Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
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
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
Efficient approximation algorithms for scheduling malleable tasks
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Scheduling malleable and nonmalleable parallel tasks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
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
An approximation algorithm for scheduling malleable tasks under general precedence constraints
ACM Transactions on Algorithms (TALG)
Higher-Dimensional Packing with Order Constraints
SIAM Journal on Discrete Mathematics
A $\frac32$-Approximation Algorithm for Scheduling Independent Monotonic Malleable Tasks
SIAM Journal on Computing
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
Strip packing with precedence constraints and strip packing with release times
Theoretical Computer Science
Scheduling and packing malleable tasks with precedence constraints of bounded width
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
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We study the problems of non-preemptively scheduling and packing malleable and parallel tasks with precedence constraints to minimize the makespan. In the scheduling variant, we allow the free choice of processors; in packing, each task must be assigned to a contiguous subset. Malleable tasks can be processed on different numbers of processors with varying processing times, while parallel tasks require a fixed number of processors.For precedence constraints of bounded width, we resolve the complexity status of the problem with any number of processors and any width bound. We present an FPTAS based on Dilworth's decomposition theorem for the NP-hard problem variants, and exact efficient algorithms for all remaining special cases. For our positive results, we do not require the otherwise common monotonous penalty assumption on the processing times of malleable tasks, whereas our hardness results hold even when assuming this restriction. We complement our results by showing that these problems are all strongly NP-hard under precedence constraints which form a tree.