[论文解读] Optimally Reliable & Cheap Payment Flows on the Lightning Network.

Rene Pickhardt, Stefan Richter|arXiv (Cornell University)|Jul 12, 2021

Blockchain Technology Applications and Security参考文献 7被引用 6

一句话总结

本文提出了一种基于轮次的、最小费用流算法，通过概率性地建模通道余额不确定性，并使用广义整数最小费用流来寻找最可靠且最便宜的多部分支付（MPP）路径，从而优化闪电网络支付。通过利用失败和成功尝试的反馈，迭代地改进成功概率估计，该方法在大型支付中实现了近乎完全的交付成功率——支付规模可达当前方法的数个数量级。

ABSTRACT

Today, payment paths in Bitcoin's Lightning Network are found by searching for shortest paths on the fee graph. We enhance this approach in two dimensions. Firstly, we take into account the probability of a payment actually being possible due to the unknown balance distributions in the channels. Secondly, we use minimum cost flows as a proper generalization of shortest paths to multi-part payments (MPP). In particular we show that under plausible assumptions about the balance distributions we can find the most likely MPP for any given set of senders, recipients and amounts by solving for a (generalized) integer minimum cost flow with a separable and convex cost function. Polynomial time exact algorithms as well as approximations are known for this optimization problem. We present a round-based algorithm of min-cost flow computations for delivering large payment amounts over the Lightning Network. This algorithm works by updating the probability distributions with the information gained from both successful and unsuccessful paths on prior rounds. In all our experiments a single digit number of rounds sufficed to deliver payments of sizes that were close to the total local balance of the sender. Early experiments indicate that our approach increases the size of payments that can be reliably delivered by several orders of magnitude compared to the current state of the art. We observe that finding the cheapest multi-part payments is an NP-hard problem considering the current fee structure and propose dropping the base fee to make it a linear min-cost flow problem. Finally, we discuss possibilities for maximizing the probability while at the same time minimizing the fees of a flow. While this turns out to be a hard problem in general as well - even in the single path case - it appears to be surprisingly tractable in practice.

研究动机与目标

• 解决由于通道余额分布未知而导致的闪电网络大额支付高失败率问题。
• 改进当前基于最短路径的路由机制，该机制忽略可靠性且无法优化多部分支付的拆分。
• 开发一种系统化、可扩展的方法，以最大化支付成功概率并最小化路由费用。
• 实现接近或超过发送方本地总余额的可靠支付交付。
• 提供一种实用的迭代算法，通过试错反馈学习，逐步优化各轮次的路由决策。

提出的方法

• 使用从估计成功概率的负对数导出的可分凸成本函数来建模通道成功概率。
• 将最优MPP表述为具有可分凸成本函数的整数最小费用流问题，可在多项式时间内求解。
• 采用基于轮次的算法，在每轮结束后使用先前结果更新的成功概率估计重新计算最小费用流。
• 结合成功和失败支付尝试的反馈，动态优化通道可靠性先验。
• 提出将基础费用移除以线性化成本函数，将问题转化为标准线性最小费用流，从而提升效率。
• 将溯源评分（如节点运行时间）整合到成功概率模型中，以增强可靠性估计。

实验结果

研究问题

• RQ1 能否通过原则性的数学框架，同时优化闪电网络多部分支付的成本与成功概率？
• RQ2 如何对通道余额分布的不确定性进行建模，并将其整合到路由决策中以提升可靠性？
• RQ3 失败和成功支付尝试的迭代反馈对大额支付收敛性和成功率有何影响？
• RQ4 在何种程度上，寻找最便宜且最可靠的MPP问题可以被高效求解？其何时会变为NP难问题？
• RQ5 在长期路由规划中，如何考虑通道流动性与节点行为的动态变化？

主要发现

• 所提出的基于轮次的算法在所有实验中仅需个位数轮次，即可实现接近发送方总本地余额的可靠支付交付。
• 与当前最先进方法相比，该方法将可可靠交付的支付规模提升了数个数量级。
• 在当前费用结构下，寻找最便宜MPP的问题是NP难的，但当移除基础费用后，问题变得可解，退化为线性最小费用流问题。
• 具有可分凸成本的广义最小费用流公式可实现多项式时间内的精确解，时间复杂度为O(log(U)·(m²+mn)·log(n))。
• 该算法在通用硬件上仍具实用性，当前公共闪电网络上的估计运行时间低于一秒。
• 集成溯源评分并动态学习支付反馈显著提升了长期路由的可靠性和适应性。