Chapter

Grid Computing

pp 61-72

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

  • Javier Bustos-JimenezAffiliated withEscuela de Ingenieria Informatica, Universidad Diego Portales
  • , Nicolas BersanoAffiliated withEscuela de Ingenieria Informatica, Universidad Diego Portales
  • , Satu Elisa SchaefferAffiliated withUniversidad Autonoma de Nuevo Leon
  • , Jose Miguel PiquerAffiliated withDepartamento de Ciencias de la Computacion, Universidad de Chile
  • , Alexandru IosupAffiliated withParallel and Distributed Systems Group, Delft University of Technology
  • , Augusto CiuffolettiAffiliated withDepartment of Computer Science, University of Pisa

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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.

Keywords

Peer-to-Peer Network size Estimation