly diminishing the quality of linearization under certain conditions. Also, SFL does not inherently prioritize smaller chunks as CSS does, which may result in less optimal chunk minimization within feerate-diagram-optimal linearizations.

In summary, the SFL algorithm offers a compelling alternative for transaction clustering linearization, balancing practical performance with ease of use. Its advantages in terms of anytime algorithm capability, enhancement of existing linearizations, load balancing, fairness, and reduced integer size requirements position it as a strong candidate for widespread adoption. However, considerations regarding its theoretical limitations and comparative disadvantages in specific aspects warrant further investigation and development.