Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection

TL;DR

This paper proposes an efficient algorithm for designing payment channel network topologies and transaction decisions to maximize throughput and reduce costs, validated through theoretical analysis and empirical study of the Lightning Network.

Contribution

It introduces an $ ext{O}(p)$ approximation algorithm for PCN topology and transaction decision optimization, with improved $ ext{O}(\sqrt{p})$ ratio under certain assumptions.

Findings

The $ ext{O}(p)$ approximation algorithm effectively minimizes costs.

Under specific assumptions, the approximation ratio improves to $ ext{O}(\sqrt{p})$.

Empirical results support the approach's applicability to the Lightning Network.

Abstract

Payment channel networks (PCNs) are a promising technology that alleviates blockchain scalability by shifting the transaction load from the blockchain to the PCN. Nevertheless, the network topology has to be carefully designed to maximise the transaction throughput in PCNs. Additionally, users in PCNs also have to make optimal decisions on which transactions to forward and which to reject to prolong the lifetime of their channels. In this work, we consider an input sequence of transactions over $p$ parties. Each transaction consists of a transaction size, source, and target, and can be either accepted or rejected (entailing a cost). The goal is to design a PCN topology among the $p$ cooperating parties, along with the channel capacities, and then output a decision for each transaction in the sequence to minimise the cost of creating and augmenting channels, as well as the cost of rejecting transactions. Our main contribution is an $\mathcal{O}(p)$ approximation algorithm for the problem with $p$ parties. We further show that with some assumptions on the distribution of transactions, we can reduce the approximation ratio to $\mathcal{O}(\sqrt{p})$. We complement our theoretical analysis with an empirical study of our assumptions and approach in the context of the Lightning Network.