Flow-time Optimization For Concurrent Open-Shop and Precedence Constrained Scheduling Models

Scheduling a set of jobs over a collection of machines is a fundamental problem that needs to be solved millions of times a day in various computing platforms: in operating systems, in large data clusters, and in data centers. Along with makespan, flow-time, which measures the length of time a job spends in a system before it completes, is arguably the most important metric to measure the performance of a scheduling algorithm. In recent years, there has been a remarkable progress in understanding flow-time based objective functions in diverse settings such as unrelated machines scheduling, broadcast scheduling, multi-dimensional scheduling, to name a few. Yet, our understanding of the flow-time objective is limited mostly to the scenarios where jobs have simple structures; in particular, each job is a single self contained entity. On the other hand, in almost all real world applications, think of MapReduce settings for example, jobs have more complex structures. In this paper, we consider two classical scheduling models that capture complex job structures: 1) concurrent open-shop scheduling and 2) precedence constrained scheduling. Our main motivation to study these problems specifically comes from their relevance to two scheduling problems that have gained importance in the context of data centers: co-flow scheduling and DAG scheduling. We design almost optimal approximation algorithms for open-shop scheduling and precedence constrained scheduling, and show hardness results.