AI 中文总结
研究比特币内存池线性化问题，提出通过将交易划分成子集并结合线性规划公式刻画。基于单纯形法特性开发SFL算法，直接在交易依赖图上操作，实验表明其能快速计算最优线性化，为矿工交易优先级提供实用框架。
AI 中文摘要
在比特币系统中，交易不断进入矿工内存池等待被纳入未来区块。非coinbase交易需花费先前交易产生的未花费输出，导致内存池中的交易存在依赖约束。同时，矿工受经济激励优先处理费率更高的交易。本文提出内存池线性化问题：给定一组有相关费用、大小和依赖关系的交易，计算一个尊重依赖关系的交易排序，在支持内存池动态更新时最大化费率效率。通过将交易划分为不相交的按总费率降序排列的尊重依赖关系的子集以及等价的线性规划公式来刻画该问题。基于单纯形法中基本可行解的结构特性，开发了一种名为生成森林线性化（SFL）的新算法。SFL直接在交易依赖图上操作，迭代合并和分割交易块以优化全局排序，并保证在最优解处终止。对合成和真实世界比特币内存池数据的评估表明，SFL始终能以比竞争方法低得多的运行时间计算出最优线性化。这些结果表明SFL为大型且快速演变的内存池中去中心化矿工的交易优先级提供了一个实用且可扩展的框架。SFL也已被纳入比特币核心代码库用于交易簇线性化。
英文摘要
In the Bitcoin system, transactions arrive continuously at miners' mempools and await inclusion in future blocks. Every non-coinbase transaction must spend one or more unspent outputs created by previous transactions, inducing dependency constraints among transactions in the mempool. At the same time, miners are economically incentivized to prioritize transactions with higher fee rates, measured as transaction fee per unit size. This paper formulates the mempool linearization problem: given a set of transactions with associated fees, sizes, and dependency relationships, compute a dependency-respecting transaction ordering that maximizes fee-rate efficiency while supporting efficient updates as the mempool evolves dynamically. The problem is characterized through a partition of transactions into disjoint dependency-respecting subsets ordered by decreasing aggregate fee rate, together with an equivalent linear programming formulation. Motivated by structural properties of basic feasible solutions in the simplex method, a new algorithm called spanning forest linearization (SFL) is developed. Operating directly on the transaction dependency graph, SFL iteratively merges and splits chunks of transactions to refine a global ordering, and is guaranteed to terminate at an optimal solution. Evaluation on both synthetic and real-world Bitcoin mempool data shows that SFL consistently computes optimal linearizations with substantially lower runtime than competing approaches, including a method based on the parametric preflow algorithm of Gallo, Grigoriadis, and Tarjan. These results indicate that SFL provides a practical and scalable framework for transaction prioritization by decentralized miners in large and rapidly evolving mempools. SFL has also been incorporated into the Bitcoin Core codebase for transaction cluster linearization.
