The Price of Bounded Preemption.
SPAA '18: 30th ACM Symposium on Parallelism in Algorithms and Architectures Vienna Austria July, 2018(2018)
摘要
In this paper we provide a tight bound for the price of preemption for scheduling jobs on a single machine (or multiple machines). The input consists of a set of jobs to be scheduled and of an integer parameter $k \ge 1$. Each job has a release time, deadline, length (also called processing time) and value associated with it. The goal is to feasibly schedule a subset of the jobs so that their total value is maximal; while preemption of a job is permitted, a job may be preempted no more than k times. The price of preemption is the worst possible (i.e., largest) ratio of the optimal non-bounded-preemptive scheduling to the optimal k-bounded-preemptive scheduling. Our results show that allowing at most k preemptions suffices to guarantee a Θ(\min\łog_k+1 n, łog_k+1 P\ )$ fraction of the total value achieved when the number of preemptions is unrestricted (where n is the number of the jobs and P the ratio of the maximal length to the minimal length), giving us an upper bound for the price; a specific scenario serves to prove the tightness of this bound. We further show that when no preemptions are permitted at all (i.e., k=0), the price is Θ(\min\n, łog P\ )$. As part of the proof, we introduce the notion of the Bounded-Degree Ancestor-Free Sub-Forest (BAS). We investigate the problem of computing the maximal-value BAS of a given forest and give a tight bound for the loss factor, which is Θ(łog_k+1 n)$ as well, where n is the size of the original forest and k is the bound on the degree of the sub-forest.
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关键词
scheduling jobs,multiple machines,bounded preemptions,bounded-degree sub-forest
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