Uniformity of improved versions of chord

Abstract

In this paper we analyse the uniformity of Chord P2P system and its improved versions defined in [1] - folded Chord. We are interested in the maximal and the minimal areas controlled by nodes in these systems. We recall known results for the classical Chord system and compare it with the new results for its modifications. It is known that the function n → n -∈2 is a threshold for a number of nodes in Chord controlling small areas (i.e. w.h.p. there exists one node controlling area of length ∈n -∈2 and for every ε>∈0 there are no nodes controlling areas of size less than n ∈-∈2∈-∈ε ). We show that the function is a similar threshold for 2-folded Chord. We also discuss the number of nodes controlling large areas and we find upper thresholds for all these P2P systems. All modifications of Chord are very soft and flexible and can be easily applied to P2P systems which use the classical Chord protocol. © 2010 Springer-Verlag Berlin Heidelberg.