Dianne Foreback | Searcharxiv

arXiv2016

Infinite Unlimited Churn

We study unlimited infinite churn in peer-to-peer overlay networks. Under this churn, arbitrary many peers may concurrently request to join or leave the overlay network; moreover these requests may never stop coming. We prove that unlimited adversarial churn, where processes may just exit the overlay network, is unsolvable. We focus on cooperative churn where exiting processes participate in the churn handling algorithm. We define the problem of unlimited infinite churn in this setting. We distinguish the fair version of the problem, where each request is eventually satisfied, from the unfair version that just guarantees progress. We focus on local solutions to the problem, and prove that a local solution to the Fair Infinite Unlimited Churn is impossible. We then present and prove correct an algorithm UIUC that solves the Unfair Infinite Unlimited Churn Problem for a linearized peer-to-peer overlay network. We extend this solution to skip lists and skip graphs.

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arXiv2016

Packet Efficient Implementation of the Omega Failure Detector

We assume that a message may be delivered by packets through multiple hops and investigate the feasibility and efficiency of an implementation of the Omega Failure Detector under such an assumption.To motivate the study, we prove that the existence and sustainability of a leader is exponentially more probable in a multi-hop Omega implementation than in a single-hop one.An implementation is: \emph{message efficient} if all but finitely many messages are sent by a single process; \emph{packet efficient} if the number of packets used to transmit a message in all but finitely many messages is linear w.r.t the number of processes, packets of different messages may potentially use different channels, thus the number of used channels is not limited; \emph{super packet efficient} if the number of channels used by packets to transmit all but finitely many messages is linear.We present the following results for deterministic algorithms. If reliability and timeliness of one message does not correlate with another, i.e., there are no channel reliability properties, then a packet efficient implementation of Omega is impossible. If eventuallytimely and fair-lossy channels are considered, we establish necessary and sufficient conditions for the existence of a message and packet efficient implementation of Omega. We also prove that the eventuality of timeliness of channels makes a super packet efficientimplementation of Omega impossible. On the constructive side, we present and prove correct a deterministic packet efficient implementation of Omega that matches the necessary conditions we established.

cs.DC↗