delvingbitcoin

How to linearize your cluster

How to linearize your cluster

Original Postby lorbax

Posted on: January 6, 2025 17:30 UTC

The email begins with a compliment on the recipient's comprehensive work but quickly moves into expressing confusion about a specific statement related to transaction feerates within a given set.

The sender is puzzled by the assertion that transactions not belonging to a subset "inc" within a larger set "pot" must have a feerate at least as high as any set that includes "inc" and excludes another subset "exc." To illustrate their confusion, they present an example involving three transactions, labeled $a$, $b$, and $c$, each with equal size but different fees. These transactions are interconnected in a hierarchical structure where $a$ depends on $b$, and $b$ depends on $c$. They note that including transaction $a$ in a set with $b$ and $c$ would actually decrease the overall feerate, contrary to the proposition under discussion.

The sender further elaborates on their example to challenge another proposition stating that every highest-feerate, topologically-valid set that includes "inc" and excludes "exc" must contain every topologically valid subset of "pot". They question whether scenarios like their example could occur, which seems to counter the proposition. Despite these concerns, the sender acknowledges that these issues only arise in the context of optimizing for what they refer to as "jump ahead," suggesting that the core algorithm remains largely effective regardless of these potential discrepancies. This indicates a nuanced understanding of the algorithm in question and points to a specific area where its logic might be improved or clarified.

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