Complex of abstract cubes and median problem
In this paper a special complex $\mathcal{K}^{n}$ 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 t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Vladimir Andrunachievici Institute of Mathematics and Computer Science
2011-06-01
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| Series: | Computer Science Journal of Moldova |
| Subjects: | |
| Online Access: | http://www.math.md/files/csjm/v19-n1/v19-n1-(pp38-63).pdf |
| _version_ | 1798005126374359040 |
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| author | Sergiu Cataranciuc Petru Soltan |
| author_facet | Sergiu Cataranciuc Petru Soltan |
| author_sort | Sergiu Cataranciuc |
| collection | DOAJ |
| description | In this paper a special complex $\mathcal{K}^{n}$ 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 |
| first_indexed | 2024-04-11T12:34:16Z |
| format | Article |
| id | doaj.art-35da13bcd9554ad39188511bdab39b2c |
| institution | Directory Open Access Journal |
| issn | 1561-4042 |
| language | English |
| last_indexed | 2024-04-11T12:34:16Z |
| publishDate | 2011-06-01 |
| publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| record_format | Article |
| series | Computer Science Journal of Moldova |
| spelling | doaj.art-35da13bcd9554ad39188511bdab39b2c2022-12-22T04:23:40ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422011-06-01191(55)3863Complex of abstract cubes and median problemSergiu Cataranciuc0Petru Soltan1Moldova State UniversityMoldova State UniversityIn this paper a special complex $\mathcal{K}^{n}$ 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, 68R10http://www.math.md/files/csjm/v19-n1/v19-n1-(pp38-63).pdfAbstract cubecomplexmultidimensional homogeneous treeabstract spheremedian |
| spellingShingle | Sergiu Cataranciuc Petru Soltan Complex of abstract cubes and median problem Computer Science Journal of Moldova Abstract cube complex multidimensional homogeneous tree abstract sphere median |
| title | Complex of abstract cubes and median problem |
| title_full | Complex of abstract cubes and median problem |
| title_fullStr | Complex of abstract cubes and median problem |
| title_full_unstemmed | Complex of abstract cubes and median problem |
| title_short | Complex of abstract cubes and median problem |
| title_sort | complex of abstract cubes and median problem |
| topic | Abstract cube complex multidimensional homogeneous tree abstract sphere median |
| url | http://www.math.md/files/csjm/v19-n1/v19-n1-(pp38-63).pdf |
| work_keys_str_mv | AT sergiucataranciuc complexofabstractcubesandmedianproblem AT petrusoltan complexofabstractcubesandmedianproblem |