Online linear optimization over permutations

Shota Yasutake, Kohei Hatano, Shuji Kijima, Eiji Takimoto, Masayuki Takeda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

27 Citations (Scopus)


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√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 .

Original languageEnglish
Title of host publicationAlgorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
Number of pages10
Publication statusPublished - 2011
Event22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan
Duration: Dec 5 2011Dec 8 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7074 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other22nd International Symposium on Algorithms and Computation, ISAAC 2011

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


Dive into the research topics of 'Online linear optimization over permutations'. Together they form a unique fingerprint.

Cite this