English

On the Convergence Rate of the One-Hop Transfer Algorithm

Optimization and Control 2026-03-31 v1

Abstract

The transfer algorithm~\cite{jiang} solves the on-chain one-hop swap routing problem. In \cite{jiang}, the convergence is proved but the convergence rate is left open. We prove that the algorithm terminates in at most O(Nκlog1ε)\mathcal{O}(N\kappa\log\frac{1}{\varepsilon}) rounds, where NN is the number of AMMs, κ\kappa a liquidity heterogeneity parameter and ε\varepsilon a tolerance parameter.

Keywords

Cite

@article{arxiv.2603.27172,
  title  = {On the Convergence Rate of the One-Hop Transfer Algorithm},
  author = {Ruichao Jiang and Long Wen},
  journal= {arXiv preprint arXiv:2603.27172},
  year   = {2026}
}