Algorithms for scheduling malleable and nonmalleable parallel tasks
Algorithms for scheduling malleable and nonmalleable parallel tasks
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation Algorithms for Scheduling Independent Malleable Tasks
Euro-Par '01 Proceedings of the 7th International Euro-Par Conference Manchester on Parallel Processing
On-Line Scheduling of Parallelizable Jobs
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
Preemptable Malleable Task Scheduling Problem
IEEE Transactions on Computers
A $\frac32$-Approximation Algorithm for Scheduling Independent Monotonic Malleable Tasks
SIAM Journal on Computing
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This paper is about scheduling parallel jobs, i.e. which can be executed on more than one machine at the same time. Malleable jobs is a special class of parallel jobs. The number of machines a malleable job is executed on may change during its execution. In this work, we consider the NP-hard problem of scheduling malleable jobs to minimize the total weighted completion time (or mean weighted flow time). For this problem, we introduce the class of ''ascending'' schedules in which, for each job, the number of machines assigned to it cannot decrease over time while this job is being processed. We prove that, under a natural assumption on the processing time functions of jobs, the set of ascending schedules is dominant for the problem. This result can be used to reduce the search space while looking for an optimal solution.