Theoretical Computer Science - Special issue on dynamic and on-line algorithms
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Speed is as powerful as clairvoyance
Journal of the ACM (JACM)
TCP is competitive against a limited adversary
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Non-clair voy ant multiprocessor scheduling of jobs with changing execution characteristics
Journal of Scheduling - Special issue: On-line scheduling
Journal of Parallel and Distributed Computing - Special issue on parallel bioinspired algorithms
Pull-based data broadcast with dependencies: be fair to users, not to items
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Non-clairvoyant batch sets scheduling: fairness is fair enough
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Scalably scheduling processes with arbitrary speedup curves
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Speed scaling of processes with arbitrary speedup curves on a multiprocessor
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Improved results for scheduling batched parallel jobs by using a generalized analysis framework
Journal of Parallel and Distributed Computing
Scheduling jobs with varying parallelizability to reduce variance
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Minimizing maximum flowtime of jobs with arbitrary parallelizability
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Online scalable scheduling for the lk-norms of flow time without conservation of work
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Scalably scheduling processes with arbitrary speedup curves
ACM Transactions on Algorithms (TALG)
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We consider Edmonds's model (1999) extended by precedence constraints. In our setting, a scheduler has to schedule non-clairvoyantly jobs consisting in DAGs of tasks arriving over time, each task going through phases of different degrees of parallelism, unknown to the scheduler. As in the original model without precedence constraints, the scheduler is only informed of the arrival and the completion of each task, at the time of these events, and nothing more. Furthermore, it is not aware of the DAG structure of each job beforehand neither of the precise characteristics of the phases of the tasks that compose each job. We consider the preemptive strategy Equi○Equi, that divides the processors evenly among the alive jobs and then divides the processing power alloted to each job evenly among its alive tasks. We show that whatever how complex the precedences are, Equi○Equi is (2 + ε)-speed 0(κ/ε)-competitive for the flowtime metric, where κ is the maximum number of independent tasks in each job. That is to say, the flowtime of the schedule computed by EquioEqui is at a constant ratio of the optimal flowtime as soon as Equi is given slightly more than twice the resources as the optimum it is compared to. Interestingly, the extra speed needed to obtain a competitive algorithm, namely (2+ε), is the same in presence of precedence constraints, as in the original setting without precedences studied by Edmonds in 1999. This means that the maximum load that the system can handle without diverging, is the same with or without precedence constraints. Furthermore, we propose a simple scheme to analyze a special class of schedulers, namely Equi-schedulers, which allows to obtain upper and lower bounds on particular precedences structures, such as independent chains, IN-trees, OUT-trees and Serial-parallel DAGs.