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

Abstract

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.

Estimating the Size of Natural Networks Using Local Information

“…In this work, we modify the W algorithm of Bustos et al [2] seeking higher generality and efficiency. First, we modify the proposed BFS procedure by including two stopping criteria to be examined after each iteration.…”

“…We refer the reader to the work of Bustos et al for details on their proposed algorithm. Bustos et al [2] found the constants a and b to be highly correlated, permitting the estimation of b in terms of a as…”

“…Another method proposed in the literature is the W algorithm [2]. The estimating is initiated by a single node making at most one question to its neighbors: requesting their adjacency list.…”

“…Many algorithms either require network size as a parameter or can benefit from such information [2]- [6]. However, there are no general algorithms for estimating the size of any given natural network.…”

Scalable Concurrency Control in a Dynamic Membership

“…In order to apply such technique, we apparently need to know a local estimate of system size: this is a quite intriguing research problem [2]. We explore an alternative which consists in using the feedback that we obtain from the observed return times; using that feedback we locally control token generation or removal.…”