The minimal dominating sets in a directed graph and the key indicators set of socio-economic system
Ural mathematical journal, Tome 9 (2023) no. 1, pp. 153-161
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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.
Keywords:
combinatorial optimization, boolean programming, minimal dominating set, key indicators.
@article{UMJ_2023_9_1_a13,
author = {Ruslan Yu. Simanchev and Inna V. Urazova and Vladimir V. Voroshilov},
title = {The minimal dominating sets in a directed graph and the key indicators set of socio-economic system},
journal = {Ural mathematical journal},
pages = {153--161},
publisher = {mathdoc},
volume = {9},
number = {1},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a13/}
}
TY - JOUR AU - Ruslan Yu. Simanchev AU - Inna V. Urazova AU - Vladimir V. Voroshilov TI - The minimal dominating sets in a directed graph and the key indicators set of socio-economic system JO - Ural mathematical journal PY - 2023 SP - 153 EP - 161 VL - 9 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a13/ LA - en ID - UMJ_2023_9_1_a13 ER -
%0 Journal Article %A Ruslan Yu. Simanchev %A Inna V. Urazova %A Vladimir V. Voroshilov %T The minimal dominating sets in a directed graph and the key indicators set of socio-economic system %J Ural mathematical journal %D 2023 %P 153-161 %V 9 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a13/ %G en %F UMJ_2023_9_1_a13
Ruslan Yu. Simanchev; Inna V. Urazova; Vladimir V. Voroshilov. The minimal dominating sets in a directed graph and the key indicators set of socio-economic system. Ural mathematical journal, Tome 9 (2023) no. 1, pp. 153-161. http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a13/