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Optimal decision tr...
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Jonsson, JakobKTH,Matematik (Avd.)
(författare)
Optimal decision trees on simplicial complexes
- Artikel/kapitelEngelska2005
Förlag, utgivningsår, omfång ...
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2005-01-07
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The Electronic Journal of Combinatorics,2005
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printrdacarrier
Nummerbeteckningar
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LIBRIS-ID:oai:DiVA.org:kth-14446
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https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-14446URI
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https://doi.org/10.37236/1900DOI
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Språk:engelska
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Sammanfattning på:engelska
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Ämneskategori:ref swepub-contenttype
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Ämneskategori:art swepub-publicationtype
Anmärkningar
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QC 20100525
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We consider topological aspects of decision trees on simplicial complexes, concentrating on how to use decision trees as a tool in topological combinatorics. By Robin Forman's discrete Morse theory, the number of evasive faces of a given dimension i with respect to a decision tree on a simplicial complex is greater than or equal to the ith reduced Betti number (over any field) of the complex. Under certain favorable circumstances, a simplicial complex admits an optimal decision tree such that equality holds for each i; we may hence read off the homology directly from the tree. We provide a recursive definition of the class of semi-nonevasive simplicial complexes with this property. A certain generalization turns out to yield the class of semi-collapsible simplicial complexes that admit an optimal discrete Morse function in the analogous sense. In addition, we develop some elementary theory about semi-nonevasive and semi-collapsible complexes. Finally, we provide explicit optimal decision trees for several well-known simplicial complexes.
Ämnesord och genrebeteckningar
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shellable nonpure complexes
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discrete morse functions
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chessboard complexes
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connected graphs
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decompositions
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evasiveness
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posets
Biuppslag (personer, institutioner, konferenser, titlar ...)
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KTHMatematik (Avd.)
(creator_code:org_t)
Sammanhörande titlar
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Ingår i:The Electronic Journal of Combinatorics: The Electronic Journal of Combinatorics12:11097-14401077-8926
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