Offline Sorting Buffers on Line

  • Rohit Khandekar
  • Vinayaka Pandit
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


We consider the offline sorting buffers problem. Input to this problem is a sequence of requests, each specified by a point in a metric space. There is a “server” that moves from point to point to serve these requests. To serve a request, the server needs to visit the point corresponding to that request. The objective is to minimize the total distance travelled by the server in the metric space. In order to achieve this, the server is allowed to serve the requests in any order that requires to “buffer” at most k requests at any time. Thus a valid reordering can serve a request only after serving all but k previous requests.

In this paper, we consider this problem on a line metric which is motivated by its application to a widely studied disc scheduling problem. On a line metric with N uniformly spaced points, our algorithm yields the first constant-factor approximation and runs in quasi-polynomial time O(m Open image in new window N Open image in new window k O(logN)) where m is the total number of requests. Our approach is based on a dynamic program that keeps track of the number of pending requests in each of O(logN) line segments that are geometrically increasing in length.


Dynamic Program Competitive Ratio Online Algorithm Hamiltonian Path Problem Constant Factor Approximation Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bar-Yehuda, R., Laserson, J.: 9-approximation algorithm for the sorting buffers problem. In: 3rd Workshop on Approximation and Online Algorithms (2005)Google Scholar
  2. 2.
    Englert, M., Westermann, M.: Reordering buffer management for non-uniform cost models. In: Proceedings of the 32nd International Colloquium on Algorithms, Langauages, and Programming, pp. 627–638 (2005)Google Scholar
  3. 3.
    Khandekar, R., Pandit, V.: Online sorting buffers on line. In: Proceedings of the Symposium on Theoretical Aspects of Computer Science, pp. 616–625 (2006)Google Scholar
  4. 4.
    Kohrt, J., Pruhs, K.: A constant approximation algorithm for sorting buffers. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 193–202. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Räcke, H., Sohler, C., Westermann, M.: Online scheduling for sorting buffers. In: Proceedings of the European Symposium on Algorithms, pp. 820–832 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rohit Khandekar
    • 1
  • Vinayaka Pandit
    • 2
  1. 1.University of WaterlooCanada
  2. 2.IBM India Research LabNew Delhi

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