3.415-Approximation for Coflow Scheduling via Iterated Rounding

TL;DR

This paper introduces a new algorithm that significantly improves approximation ratios for Coflow Scheduling problems, achieving near-optimal solutions in asymptotic settings through innovative LP rounding techniques.

Contribution

The paper presents a novel iterated LP rounding algorithm that improves approximation ratios for Coflow Scheduling, addressing open questions and establishing near-optimal bounds.

Findings

Achieves a 3.415-approximation for Coflow Scheduling.

Provides a 4.36-approximation for Coflow Scheduling with release dates.

In asymptotic cases, attains a near-optimal 2+epsilon approximation.

Abstract

We provide an algorithm giving a $\frac{140}{41}$($<3.415$)-approximation for Coflow Scheduling and a $4.36$-approximation for Coflow Scheduling with release dates. This improves upon the best known $4$- and respectively $5$-approximations and addresses an open question posed by Agarwal, Rajakrishnan, Narayan, Agarwal, Shmoys, and Vahdat [Aga+18], Fukunaga [Fuk22], and others. We additionally show that in an asymptotic setting, the algorithm achieves a ($2+\epsilon$)-approximation, which is essentially optimal under $\mathbb{P}\neq\mathbb{NP}$. The improvements are achieved using a novel edge allocation scheme using iterated LP rounding together with a framework which enables establishing strong bounds for combinations of several edge allocation algorithms.