A Dijkstra-based Lightning Network routing algorithm is correct and polynomial for consistent (non-negative-rate) fee functions, and the routing problem is NP-hard for arbitrary fee functions.
NP-hardness of shortest path problems in networks with non-fifo time-dependent travel times.Information Processing Letters, 179:106287, 2023
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An Analysis of the Correctness and Computational Complexity of Path Planning in Payment Channel Networks
A Dijkstra-based Lightning Network routing algorithm is correct and polynomial for consistent (non-negative-rate) fee functions, and the routing problem is NP-hard for arbitrary fee functions.