Busy Time Scheduling on a Bounded Number of Machines (Extended Abstract)

  • Frederic KoehlerEmail author
  • Samir Khuller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)


In this paper we consider a basic scheduling problem called the busy time scheduling problem - given n jobs, with release times \(r_j\), deadlines \(d_j\) and processing times \(p_j\), and m machines, where each machine can run up to g jobs concurrently, our goal is to find a schedule to minimize the sum of the “on” times for the machines. We develop the first correct constant factor online competitive algorithm for the case when g is unbounded, and give a \(O(\log P)\) approximation for general g, where P is the ratio of maximum to minimum processing time. When g is bounded, all prior busy time approximation algorithms use an unbounded number of machines; note it is NP-hard just to test feasibility on fixed m machines. For this problem we give both offline and online (requiring “lookahead”) algorithms, which are O(1) competitive in busy time and \(O(\log P)\) competitive in number of machines used.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsMITCambridgeUSA
  2. 2.Department of Computer ScienceUniversity of MarylandCollege ParkUSA

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