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With the growing usage of Bitcoin and other cryptocurrencies, many scalability challenges have emerged. A promising scaling solution, exemplified by the Lightning Network, uses a network of bidirectional payment channels that allows fast transactions between two parties. However, routing payments on these networks efficiently is non-trivial, since payments require finding paths with sufficient funds, and channels can become unidirectional over time blocking further transactions through them. Today's payment channel networks exacerbate these problems by attempting to deliver all payments atomically.
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Sivaraman et al. (2018) studied this question.
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