Linear Programming in the Semi-streaming Model with Application to the Maximum Matching Problem

TL;DR

This paper develops linear programming techniques tailored for the semi-streaming model to efficiently solve the maximum matching problem in massive graphs, improving existing results and addressing new variants.

Contribution

It adapts and optimizes linear programming approaches for the semi-streaming model, achieving improved bounds and novel results for maximum matching.

Findings

Enhanced algorithms for maximum matching in semi-streaming

Improved approximation ratios over previous methods

New results on variants of the maximum matching problem

Abstract

In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs has increased. This is a model where edges are streamed-in in an adversarial order and we are allowed a space proportional to the number of vertices in a graph. In recent years, there has been several new results in this semi-streaming model. However broad techniques such as linear programming have not been adapted to this model. We present several techniques to adapt and optimize linear programming based approaches in the semi-streaming model with an application to the maximum matching problem. As a consequence, we improve (almost) all previous results on this problem, and also prove new results on interesting variants.