The concept introduces a novel structure where transactions are organized into clusters based on their connectivity, enabling more efficient transaction relay, block validation, building, and eviction processes. This structuring also facilitates Replace-By-Fee (RBF) evaluations and improves fee estimation accuracy.

Clusters are defined as groups of transactions interconnected by parent-child relationships, with each cluster maintaining a precomputed and constantly updated linearization representing the sequence in which its transactions would ideally be mined. These linearizations are crucial for constructing blocks by selecting high-feerate transactions while ensuring that parent transactions precede their children. Additionally, chunks—subsets of transactions within a linearization that would be included in a block together—are identified to optimize mining efficiency and fee collection.

The process involves complex algorithms aimed at determining the optimal arrangement of transactions within clusters to maximize the feerate, i.e., the fee per unit size of a transaction. The concept relies heavily on the construction and maintenance of feerate diagrams, graphical representations that help visualize the cumulative fee versus size relationship of transactions. These diagrams facilitate comparisons between different linearizations or cluster arrangements, aiding in identifying the most effective transaction sequencing for inclusion in a block.

Significant computational resources are dedicated to finding high-feerate subsets within a cluster, a task that is abstracted in this discussion but is pivotal for achieving optimal linearization. While the practical application of these concepts requires intricate details and algorithms beyond the scope of this summary, the overall goal remains clear: to streamline transaction processing and block creation in Bitcoin Core through efficient mempool management.

Implementations of these ideas have been proposed in Bitcoin Core PRs, showcasing concrete steps towards integrating cluster linearization into the system. These include methods for merging linearizations, optimizing them through incremental improvements, and post-processing techniques to refine transaction sequencing further. Such efforts highlight the ongoing advancements in optimizing blockchain technology for better performance and scalability.

This exploration of cluster linearization sheds light on the continuous efforts to enhance Bitcoin Core’s functionality, focusing on optimizing the mempool's handling for improved transaction processing and block generation. By redefining how transactions are organized and processed, cluster linearization represents a significant step forward in the blockchain's evolution, promising increased efficiency and effectiveness in network operations.