I'm aware a quick Google wields tons of results and the literature on this topic is very rich, and that is exactly the problem. Among the universe of possible solutions I'm not sure which specifically is the best, up-to-date choice for my specific needs.
I'm trying to implement a p2p network over the internet with the only and one feature of broadcasting messages to online nodes. In order to connect to the network, you must be able to point to existing IPs. When you do, you discover some peers and keep an active connection with them. You then can send messages to every other node. There is no direct communication, every message sent is received by everyone else. I want this network to be as performant as possible, and work on top of UDP.
What are the names of some state of art algorithms to solve this problem on the shape here specified?
A broadcast of a single message in an overlay network over the internet is a fairly simple affair. You join the network, build a randomized or structured routing table of neighbors, flood neighbors with the message, they do the same with their neighbors, minus some pruning to avoid forwarding loops.
Complexity arises from additional constraints and requirements which vary from network to network. E.g. trust problems in anonymous settings, latency optimizations, optimizing high-bandwidth streams of many messages (p2p-assisted live video broadcasting), etc.