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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Online Linear Optimization over Permutations
verfasst von : Shota Yasutake, Kohei Hatano, Shuji Kijima, Eiji Takimoto, Masayuki Takeda
Erschienen in: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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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
.