
An EPTAS for machine scheduling with bagconstraints
Machine scheduling is a fundamental optimization problem in computer sci...
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Workflow Scheduling in the Cloud with Weighted Upwardrank Priority Scheme Using Random Walk and Uniform Spare Budget Splitting
We study a difficult problem of how to schedule complex workflows with p...
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Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines
In this paper we consider the problem of scheduling on parallel machines...
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Scheduling with Contact Restrictions – A Problem Arising in Pandemics
We study a scheduling problem arising in pandemic times where jobs shoul...
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Exact Lexicographic Scheduling and Approximate Rescheduling
In industrial scheduling, an initial planning phase may solve the nomina...
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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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The Preemptive Resource Allocation Problem
We revisit a classical scheduling model to incorporate modern trends in ...
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Budget Minimization with Precedence Constraints
Budget Minimization is a scheduling problem with precedence constraints, i.e., a scheduling problem on a partially ordered set of jobs (N, ). A job j ∈ N is available for scheduling, if all jobs i ∈ N with i j are completed. Further, each job j ∈ N is assigned real valued costs c_j, which can be negative or positive. A schedule is an ordering j_1, ..., j_ N of all jobs in N. The budget of a schedule is the external investment needed to complete all jobs, i.e., it is _l ∈{0, ..., N }∑_1 < k < l c_j_k. The goal is to find a schedule with minimum budget. Rafiey et al. (2015) showed that Budget Minimization is NPhard following from a reduction from a molecular folding problem. We extend this result and prove that it is NPhard to α(N)approximate the minimum budget even on bipartite partial orders. We present structural insights that lead to arguably simpler algorithms and extensions of the results by Rafiey et al. (2015). In particular, we show that there always exists an optimal solution that partitions the set of jobs and schedules each subset independently of the other jobs. We use this structural insight to derive polynomialtime algorithms that solve the problem to optimality on seriesparallel and convex bipartite partial orders.
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