On Stabilizing Departures in Overlay Networks

A fundamental problem for peer-to-peer systems is to maintain connectivity while nodes are leaving, i.e., the nodes requesting to leave the peer-topeer system are excluded from the overlay network without affecting its connectivity. There are a number of studies for safe node exclusion if the overlay is in a well-defined state initially. Surprisingly, the problem has not been formally studied yet for the case in which the overlay network is in an arbitrary initial state, i.e., we are looking for a self-stabilizing solution for excluding leaving nodes. We study this problem in two variants: the Finite Departure Problem (FDP) and the Finite Sleep Problem (FSP). In the FDP the leaving nodes have to irrevocably decide when it is safe to leave the network, whereas in the FSP , this leaving decision does not have to be final: the nodes may resume computation if necessary. We show that there is no self-stabilizing distributed algorithm for theFDP , even in a synchronous message passing model. To allow a solution, we introduce an oracle called NIDEC and show that it is sufficient even for the asynchronous message passing model by proposing an algorithm that can solve the FDP using NIDEC. We also show that a solution to the FSP does not require an oracle.