THE MINIMAL DOMINATING SETS IN A DIRECTED GRAPH AND THE KEY INDICATORS SET OF SOCIO–ECONOMIC SYSTEM
The paper deals with a digraph with non-negative vertex weights. A subset \(W\) of the set of vertices is called dominating if any vertex that not belongs to it is reachable from the set \(W\) within precisely one step. A dominating set is called minimal if it ceases to be dominating when removing...
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| Vydané v: | Ural mathematical journal Ročník 9; číslo 1; s. 153 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
27.07.2023
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| Predmet: | |
| ISSN: | 2414-3952, 2414-3952 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | The paper deals with a digraph with non-negative vertex weights. A subset \(W\) of the set of vertices is called dominating if any vertex that not belongs to it is reachable from the set \(W\) within precisely one step. A dominating set is called minimal if it ceases to be dominating when removing any vertex from it. The paper investigates the problem of searching for a minimal dominating set of maximum weight in a vertex-weighted digraph. An integer linear programming model is proposed for this problem. The model is tested on random instances and the real problem of choosing a family of key indicators in a specific socio-economic system. The paper compares this model with the problem of choosing a dominating set with a fixed number of vertices. |
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| ISSN: | 2414-3952 2414-3952 |
| DOI: | 10.15826/umj.2023.1.014 |