Optimal online scheduling of parallel jobs with dependencies
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Dynamic scheduling on parallel machines
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Complexity of scheduling multiprocessor tasks with prespecified processor allocations
Discrete Applied Mathematics
An approximation algorithm for scheduling on three dedicated machines
Discrete Applied Mathematics
Scheduling Parallel Machines On-line
SIAM Journal on Computing
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SIAM Journal on Computing
Optical WDM Networks: Principles and Practice
Optical WDM Networks: Principles and Practice
Developments from a June 1996 seminar on Online algorithms: the state of the art
Developments from a June 1996 seminar on Online algorithms: the state of the art
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
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,
On-Line Scheduling of Parallel Jobs with Runtime Restrictions
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Scheduling Independent Multiprocessor Tasks
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Multi-Destination Communication in Broadcast WDM Networks: A Survey
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A next-generation optical regional access network
IEEE Communications Magazine
Guest Editorial Network Support for Multipoint Communication
IEEE Journal on Selected Areas in Communications
Guest editorial protocols and architectures for next generation optical WDM networks
IEEE Journal on Selected Areas in Communications
Open block scheduling in optical communication networks
Theoretical Computer Science - Approximation and online algorithms
Parallel task scheduling on multicore platforms
ACM SIGBED Review - Special issue: The work-in-progress (WIP) session of the RTSS 2005
Exploiting incomplete information to manage multiprocessor tasks with variable arrival rates
Computers and Operations Research
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We study the off and on-line versions of the well known problem of scheduling a set of n independent multiprocessor tasks with pre-specified processor allocations on a set of identical processors in order to minimize the makespan. Recently, in [12], it has been proven that in the case when all tasks have unit processing time the problem cannot be approximated within a factor of m1/2 - 驴, neither for some 驴 0, unless P= NP; nor for any 驴 0, unless NP=ZPP. For this special case we give a simple algorithm based on the classical first-fit technique. We analyze the algorithm for both tasks arrive over time and tasks arrive over list on-line scheduling versions, and show that its competitive ratio is bounded by 2驴m and 2驴m + 1, respectively. Here we also use some preliminary results on (vertex) coloring of k-tuple graphs. For the case of arbitrary processing times, we show that any algorithm which uses the first-fit technique cannot be better than m competitive. Then, by using our split-round technique, we give a 3驴m-approximation algorithm for the off-line version of the problem. Finally, by using some ideas from [20], we adapt the algorithm to the on-line case, in the paradigm of tasks arriving over time in which the existence of a task is unknown until its release date, and show that its competitive ratio is bounded by 6驴m. Due to the conducted experimental results, we conclude that our algorithms can perform well in practice.