Hierarchy-Based Algorithms for Minimizing Makespan under Precedence and Communication Constraints

04/28/2020
by   Janardhan Kulkarni, et al.
0

We consider the classic problem of scheduling jobs with precedence constraints on a set of identical machines to minimize the makespan objective function. Understanding the exact approximability of the problem when the number of machines is a constant is a well-known question in scheduling theory. Indeed, an outstanding open problem from the classic book of Garey and Johnson asks whether this problem is NP-hard even in the case of 3 machines and unit-length jobs. In a recent breakthrough, Levey and Rothvoss gave a (1+ϵ)-approximation algorithm, which runs in nearly quasi-polynomial time, for the case when job have unit lengths. However, a substantially more difficult case where jobs have arbitrary processing lengths has remained open. We make progress on this more general problem. We show that there exists a (1+ϵ)-approximation algorithm (with similar running time as that of Levey and Rothvoss) for the non-migratory setting: when every job has to be scheduled entirely on a single machine, but within a machine the job need not be scheduled during consecutive time steps. Further, we also show that our algorithmic framework generalizes to another classic scenario where, along with the precedence constraints, the jobs also have communication delay constraints. Both of these fundamental problems are highly relevant to the practice of datacenter scheduling.

READ FULL TEXT
08/05/2021

Scheduling with Communication Delay in Near-Linear Time

We consider the problem of efficiently scheduling jobs with precedence c...
04/21/2020

Scheduling with Communication Delays via LP Hierarchies and Clustering

We consider the classic problem of scheduling jobs with precedence const...
05/28/2022

An efficient polynomial-time approximation scheme for parallel multi-stage open shops

Various new scheduling problems have been arising from practical product...
03/07/2018

Approximation algorithms for two-machine flow-shop scheduling with a conflict graph

Path cover is a well-known intractable problem that finds a minimum numb...
07/06/2018

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 ...
07/18/2019

Makespan Minimization with OR-Precedence Constraints

We consider a variant of the NP-hard problem of assigning jobs to machin...
10/20/2017

Fault-tolerant parallel scheduling of arbitrary length jobs on a shared channel

We study the problem of scheduling jobs on fault-prone machines communic...