A graph theoretical lower bound on maintenance overhead of structured P2P overlays

ABSTRACT

Maintenance overhead of a structured peer-to-peer network under churn depends on many factors. One of these factors is the created and maintained overlay topology. We describe these structured overlays as sets of possible overlay graphs for both stable and transient states due to network node leave and join events. We use the graph edit distance concept to determine the minimal communication cost of moving from a transient state to a stable state. Based on these communication costs we establish a theoretical lower bound on the maintenance overhead as the function of the churn rate. By using our model it is possible to determine whether the overlay topology maintained by the self-organizing algorithm of a structured peer-to-peer system is a bottleneck under dynamically changing environments. We analyze the Chord and the eQuus systems as examples.