Finite-State Online Algorithms and Their Automated Competitive Analysis

  • Takashi Horiyama
  • Kazuo Iwama
  • Jun Kawahara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


In this paper we study the Revocable Online Knapsack Problem (ROKP) which is an extension of the Online Knapsack Problem [8]. We prove an optimal upper bound of 1/t for the competitive ratio of ROKP, where t is a real root of 4x 3 + 5x 2x – 4 = 0 (t ≈0.76850 and 1/t ≈1.3012). To prove this result, we made a full use of computer programs as follows: For the base algorithm that is designed in a conventional manner, we first construct an equivalent finite state diagram with about 300 states. Then for each state, we generate a finite set of inequalities such that the competitive ratio at that state is at most 1/t if the set of inequalities do not have a real solution. The latter can be checked by Mathematica. The number of inequalities generated was approximately 600 in total, and our computation time was 30 minutes using Athlon XP 2600+.


Base Algorithm Competitive Ratio Online Algorithm State Diagram Execution Sequence 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Takashi Horiyama
    • 1
  • Kazuo Iwama
    • 1
  • Jun Kawahara
    • 1
  1. 1.Graduate School of InformaticsKyoto UniversityKyotoJapan

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