The heart of this optimization lies in the development and application of advanced linearization algorithms. These algorithms prioritize transactions based on their fee rates while maintaining the necessary topological order. Through iterative processes, they aim to identify subsets of transactions that have the highest fee rates, which is considered a complex, potentially NP-hard problem. By focusing on these high-fee-rate subsets, the algorithms seek to maximize the efficiency of transaction processing.

Efficient linearization involves not just straightforward sorting but also the employment of post-processing techniques to refine the outcomes further. These strategies include addressing the connected components within a cluster separately, thereby optimizing the process by breaking down larger clusters into smaller, more manageable groups. Additionally, bottleneck splitting serves as a targeted approach to dissect clusters at crucial transactions, facilitating piecemeal processing of the remaining transactions. This intricate approach to linearization emphasizes the importance of choosing transactions not only for their individual fee rates but also for their roles in reducing the overall search space.

The current state of these algorithms incorporates several key tactics to enhance efficiency and performance. For instance, bounding the evaluation of potential subsets with conservative upper estimates of their quality and employing a 'jump ahead' technique to quickly incorporate certain transactions based on their ancestry are methods aimed at streamlining the selection process. Furthermore, the utilization of Last-In-First-Out (LIFO) stack approaches for processing work items, alongside caching strategies to minimize recalculations, underscores the algorithm's focus on optimizing computational efforts. Early termination of evaluations when a potential subset's feerate falls short of the current best subset also plays a crucial role in ensuring efficiency.

The practical implementation of these concepts, as showcased in the current implementation, slightly deviates from its theoretical underpinnings. While it does not universally apply the strategy of connected-component splitting, it nevertheless incorporates many of the suggested improvements. These include managing multiple LIFO stacks for work items and making strategic transaction selections to minimize the search space effectively. This nuanced approach highlights the continuous evolution and adaptation of linearization strategies in optimizing transaction processing within cryptocurrency networks.