The Price of Bounded Preemption

Noga Alon, Yossi Azar, Mark Berlin

Research output: Contribution to journalArticlepeer-review

Abstract

In this article 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 ≥ 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 {logk+1 n, logk+1P}) 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, log 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(logk+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.

Original languageEnglish (US)
Article number3434377
JournalACM Transactions on Parallel Computing
Volume8
Issue number1
DOIs
StatePublished - Apr 2021

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Hardware and Architecture
  • Computer Science Applications
  • Computational Theory and Mathematics

Keywords

  • Scheduling jobs
  • bounded preemptions
  • bounded-degree sub-forest
  • multiple machines

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