Spanning-forest cluster linearization

In exploring the optimization of transaction processing, particularly concerning the fairness and efficiency of split operations in a network, several strategies have been considered to enhance the overall performance. The identification and implementation of the most effective split operation are crucial for maintaining an optimal state within a network. Three distinct approaches have been outlined: selecting the active dependency with the highest $q()$ value, employing a round-robin method over all chunks until a positive-$q()$ dependency is found and then choosing the highest among them, and a similar round-robin technique applied over transactions to equally distribute activity and potentially improve the fee rate by isolating less efficient children and subtrees.

The initial preference for ensuring fairness involved giving each transaction an equal opportunity to enhance its fee rate through strategic splitting, based on the assumption that this method would uniformly balance activity across all transactions. However, upon further analysis and external input, it was identified that this approach might not always lead to an improvement in every step, as there exists a possibility of repeating the same state despite the introduction of randomness to the process. This realization prompted a shift towards the second approach, which still aims to distribute work fairly but does so by focusing on transaction chunks. This method assumes that once transactions from different parties have been adequately split into separate chunks, any potential for unfair advantage or optimization has been addressed, at least until transactions cannot be further divided, suggesting they might already be in an optimal configuration. Nonetheless, the intricacy increases when optimal chunks comprise transactions from multiple parties, raising questions about the best strategy for such scenarios.

The principle that every action taken should contribute to progress underlies these strategies. It is argued that if the first approach guarantees continual advancement, so should the second, barring a theoretical scenario where only splits followed by immediate self-merges occur, potentially leading to a cyclic state. However, removing all but one splittable chunk from such a cycle would violate the premise that the first method always progresses, thereby supporting the belief that the second method should also inherently promote forward movement.

Given the challenges of optimizing transaction processing, including the difficulty of linearizing certain clusters, the integration of randomization into the algorithm has emerged as a viable solution to prevent deterministic exploitation. By incorporating randomness in various aspects of the transaction handling process—from assigning random index values to transactions to randomizing the order of dependency lists and the selection process for splits and merges—an additional layer of unpredictability is introduced. This strategy aims to thwart potential attackers from causing targeted disruptions within the network, thus enhancing the robustness of the transaction linearization process. Despite potential drawbacks like inconsistent relay behavior, the benefits of preventing deterministic attacks are deemed to outweigh these concerns, especially considering the expectation that most clusters not created with adversarial intent can be efficiently linearized in a negligible timeframe using structured financial lists (SFL).