The essence of this approach lies in its utilization of a series of sets, denoted as $S_i$, which are derived from a static pool of topologically-valid sets determined through fuzz testing. This methodology is applied to an initial cluster, also generated via fuzz testing, to establish a preliminary linearization framework.

The evaluation metrics for the effectiveness of this linearization strategy are multi-fold. Firstly, it's imperative that the resultant linearization adheres to topological principles, ensuring that the structure remains logically coherent. Secondly, the quality of the linearization's diagram post-process must be equivalent to, if not surpass, that of the initial diagram. This criterion underscores the importance of maintaining or enhancing the visual and structural clarity of the linearization throughout the process. Lastly, and perhaps most critically, the feerate diagram for each set size $\operatorname{size}(S_i)$ must meet or exceed a specific threshold, $\operatorname{fee}(S_i)$, for every set $i$ considered.

A pivotal discovery within this exploration is the realization that omitting any of the $2^n-1$ intersections from consideration results in failures to meet the last mentioned condition. This outcome highlights the fundamental importance of these intersections in achieving the desired feerate outcomes. Thus, the research implicitly suggests that the intersections play a crucial role in not only maintaining but potentially enhancing the feerate efficiency of the linearization process, thereby underscoring their indispensability in the optimization of linearization strategies within the context of fuzz testing.