Compositional competitiveness for distributed algorithms

TL;DR

This paper introduces a new throughput-based measure of competitiveness for distributed algorithms that is compositional, allowing the combination of algorithms with predictable competitive ratios, demonstrated through collect operations.

Contribution

It defines a novel throughput-competitiveness measure for distributed algorithms that supports compositional analysis, and proves competitiveness of algorithms for collect operations.

Findings

Proves throughput-competitiveness of a class of collect algorithms.

Demonstrates compositional construction of competitive distributed algorithms.

Provides the first examples of such algorithms obtained by composition.

Abstract

We define a measure of competitive performance for distributed algorithms based on throughput, the number of tasks that an algorithm can carry out in a fixed amount of work. This new measure complements the latency measure of Ajtai et al., which measures how quickly an algorithm can finish tasks that start at specified times. The novel feature of the throughput measure, which distinguishes it from the latency measure, is that it is compositional: it supports a notion of algorithms that are competitive relative to a class of subroutines, with the property that an algorithm that is k-competitive relative to a class of subroutines, combined with an l-competitive member of that class, gives a combined algorithm that is kl-competitive. In particular, we prove the throughput-competitiveness of a class of algorithms for collect operations, in which each of a group of n processes obtains all values stored in an array of n registers. Collects are a fundamental building block of a wide variety of shared-memory distributed algorithms, and we show that several such algorithms are competitive relative to collects. Inserting a competitive collect in these algorithms gives the first examples of competitive distributed algorithms obtained by composition using a general construction.