  Off-chain transaction channels represent one of the leading techniques to
scale the transaction throughput in cryptocurrencies such as Bitcoin. They
allow multiple agents to route payments through one another. So far, the
topology and construction of payment networks has not been explored much.
Participants are expected to minimize costs that are due to the allocation of
liquidity as well as blockchain record fees. In this paper we study the
optimization of maintenance costs of such networks. We present for the first
time, a closed model for symmetric off-chain channels, and provide efficient
algorithms for constructing minimal cost spanning-tree networks under this
model. We prove that for any network demands, a simple hub topology provides a
2-approximation to the minimal maintenance cost showing that spanning trees in
general are efficient. We also show an unbounded price of anarchy in a greedy
game between the transactors, when each player wishes to minimize his costs by
changing the network's structure. Finally, we simulate and compare the costs of
payment networks with scale free demand topologies.
