On the extension complexity of polytopes separating subsets of the Boolean cube

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00572825" target="_blank" >RIV/67985840:_____/23:00572825 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00454-022-00419-3" target="_blank" >https://doi.org/10.1007/s00454-022-00419-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-022-00419-3" target="_blank" >10.1007/s00454-022-00419-3</a>

Result language
angličtina
Original language name
On the extension complexity of polytopes separating subsets of the Boolean cube
Original language description
We show that for every A⊆ { 0 , 1 } n, there exists a polytope P⊆ Rn with P∩ { 0 , 1 } n= A and extension complexity O(2 n/2) , and that there exists an A⊆ { 0 , 1 } n such that the extension complexity of any P with P∩ { 0 , 1 } n= A must be at least 2 n(1-o(1))/3. We also remark that the extension complexity of any 0/1-polytope in Rn is at most O(2 n/ n) and pose the problem whether the upper bound can be improved to O(2 cn) , for c< 1.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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