Complex of abstract cubes and median problem
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CATARANCIUC, Sergiu, SOLTAN, Petru. Complex of abstract cubes and median problem. In: Computer Science Journal of Moldova, 2011, nr. 1(55), pp. 38-63. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 1(55) / 2011 / ISSN 1561-4042 /ISSNe 2587-4330

Complex of abstract cubes and median problem
CZU: 515.142.21+519.179.1

Pag. 38-63

Cataranciuc Sergiu, Soltan Petru
Moldova State University
Disponibil în IBN: 6 decembrie 2013


In this paper a special complex K of abstract cubes [2, 3], which contains only n-dimensional cubes is examined. The border of this complex is an abstract (n - 1)-dimensional sphere. It is proved that the abstract sphere contains at least one 0- dimensional cube, which belongs to exactly n cubes with dimension 1, if the complex is a homogeneous n-dimensional tree. This result allows to solve, in an efficient way, the problem of median for a skeleton of size 1 of the tree with weighted vertices and edges. The algorithm to calculate the median without using any metric is described. The proposed algorithm can be applied with some modifications, for arbitrary complex of abstract cubes. Mathematics subject classification: 18F15, 32Q60, 68R10

Abstract cube, multidimensional homogeneous tree, abstract sphere,