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.
In text/plain format

Archived Files and Locations

application/pdf  198.5 kB
file_x6ijmzzf35fqheicrmwbcd4fbm
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2016-07-13
Version   v3
Language   en ?
arXiv  1603.06822v3
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 6a537cf2-c5d0-40ff-b073-1aeb94ff4d2e
API URL: JSON