And to make this easily demonstrable, I implemented the algorithm in Haskell, albeit I haven't yet been able to test it enough to make sure it properly works for all cases (in particular, the single test case that's in the repo currently only tests SymmetricExchanges).
https://codeberg.org/fogti/nwc-decomb
Neat little set of experiments I did :)
https://harrison.totty.dev/p/positroid-structure-relu-networks
'Deletion Robust Non-Monotone Submodular Maximization over Matroids', by Paul Dütting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Morteza Zadimoghaddam.
http://jmlr.org/papers/v26/23-1219.html
#matroid #matroids #algorithms
Great introductory article on #matroid s:
Neel, David L., and Nancy Ann Neudauer. 2009. “Matroids You Have Known.” Mathematics Magazine 82 (1): 26–41. https://doi.org/10.1080/0025570X.2009.11953589.
#Matroid s are a specific kind of sets that contain other sets, but for any set they contain, they also need to contain its subsets. For more look here:
https://en.wikipedia.org/wiki/Matroid
Looking oddly specific, they're in fact an interesting structure which pops out in the study of many combinatorial subjects like graph theory, and, as I just learned, #homology!
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Harrison Totty
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