This is a brief summary of the paper On the Impact of Attachment Strategies for Payment Channel Networks by Kimberly Lange, Elias Rohrer, and Florian Tschorsch. Here is a link to the prettier writeup on substack.
Summary
There is a financial incentive for creating channels in the Lightning Network that increase a node's connectivity and/or centrality. However, there is a conflict between the self-motivated node and the long-term development of the network. For example, centralization leads to cheaper fees but at the expense of network robustness. The authors investigate six attachment strategies, their advantages, and their impact on the Lightning Network topology.
Joining the Network
In general, an attachment strategy S takes as parameters G, k, and cap where G is a snapshot of the Lightning Network, k is the budget (# of channels), and cap is the capacity, and returns a list of nodes with which to open channels. Note that the authors don't consider nodes with pre-existing channels. An attachment strategy is for a joining node to use.
The authors identified 3 main motivations that a node might have when joining the network:
- End-users who are interested in improving their local connectivity and their cost to use the network.
- Service provides who are interesting in earning transaction fees and selling liquidity.
- The network. This is the altruistic motivation to improve robustness, decrease centralization, and make the network cheaper for all.
Network Attachment Strategies
Simpler Strategies:
- Random - suggest k nodes uniformly at random.
- Highest Degree - suggest k nodes with highest degree.
- Betweenness Centrality - suggest k nodes with the highest betweenness centrality (an indicator of how many cheapest paths a node lies on).
Motivated Strategies:
- k-Center - suggest k nodes which minimize the joining node’s maximum distrance from all other nodes.
- k-Median - suggest k nodes which minimize the joining node’s average distance from all other nodes,
- Maximum Betweenness Improvement (MBI) - suggest k nodes which maximize the number of cheapest paths that the joining node lies on.
Network Simulator
The authors used a custom network simulator to analyze each othese six attachment strategies. The network simulator is capable of simulating channel openings and payment processing. They evaluate metrics from both a node-centric PoV and from a network-wide PoV. Metrics such as transaction succcess rate, cost to use the network and fee revenue. The simulator uses a snapshot of the Lightning Network taken on May 1, 2020.
Transaction Success
Experiment setup:
- The network simulator simulates a joining node opening channels according to a given attachment strategies and budget.
- Afterwards, the network simulator attempts 1,000 fixed-size payments between the joining node and randomly selected nodes and records the success ratio.
- This experiment is repeated for each attachment strategy, for a range of budgets from 1 to 15 and for 3 different payment sizes: 100 sats, 10,000 sats, and 1M sats.
Note that the dashed line indicates network average success rate.
Observations:
- Unsurprisingly, having a greater budget leads to greater payment success.
- All but Random perform better than network average on small payment size.
- Preferential attachment strategies (Betweenness and Highest Degree) performed best, especially for larger payment sizes.
Transaction Fees/Routed Transactions
Experiment Setup:
Similar setup as the above experiment with a few difference:
- The network simulator simulates a joining node opening channels according to a given attachment strategies and budget.
- Afterwards, the network simulator attempts 10,000 fixed-size payments between pairs of randomly selected nodes and records the traffic routed by the joining node and the cost for the joining node to use the network.
- This experiment is repeated for each attachment strategy, for a range of budgets from 1 to 15 and for a single payment size: 10,000 sats.
Observations:
- Random requires opening at least 6 channels to reach the below average network fee.
- Most strategies lead to lower fees, but k-Median performs best in this regard followed by MBI.
- MBI lead to the greatest increase in routed traffic, allowing the joining node to route 6% of network traffic after opening 15 channels.
Runtime Analysis
The authors also recorded the runtime of each strategy in this experiment.
Observations:
- The runtimes of Highest Degree, Betweenness, and k-Center stay consistent.
- The runtime of k-Median increases about 2 seconds with each additional channel.
- Each additional channel increases the runtime of MBI by about 2,500 seconds or 40 minutes.
The last experiment of this paper did not include the MBI strategy because of it’s intractible runtime. If you would like to learn more about my research finding a much faster MBI strategy, feel free to email me or message me on Twitter.
Long-term Impact
Experiment setup:
- The network simulator simulates 5,000 nodes joining the network using a certain strategy. Each nodes is given a budget of 10 channels.
- After every interval of 500 joining nodes, the network simulates 1,000 payments of 100 sats and records the following metrics: (a) centralization, (b) diameter, (c) payment success rate, (d) and cost to use the network.
- Prefential attachment strategies like Betweenness and Highest Degree have little impact on improving centralization and network diameter.
- After 500 nodes, k-Center is the only strategy to bring payment success rate to 100%.
- k-Center is also the best performing strategy for lowering fees, while Random actually lead to increased fees.
References
Elias Rohrer; Julian Malliaris; Florian Tschorsch (2021)
On the Impact of Attachment Strategies for Payment Channel Networks
2021 IEEE International Conference on Blockchain and Cryptocurrency
Technical corrections/questions welcome! :)