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Register a new userFlow Time Scheduling with Uncertain Processing Time
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Added by
Stefano Leonardi
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We consider the problem of online scheduling on a single machine in order to minimize weighted flow time. The existing algorithms for this problem (STOC 01, SODA 03, FOCS 18) all require exact knowledge of the processing time of each job. This assumption is crucial, as even a slight perturbation of the processing time would lead to polynomial competitive ratio. However, this assumption very rarely holds in real-life scenarios. In this paper, we present the first algorithm for weighted flow time which do not require exact knowledge of the processing times of jobs. Specifically, we introduce the Scheduling with Predicted Processing Time (SPPT) problem, where the algorithm is given a prediction for the processing time of each job, instead of its real processing time. For the case of a constant factor distortion between the predictions and the real processing time, our algorithms match all the best known competitiveness bounds for weighted flow time -- namely $O(log P), O(log D)$ and $O(log W)$, where $P,D,W$ are the maximum ratios of processing times, densities, and weights, respectively. For larger errors, the competitiveness of our algorithms degrades gracefully.
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Shortest Remaining Processing Time (SRPT) is a well known preemptive scheduling algorithm for uniprocessor and multiprocessor systems. SRPT finds applications in the emerging areas such as scheduling of clients requests that are submitted to a web server for accessing static web pages, managing the access requests to files in multiuser database systems and routing of packets across several links as per bandwidth availability in data communications. SRPT has been proved to be optimal for the settings, where the objective is to minimize the mean response time of a list of jobs. According to our knowledge, there is less attention on the study of online SRPT with respect to the minimization of makespan as a performance criterion. In this paper, we study the SRPT algorithm for online scheduling in multiprocessor systems with makespan minimization as an objective. We obtain improved constant competitiveness results for algorithm SRPT for special classes of online job sequences based on practical real life applications.
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We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a $O(log P)$-competitive algorithm, where $P$ is the maximum-to-minimum processing time ratio, improving upon the $O(log^{2}P)$-competitive algorithm of Chekuri, Khanna and Zhu (STOC 2001). We also design a $O(log D)$-competitive algorithm, where $D$ is the maximum-to-minimum density ratio of jobs. Finally, we show how to combine these results with the result of Bansal and Dhamdhere (SODA 2003) to achieve a $O(log(min(P,D,W)))$-competitive algorithm (where $W$ is the maximum-to-minimum weight ratio), without knowing $P,D,W$ in advance. As shown by Bansal and Chan (SODA 2009), no constant-competitive algorithm is achievable for this problem.
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