Mathematical Methods of Operations Research

, Volume 56, Issue 3, pp 407–412 | Cite as

A polynomial algorithm for P | pj=1, rj, outtree | ∑ Cj

  • Peter Brucker
  • Johann Hurink
  • Sigrid Knust

Abstract.

A polynomial algorithm is proposed for two scheduling problems for which the complexity status was open. A set of jobs with unit processing times, release dates and outtree precedence relations has to be processed on parallel identical machines such that the total completion time ∑ Cj is minimized. It is shown that the problem can be solved in O(n2) time if no preemption is allowed. Furthermore, it is proved that allowing preemption does not reduce the optimal objective value, which verifies a conjecture of Baptiste & Timkovsky [1].

Key words: scheduling parallel machines outtree complexity results 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Peter Brucker
    • 1
  • Johann Hurink
    • 2
  • Sigrid Knust
    • 3
  1. 1.Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069 Osnabrück, Germany (e-mail: peter@mathematik.uni-osnabrueck.de)DE
  2. 2.University of Twente, Faculty of Mathematical Sciences, P.O. Box 217, 7500 AE Enschede, The Netherlands (e-mail: J.L.Hurink@math.utwente.nl)NL
  3. 3.Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069 Osnabrück, Germany (e-mail: sigrid@mathematik.uni-osnabrueck.de)DE

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