Dynamic Analysis of the Arrow Distributed Directory Protocol in General Networks

TL;DR

This paper demonstrates that the Arrow distributed directory protocol achieves an O(log n) competitive ratio on general networks using probabilistic tree embeddings, even under dynamic, concurrent, and asynchronous conditions.

Contribution

It introduces a randomized distributed queueing algorithm based on the Arrow protocol with proven constant competitive ratio on hierarchically well separated trees.

Findings

Achieves O(log n) competitive ratio on general networks.

Proves constant competitive ratio on hierarchically well separated trees.

Works under dynamic, concurrent, and asynchronous request conditions.

Abstract

The Arrow protocol is a simple and elegant protocol to coordinate exclusive access to a shared object in a network. The protocol solves the underlying distributed queueing problem by using path reversal on a pre-computed spanning tree (or any other tree topology simulated on top of the given network). It is known that the Arrow protocol solves the problem with a competitive ratio of O(log D) on trees of diameter D. This implies a distributed queueing algorithm with competitive ratio O(s*log D) for general networks with a spanning tree of diameter D and stretch s. In this work we show that when running the Arrow protocol on top of the well-known probabilistic tree embedding of Fakcharoenphol, Rao, and Talwar [STOC 03], we obtain a randomized distributed queueing algorithm with a competitive ratio of O(log n) even on general network topologies. The result holds even if the queueing requests occur in an arbitrarily dynamic and concurrent fashion and even if communication is asynchronous. From a technical point of view, the main of the paper shows that the competitive ratio of the Arrow protocol is constant on a special family of tree topologies, known as hierarchically well separated trees.