I’d like to share my latest research notebook, A Geometric Approach for Optimal Channel Rebalancing, which builds upon the mathematical theory of payment channel networks to provide a framework for improving liquidity management in payment channel networks. This work builds on earlier discussions about channel depletion and topology cycles and was hinted as one possible mitigation in this Delving Bitcoin thread.

While off-chain rebalancing does not affect the expected rate of payment feasibility in theory, in practice, unbalanced channels lead to frequent routing failures even if the payment was feasible. This notebook investigates whether structured, globally optimal replenishment can mitigate this issue—even when starting from a severely depleted network.

lightning

> *by renepickhardt*
>
> I’d like to share my latest research notebook, A Geometric Approach for Optimal Channel Rebalancing, which builds upon the mathematical theory of payment channel networks to provide a framework for improving liquidity management in payment channel networks. This work builds on earlier discussions about channel depletion and topology cycles and was hinted as one possible mitigation in this Delving Bitcoin thread.
>
> ### Motivation
>
> While off-chain rebalancing does not affect the expected rate of payment feasibility in theory, in practice, unbalanced channels lead to frequent routing failures even if the payment was feasible. This notebook investigates whether structured, globally optimal replenishment can mitigate this issue—even when starting from a severely depleted network.
>
> **[...read more at delvingbitcoin.org](https://delvingbitcoin.org/t/research-update-a-geometric-approach-for-optimal-channel-rebalancing/1768)**

MotivationMotivation