Ruslan Yu. Simanchev     (Dostoevsky Omsk State University, Prospect Mira 55a, Omsk, 644077, Russia; Omsk Scientific Center of SB RAS, Prospect K. Marksa 15, Omsk, 644024, Russian Federation)
Inna V. Urazova     (Dostoevsky Omsk State University, Prospect Mira 55a, Omsk, 644077, Russian Federation)
Vladimir V. Voroshilov     (Dostoevsky Omsk State University, Prospect Mira 55a, Omsk, 644077, Russian Federation)


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.


Combinatorial Optimization, Boolean programming, Minimal dominating set, Key indicators

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