The Necessity of Supernodes in P2P networks and Distributed Hash Tables
David Hadaller, Tyrel Russell investigated searching in P2P networks
with the goal of showing that supernodes are necessary for efficient
searching. We are taking an theoretic approach and aim to establish
some results which relate the maximum degree of nodes in a graph with
the graphs diameter, which for our purposes, nicely represents the maximum
time for a search in a P2P network. We were able to show a diameter of
less than the log of the number of nodes in a network is not possible
without supernodes, and then construct a graph with diameter of loglog
of the number of nodes using a supernodes.