Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
An algorithm for linear programming which requires O((m+n)n2 + (m+n)1.5n)L) arithmetic operations
Mathematical Programming: Series A and B
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Dynamic scheduling on parallel machines
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Algorithms for scheduling malleable and nonmalleable parallel tasks
Algorithms for scheduling malleable and nonmalleable parallel tasks
Scheduling malleable and nonmalleable parallel tasks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
On an on-line scheduling problem for parallel jobs
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximate Max-Min Resource Sharing for Structured Concave Optimization
SIAM Journal on Optimization
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Scheduling parallel jobs to minimize the makespan
Journal of Scheduling
A 5/4-approximation algorithm for scheduling identical malleable tasks
Theoretical Computer Science - Approximation and online algorithms
A $\frac32$-Approximation Algorithm for Scheduling Independent Monotonic Malleable Tasks
SIAM Journal on Computing
Approximation schemes for constrained scheduling problems
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Scheduling for Parallel Processing
Scheduling for Parallel Processing
Approximation Algorithms for Scheduling Parallel Jobs
SIAM Journal on Computing
Approximation algorithms for min-max and max-min resource sharing problems, and applications
Efficient Approximation and Online Algorithms
New approximability results for 2-dimensional packing problems
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
A (2+ε)-approximation for scheduling parallel jobs in platforms
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
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In this paper we study a scheduling problem with moldable and non-moldable parallel tasks on $m$ processors. A non-moldable parallel task is one that runs in parallel on a specific given number of processors. The goal is to find a non-preemptive schedule on the m processors which minimizes the makespan, or the latest task completion time. The previous best result is the list scheduling algorithm with an absolute approximation ratio of 2. On the other hand, there does not exist an approximation algorithm for scheduling non-moldable parallel tasks with ratio smaller than 1.5, unless P=NP. In this paper we show that a schedule with length (1.5 + ε) OPT can be computed for the scheduling problem in time O(n log n) + f(1/ε). Furthermore we present an (1.5 + ε) approximation algorithm for scheduling moldable parallel tasks.