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The matroid secretary problem for minor-closed classes and random
matroids
release_ezcpixjkbvbofgaxzxetu37ghi
by
Tony Huynh, Peter Nelson
Released
as a article
.
2016
Abstract
We prove that for every proper minor-closed class M of matroids
representable over a prime field, there exists a constant-competitive matroid
secretary algorithm for the matroids in M. This result relies on the
extremely powerful matroid minor structure theory being developed by Geelen,
Gerards and Whittle.
We also note that for asymptotically almost all matroids, the matroid
secretary algorithm that selects a random basis, ignoring weights, is
(2+o(1))-competitive. In fact, assuming the conjecture that almost all
matroids are paving, there is a (1+o(1))-competitive algorithm for almost all
matroids.
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1603.06822v3
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