Structure of a simple scheduling polyhedron
Mathematical Programming: Series A and B
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Minimizing the flow time without migration
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
New and improved algorithms for minsum shop scheduling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Decomposition Algorithms for Stochastic Programming on a Computational Grid
Computational Optimization and Applications
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improved Scheduling Algorithms for Minsum Criteria
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Nimrod: a tool for performing parametrised simulations using distributed workstations
HPDC '95 Proceedings of the 4th IEEE International Symposium on High Performance Distributed Computing
An Enabling Framework for Master-Worker Applications on the Computational Grid
HPDC '00 Proceedings of the 9th IEEE International Symposium on High Performance Distributed Computing
A note on the complexity of the concurrent open shop problem
Journal of Scheduling
Distributed order scheduling and its application to multi-core dram controllers
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Minimizing the sum of weighted completion times in a concurrent open shop
Operations Research Letters
Minimizing the total weighted completion time of fully parallel jobs with integer parallel units
Theoretical Computer Science
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We consider scheduling problems in which a job consists of components of different types to be processed on m machines. Each machine is capable of processing components of a single type. Different components of a job are independent and can be processed in parallel on different machines. A job is considered as completed only when all its components have been completed. We study both completion time and flowtime aspects of such problems. We show both lowerbounds and upperbounds for the completion time problem. We first show that even the unweighted completion time with single release date is MAX-SNP hard. We give an approximation algorithm based on linear programming which has an approximation ratio of 3 for weighted completion time with multiple release dates. We give online algorithms for the weighted completion time which are constant factor competitive. For the flowtime, we give only lowerbounds in both the offline and online settings. We show that it is NP-hard to approximate flowtime within Ω(log m) in the offline setting. We show that no online algorithm for the flowtime can have a competitive ratio better than Ω(√m).