
Scheduling with Communication Delay in NearLinear Time
We consider the problem of efficiently scheduling jobs with precedence c...
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Approximation algorithms for twomachine flowshop scheduling with a conflict graph
Path cover is a wellknown intractable problem that finds a minimum numb...
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On the Hardness of Scheduling With NonUniform Communication Delays
In the scheduling with nonuniform communication delay problem, the inpu...
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Flowtime Optimization For Concurrent OpenShop and Precedence Constrained Scheduling Models
Scheduling a set of jobs over a collection of machines is a fundamental ...
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Parameterized Complexity of Scheduling Chains of Jobs with Delays
In this paper, we consider the parameterized complexity of the following...
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Makespan Minimization with ORPrecedence Constraints
We consider a variant of the NPhard problem of assigning jobs to machin...
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Exact Algorithms for Scheduling Problems on Parallel Identical Machines with Conflict Jobs
Machine scheduling problems involving conflict jobs can be seen as a con...
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HierarchyBased Algorithms for Minimizing Makespan under Precedence and Communication Constraints
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 wellknown question in scheduling theory. Indeed, an outstanding open problem from the classic book of Garey and Johnson asks whether this problem is NPhard even in the case of 3 machines and unitlength jobs. In a recent breakthrough, Levey and Rothvoss gave a (1+ϵ)approximation algorithm, which runs in nearly quasipolynomial 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 nonmigratory 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.
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