  Payment channel networks, such as Bitcoin's Lightning Network, promise to
improve the scalability of blockchain systems by processing the majority of
transactions off-chain. Due to the design, the positioning of nodes in the
network topology is a highly influential factor regarding the experienced
performance, costs, and fee revenue of network participants. As a consequence,
today's Lightning Network is built around a small number of highly-connected
hubs. Recent literature shows the centralizing tendencies to be
incentive-compatible and at the same time detrimental to security and privacy.
The choice of attachment strategies therefore becomes a crucial factor for the
future of such systems. In this paper, we provide an empirical study on the
(local and global) impact of various attachment strategies for payment channel
networks. To this end, we introduce candidate strategies from the field of
graph theory and analyze them with respect to their computational complexity as
well as their repercussions for end users and service providers. Moreover, we
evaluate their long-term impact on the network topology.
