Infinite Unlimited Churn

TL;DR

This paper investigates the problem of unlimited, ongoing peer join and leave requests in peer-to-peer networks, proving impossibility results for some cases and providing algorithms for others, including skip lists and graphs.

Contribution

It introduces the problem of infinite unlimited churn, proves the impossibility of local solutions for the fair version, and presents a solution for the unfair version applicable to multiple overlay structures.

Findings

Unsolvability of local solutions for fair infinite churn.

A correct algorithm for unfair infinite churn in linearized overlays.

Extension of the algorithm to skip lists and skip graphs.

Abstract

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.