Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
Complexity of scheduling multiprocessor tasks with prespecified processor allocations
Discrete Applied Mathematics
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
On chromatic sums and distributed resource allocation
Information and Computation
A PTAS for minimizing the weighted sum of job completion times on parallel machines
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A polynomial time approximation scheme for general multiprocessor job scheduling (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Scheduling parallel tasks to minimize average response time
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
General Multiprocessor Task Scheduling: Approximate Solutions in Linear Time
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
On Minimizing Average Weighted Completion Time of Multiprocessor Tasks with Release Dates
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Improved Scheduling Algorithms for Minsum Criteria
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Scheduling to Minimize the Average Completion Time of Dedicated Tasks
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Scheduling Independent Multiprocessor Tasks
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Minimizing the total weighted completion time of fully parallel jobs with integer parallel units
Theoretical Computer Science
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We study the problem of scheduling n independent general multiprocessor tasks on a fixed number of processors, where the objective is to compute a non-preemptive schedule minimizing the average weighted completion time. For each task, its execution time is given as a function of the subset of processors assigned to the task. We propose here a polynomial-time approximation scheme for the problem that computes a (1 + Ɛ)-approximate solution in O(n log n) time for any fixed Ɛ 0 accuracy. This provides a generalization and integration of some recent polynomial-time approximation schemes for scheduling jobs on unrelated machines [1,18] and multiprocessor tasks on dedicated processors [2], respectively, with the average weighted completion time objective, since the latter models are included as special cases in our problem.