Distributed and Streaming Linear Programming in Low Dimensions

TL;DR

This paper investigates efficient algorithms for low-dimensional linear programming problems in distributed and streaming models, focusing on large datasets common in machine learning tasks, and provides bounds that are nearly tight for fixed dimensions.

Contribution

It offers both upper and lower bounds for LP-type problems in distributed and streaming models, specifically addressing low-dimensional cases with large datasets.

Findings

Bounds are almost tight for fixed dimensions.

Applicable to machine learning tasks like SVMs and robust regression.

Enhances understanding of LP problems in big data environments.

Abstract

We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low dimensional LP-type problems appear frequently in various machine learning tasks such as robust regression, support vector machines, and core vector machines. As supporting large-scale machine learning queries in database systems has become an important direction for database research, obtaining efficient algorithms for low dimensional LP-type problems on massive datasets is of great value. In this paper we give both upper and lower bounds for LP-type problems in distributed and streaming models. Our bounds are almost tight when the dimensionality of the problem is a fixed constant.