Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection

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.