# An Improved Bound for Minimizing the Total Weighted Completion Time of Coflows in Datacenters

## TL;DR

This paper presents a new polynomial-time deterministic algorithm for scheduling coflows in datacenter networks, achieving better approximation ratios than previous methods for minimizing total weighted completion time.

## Contribution

It introduces an improved linear programming formulation and a simple list scheduling policy that together yield a better approximation ratio for coflow scheduling.

## Key findings

- The algorithm achieves an approximation ratio of 5, improving from 12.
- For coflows released at time zero, the ratio improves to 4 from 8.
- Simulation results confirm the algorithm's superior performance over prior approaches.

## Abstract

In data-parallel computing frameworks, intermediate parallel data is often produced at various stages which needs to be transferred among servers in the datacenter network (e.g. the shuffle phase in MapReduce). A stage often cannot start or be completed unless all the required data pieces from the preceding stage are received. \emph{Coflow} is a recently proposed networking abstraction to capture such communication patterns. We consider the problem of efficiently scheduling coflows with release dates in a shared datacenter network so as to minimize the total weighted completion time of coflows. Several heuristics have been proposed recently to address this problem, as well as a few polynomial-time approximation algorithms with provable performance guarantees. Our main result in this paper is a polynomial-time deterministic algorithm that improves the prior known results. Specifically, we propose a deterministic algorithm with approximation ratio of $5$, which improves the prior best known ratio of $12$. For the special case when all coflows are released at time zero, our deterministic algorithm obtains approximation ratio of $4$ which improves the prior best known ratio of $8$. The key ingredient of our approach is an improved linear program formulation for sorting the coflows followed by a simple list scheduling policy. Extensive simulation results, using both synthetic and real traffic traces, are presented that verify the performance of our algorithm and show improvement over the prior approaches.