On the complexity of dynamic programming for sequencing problems with precedence constraints
Annals of Operations Research
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
On the Complexity of Adjacent Resource Scheduling
Journal of Scheduling
Strip packing with precedence constraints and strip packing with release times
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
An approximation algorithm for scheduling malleable tasks under general precedence constraints
ACM Transactions on Algorithms (TALG)
Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width
Journal of Combinatorial Optimization
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We study two related problems in non-preemptive scheduling and packing of malleable tasks with precedence constraints to minimize the makespan. We distinguish the scheduling variant, in which we allow the free choice of processors, and the packing variant, in which a task must be assigned to a contiguous subset of processors. For precedence constraints of bounded width, we completely resolve the complexity status for any particular problem setting concerning width bound and number of processors, and give polynomial-time algorithms with best possible performance. For both, scheduling and packing malleable tasks, we present an FPTAS for the NP-hard problem variants and exact algorithms for all remaining special cases. To obtain the positive results, we do not require the common monotonous penalty assumption on processing times, whereas our hardness results hold even when assuming this restriction. With the close relation between contiguous scheduling and strip packing, our FPTAS is the first (and best possible) constant factor approximation for (malleable) strip packing under special precedence constraints.