Estimating The Size Of Peer-To-Peer Networks Using Lambert’s W Function

In this work, we address the problem of locally estimating the size of a Peerto- Peer (P2P) network using local information. We present a novel approach for estimating the size of a peer-to-peer (P2P) network, fitting the sum of new neighbors discovered at each iteration of a breadth-first search (BFS) with a logarithmic function, and then using Lambert’s W function to solve a root of a ln(n)+b–n = 0, where n is the network size. With rather little computation, we reach an estimation error of at most 10 percent, only allowing the BFS to iterate to the third level