Scheduling Coflows for Minimizing the Total Weighted Completion Time in Identical Parallel Networks

TL;DR

This paper addresses the complex problem of coflow scheduling in parallel data center networks, proposing approximation algorithms for both divisible and indivisible coflows to minimize total weighted completion time.

Contribution

It introduces new approximation algorithms for coflow scheduling in identical parallel networks, extending prior work beyond single-switch models.

Findings

For divisible coflows, a $(6-rac{2}{m})$-approximation algorithm is proposed.

For indivisible coflows, a $(4m+1)$-approximation algorithm is developed.

Algorithms account for arbitrary release times and improve scheduling efficiency.

Abstract

Coflow is a recently proposed network abstraction to capture communication patterns in data centers. The coflow scheduling problem in large data centers is one of the most important $NP$-hard problems. Previous research on coflow scheduling focused mainly on the single-switch model. However, with recent technological developments, this single-core model is no longer sufficient. This paper considers the coflow scheduling problem in identical parallel networks. The identical parallel network is an architecture based on multiple network cores running in parallel. Coflow can be considered as divisible or indivisible. Different flows in a divisible coflow can be transmitted through different network cores. Considering the divisible coflow scheduling problem, we propose a $(6-\frac{2}{m})$-approximation algorithm with arbitrary release times, and a $(5-\frac{2}{m})$-approximation without release time, where $m$ is the number of network cores. On the other hand, when coflow is indivisible, we propose a $(4m+1)$-approximation algorithm with arbitrary release times, and a $(4m)$-approximation without release time.