A probabilistic analysis of Kademlia networks

Abstract

Kademlia [3] is currently the most widely used searching algorithm in p2p (peer-to-peer) networks. This work studies an essential question about Kademlia from a mathematical perspective: how long does it take to locate a node in the network? To answer it, we introduce a random graph K and study how many steps are needed to locate a given vertex in K using Kademlia's algorithm, which we call the routing time. Two slightly different versions of K are studied. In the first one, vertices of K are labeled with fixed IDs. In the second one, vertices are assumed to have randomly selected IDs. In both cases, we show that the routing time is about c logn, where n is the number of nodes in the network and c is an explicitly described constant. © 2013 Springer-Verlag.