Scheduling Coflows for Minimizing the Maximum Completion Time in Heterogeneous Parallel Networks

Coflow represents a network abstraction that models communication patterns within data centers. Scheduling coflows is a significant issue in large data center environments and is classified as an $\mathcal{NP}$-hard problem. This paper focuses on the scheduling of coflows in heterogeneous parallel networks, which are characterized by architectures that feature multiple network cores operating simultaneously. We introduce two pseudo-polynomial-time algorithms and two polynomial-time approximation algorithms aimed at minimizing the maximum completion time, known as makespan, in these heterogeneous parallel networks. Our approach includes a randomized algorithm with an expected approximation ratio of 1.5. Building on this, we present a deterministic algorithm that employs derandomization techniques, offering a performance guarantee of $1.5 + \frac{1}{2 \cdot LB}$, where $LB$ is the lower bound of the makespan for each instance. To tackle concerns regarding time complexity, we implement an exponential partitioning of time intervals and propose a randomized algorithm with an expected approximation ratio of $1.5 + ε$ in polynomial time, where $ε>0$. Furthermore, we develop a deterministic algorithm with a performance guarantee of $1.5+\frac{1}{2\cdot LB}+ε$, also within polynomial time. When the flow size is sufficiently large, this algorithm can achieve an approximation ratio of $1.5+ε$. These advancements significantly improve the best-known approximation ratio, previously $2+ε$.