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ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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DISC'11 Proceedings of the 25th international conference on Distributed computing
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Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
How to Allocate Tasks Asynchronously
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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Consider a system in which tasks of different execution times arrive continuously and have to be executed by a set of processors that are prone to crashes and restarts. In this paper we model and study the impact of parallelism and failures on the competitiveness of such an online system. In a fault-free environment, a simple Longest-in-System scheduling policy, enhanced by a redundancy-avoidance mechanism, guarantees optimality in a long-term execution. In the presence of failures though, scheduling becomes a much more challenging task. In particular, no parallel deterministic algorithm can be competitive against an offline optimal solution, even with one single processor and tasks of only two different execution times. We find that when additional energy is provided to the system in the form of processor speedup, the situation changes. Specifically, we identify thresholds on the speedup under which such competitiveness cannot be achieved by any deterministic algorithm, and above which competitive algorithms exist. Finally, we propose algorithms that achieve small bounded competitive ratios when the speedup is over the threshold.