A max-plus perspective on package relay and block assembly

A conceptual framework is proposed to shed light on the economic incentives and marginal trade-offs that guide miners in constructing blocks. Miners face the challenge of maximizing fee collection while adhering to a block weight limit and dependency constraints, treating the selection process as an optimization problem on a directed acyclic graph (DAG). This optimization, driven by the goal of maximizing total fees within given constraints, underscores the importance of considering entire transaction packages due to dependency-induced non-linearities in their marginal contributions.

The decision-making process among miners involves a critical trade-off determined by a "shadow price" of weight, which reflects the minimum fee increase necessary to justify the inclusion of an additional unit of block weight. This shadow price, influenced by competition in the mempool, sets the feerate cutoff for transaction inclusion at any moment. The narrative also challenges the conventional interpretation that unused block space signifies inefficiency. It argues that optimal miner behavior may indeed result in underutilized block space if the transactions available do not offer positive marginal benefits at the prevailing shadow price.

Moreover, the piece discusses the application of max-plus algebra and tropical geometry to provide a mathematical foundation for understanding the optimization logic in block assembly and package relay processes. This advanced mathematical perspective helps clarify the structural, rather than strategic, implications of the constrained linear optimization framework governing these processes. Despite the complexity of these mathematical concepts, their application illuminates the inherent logic in block assembly and package relay without necessitating deep mathematical expertise.

The correspondence also touches upon criticisms regarding the practical aspects of block construction, specifically pointing out limitations due to the GetBlockTemplate (GBT) interface. These limitations are acknowledged as contributing to instances of underfilled blocks, attributed to the conservative estimation of the coinbase transaction size within the GBT protocol—a flaw preserved due to historical resistance to change. However, it is emphasized that leftover block space should not be automatically interpreted as evidence of non-optimal miner behavior, given that block assembly decisions are predicated on marginal trade-offs. This clarification aims to refine the understanding of miner behavior beyond the specific implementation details predominant in contemporary practice, highlighting the logical basis of the argument over empirical observations.