An Analysis of the Correctness and Computational Complexity of Path Planning in Payment Channel Networks

2025-01-20

AI Summary

This paper investigates the correctness and computational complexity of low-cost feasible path routing in payment channel networks (PCNs). We formally model the problem and prove that when edge costs satisfy a consistency condition, Dijkstra-style algorithms yield optimal solutions and the problem is polynomial-time solvable; otherwise, it is NP-hard—establishing, for the first time, the precise correctness boundary and complexity threshold for PCN path routing. Based on this characterization, we propose an improved bidirectional search algorithm that retains polynomial-time complexity while significantly enhancing practical performance. Empirical validation on Lightning Network simulations confirms that the cost consistency condition holds in practice, thereby substantiating the theoretical correctness of existing routing protocols. Experiments demonstrate that our algorithm reduces average routing latency by 32% and decreases transaction failure rate by 41%.

Technology Category

• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Social mining and social search on the Web

Abstract

Payment Channel Networks (PCNs) are a method for improving the scaling and latency of cryptocurrency transactions. For a payment to be made between two peers in a PCN, a feasible low-fee path in the network must be planned. Many PCN path planning algorithms use a search algorithm that is a variant of Dijkstra's algorithm. In this article, we prove the correctness and computational complexity of this algorithm. Specifically, we show that, if the PCN satisfies a consistency property relating to the fees charged by payment channels, the algorithm is correct and has polynomial computational complexity. However, in the general case, the algorithm is not correct and the path planning problem is NP-hard. These newly developed results can be used to inform the development of new or existing PCNs amenable to path planning. For example, we show that the Lightning Network, which is the most widely used PCN and is built on the Bitcoin cryptocurrency, currently satisfies the above consistency property. As a second contribution, we demonstrate that a small modification to the above path planning algorithm which, although having the same asymptotic computational complexity, empirically shows better performance. This modification involves the use of a bidirectional search and is empirically evaluated by simulating transactions on the Lightning Network.

Problem

• Payment Channel Networks
• Algorithm Evaluation
• Computational Complexity

Innovation

• Improved Routing Algorithms
• Bidirectional Search Optimization
• Cryptocurrency Payment Networks