Journal of Scheduling

, Volume 20, Issue 5, pp 423–442 | Cite as

Reordering buffer management with advice

  • Anna Adamaszek
  • Marc P. Renault
  • Adi Rosén
  • Rob van Stee


In the reordering buffer management problem, a sequence of colored items arrives at a service station to be processed. Each color change between two consecutively processed items generates some cost. A reordering buffer of capacity k items can be used to preprocess the input sequence in order to decrease the number of color changes. The goal is to find a scheduling strategy that, using the reordering buffer, minimizes the number of color changes in the given sequence of items. We consider the problem in the setting of online computation with advice. In this model, the color of an item becomes known only at the time when the item enters the reordering buffer. Additionally, together with each item entering the buffer, we get a fixed number of advice bits, which can be seen as information about the future or as information about an optimal solution (or an approximation thereof) for the whole input sequence. We show that for any \(\varepsilon > 0\) there is a \((1+\varepsilon )\)-competitive algorithm for the problem which uses only a constant (depending on \(\varepsilon \)) number of advice bits per input item. This also immediately implies a \((1+\varepsilon )\)-approximation algorithm which has \(2^{O(n\log 1/\varepsilon )}\) running time (this should be compared to the trivial optimal algorithm which has a running time of \(k^{O(n)}\)). We complement the above result by presenting a lower bound of \(\varOmega (\log k)\) bits of advice per request for any 1-competitive algorithm.


Reordering buffer management Online algorithms Online algorithms with advice Competitive analysis 



We would like to thank the reviewers for their thorough reading of the paper and their helpful comments, which helped us to improve the presentation of the paper. The first author is supported by the DFF-MOBILEX mobility grant from the Danish Council for Independent Research. The second and third authors were partially supported by ANR Project NeTOC.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Anna Adamaszek
    • 1
  • Marc P. Renault
    • 2
  • Adi Rosén
    • 2
  • Rob van Stee
    • 3
  1. 1.University of CopenhagenCopenhagenDenmark
  2. 2.CNRS and Université Paris DiderotParisFrance
  3. 3.University of LeicesterLeicesterUnited Kingdom

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