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Online Linear Optimization over Permutations

  • Shota Yasutake
  • Kohei Hatano
  • Shuji Kijima
  • Eiji Takimoto
  • Masayuki Takeda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

This paper proposes an algorithm for online linear optimization problem over permutations; the objective of the online algorithm is to find a permutation of {1,…,n} at each trial so as to minimize the “regret” for T trials. The regret of our algorithm is \(O(n^2 \sqrt{T \ln n})\) in expectation for any input sequence. A naive implementation requires more than exponential time. On the other hand, our algorithm uses only O(n) space and runs in O(n 2) time in each trial. To achieve this complexity, we devise two efficient algorithms as subroutines: One is for minimization of an entropy function over the permutahedron P n , and the other is for randomized rounding over P n .

Keywords

Completion Time Convex Combination Competitive Ratio Online Algorithm Precedence Constraint 
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 2011

Authors and Affiliations

  • Shota Yasutake
    • 1
  • Kohei Hatano
    • 1
  • Shuji Kijima
    • 1
  • Eiji Takimoto
    • 1
  • Masayuki Takeda
    • 1
  1. 1.Department of InformaticsKyushu UniversityJapan

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