Abstract
Let A be any fixed cut-off restart algorithm running in parallel on multiple processors. If the algorithm is only allowed to run for up to time D, then it is no longer guaranteed that a result can be found. In this case, the probability of finding a solution within the time D becomes a measure for the quality of the algorithm. In this paper we address this issue and provide upper and lower bounds for the probability of A finding a solution before a deadline passes under varying assumptions. We also show that the optimal restart times for a fixed cut-off algorithm running in parallel is identical for the optimal restart times for the algorithm running on a single processor. Finally, we conclude that the odds of finding a solution scale superlinearly in the number of processors.
Highlights
Restart strategies are commonly used in probabilistic algorithms
We show that the optimal restart time regarding completion probability in the case of a fixed cut-off algorithm running on a single processor is optimal for the algorithm running in parallel on multiple processors
The optimal restart time regarding completion probability for a fixed-cutoff strategy running on a single processor is identical to the optimal restart time for a fixed-cutoff strategy running on multiple processors
Summary
Restart strategies are commonly used in probabilistic algorithms. If the current computation takes too long, the algorithm is started over with a different random seed. Deciding when to restart is an important task in designing an algorithm and several strategies are known. Luby et al introduced the fixed cut-off strategy . .) in [1] This means after t steps the algorithm is restarted. They showP ed that this strategy is optimal for a certain value of t.
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