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Competitiveness and response time in on-line algorithms

  • Vladimir Estivill-Castro
  • Murray Sherk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 557)

Abstract

The study of competitive algorithms has concentrated on competitiveness — comparing online algorithms to optimal off-line algorithms on sequences of operations. Published algorithms proven (or suggested) to be competitive invariably have pessimal response time i.e. their worst-case single operation time is as bad as possible. We consider whether or not such algorithms can be adapted to improve the response time without sacrificing competitiveness. We consider lists, off-line static search trees, dynamic search trees, and the k-server problem on a line segment of length L. For lists, pessimal response time is unavoidable. For off-line static search trees our algorithm is 2-competitive and has response time 2 log n. For dynamic search trees our algorithm has logarithmic amortized time and is statically optimal (like splay trees), but the response time is O(√n log n) and Ω(log2n). For the k-server problem we prove that any algorithm with O(optimal) response time has a competitive ratio of at least Ω(L/k). This is achieved by a simple on-line algorithm. We also show that even a weak limit on response time for the k-server problem (e.g. response time less than half pessimal) yields an Ω(L/k) separation between on-line and off-line algorithms. Our results apply to high-performance multi-head disk drives where response time is critical.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Vladimir Estivill-Castro
    • 1
  • Murray Sherk
    • 2
  1. 1.Department of Computer ScienceYork UniversityNorth YorkCanada
  2. 2.University of Science & Technology in ChinaHefeiPeople's Republic of China

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