Improved approximation guarantees for weighted matching in the semi-streaming model

TL;DR

This paper advances the semi-streaming algorithms for weighted matching by presenting a deterministic approach with improved approximation guarantees and analyzing the limits of preemptive online algorithms.

Contribution

It introduces a new deterministic algorithm with a 4.91+epsilon guarantee and establishes a lower bound of 4.967 for preemptive online algorithms, highlighting the gap for future improvements.

Findings

Deterministic algorithm with 4.91+epsilon approximation guarantee.

Lower bound of 4.967 for preemptive online algorithms.

Improved understanding of the limits of semi-streaming matching algorithms.

Abstract

We study the maximum weight matching problem in the semi-streaming model, and improve on the currently best one-pass algorithm due to Zelke (Proc. of STACS2008, pages 669-680) by devising a deterministic approach whose performance guarantee is 4.91+epsilon. In addition, we study preemptive online algorithms, a sub-class of one-pass algorithms where we are only allowed to maintain a feasible matching in memory at any point in time. All known results prior to Zelke's belong to this sub-class. We provide a lower bound of 4.967 on the competitive ratio of any such deterministic algorithm, and hence show that future improvements will have to store in memory a set of edges which is not necessarily a feasible matching.