Distributed Computation for the Non-metric Data Placement Problem using Glauber Dynamics and Auctions

TL;DR

This paper introduces the first distributed algorithms for the non-metric data placement problem, utilizing Glauber dynamics and auctions to approximate optimal solutions despite inapproximability results.

Contribution

It develops novel distributed algorithms based on Glauber dynamics and auctions, providing approximation guarantees and analyzing convergence for the non-metric data placement problem.

Findings

Glauber dynamics converge to optimal solutions with high probability.

The auction-based algorithm achieves performance guarantees related to revenue and social welfare.

The problem is shown to be inapproximable within a logarithmic factor.

Abstract

We consider the non-metric data placement problem and develop distributed algorithms for computing or approximating its optimal integral solution. We first show that the non-metric data placement problem is inapproximable up to a logarithmic factor. We then provide a game-theoretic decomposition of the objective function and show that natural Glauber dynamics in which players update their resources with probability proportional to the utility they receive from caching those resources will converge to an optimal global solution for a sufficiently large noise parameter. In particular, we establish the polynomial mixing time of the Glauber dynamics for a certain range of noise parameters. Finally, we provide another auction-based distributed algorithm, which allows us to approximate the optimal global solution with a performance guarantee that depends on the ratio of the revenue vs. social welfare obtained from the underlying auction. Our results provide the first distributed computation algorithms for the non-metric data placement problem.