Title:
On the Hypercube Subset Partitioning Varieties
Author:
Type:
Co-author(s) :
Aslanyan Levon ; Ryazanov Vladimir
Uncontrolled Keywords:
Boolean functions ; computational complexity ; computational geometry ; set theory
Abstract:
In this paper, the problem of a quantitative description of partitions (QDP) of arbitrary m-subsets of the n-dimensional unit cube is considered for a given m, 0 ≤ m ≤ 2 n . A necessary condition for the existence of a given QDP-subset is achieved in terms of minimal and maximal layers that are known by earlier publications. It is shown that QDP are in a correspondence to the upper homogeneous area elements of the n-cube and to the monotone Boolean functions. The NP-hardness of the QDP problem is proved. QDP singular points on different layers of the cube are described.
Publisher:
DOI:
10.1109/CSITechnol.2019.8895211
Journal or Publication Title:
2019 Computer Science and Information Technologies (CSIT)
URL:
Affiliation:
Institute for Informatics and Automation Problems of NAS RA ; Computer Center of Federal Research Center CSC RAS
Country:
Year:
Time period:
Conference title:
2019 Computer Science and Information Technologies (CSIT)