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Title: On the Hardness of Scheduling With Non-Uniform Communication Delays
In the problem of scheduling with non-uniform communication delays, the input is a set of jobs with precedence constraints. Associated with every precedence constraint between a pair of jobs is a communication delay, the time duration the scheduler has to wait between the two jobs if they are scheduled on different machines. The objective is to assign the jobs to machines to minimize the makespan of the schedule. Despite being a fundamental problem in theory and a consequential problem in practice, the approximability of scheduling problems with communication delays is not very well understood. One of the top ten open problems in scheduling theory, in the influential list by Schuurman and Woeginger and its latest update by Bansal, asks if the problem admits a constant-factor approximation algorithm. In this paper, we answer this question in the negative by proving a logarithmic hardness for the problem under the standard complexity theory assumption that NP-complete problems do not admit quasi-polynomial-time algorithms. Our hardness result is obtained using a surprisingly simple reduction from a problem that we call Unique Machine Precedence constraints Scheduling (UMPS). We believe that this problem is of central importance in understanding the hardness of many scheduling problems and we conjecture that it is very hard to approximate. Among other things, our conjecture implies a logarithmic hardness of related machine scheduling with precedences, a long-standing open problem in scheduling theory and approximation algorithms.  more » « less
Award ID(s):
1651861
NSF-PAR ID:
10342245
Author(s) / Creator(s):
; ; ; ; ;
Editor(s):
Naor, Joseph; Buchbinder, Niv
Date Published:
Journal Name:
Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms
ISSN:
1071-9040
Page Range / eLocation ID:
316-328
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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