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Avtomat. i Telemekh., 2010, Issue 1, Pages 130–143 (Mi at910)  

This article is cited in 1 scientific paper (total in 1 paper)

Control in Social Economic Systems

Dominating, weakly stable, and uncovered sets: Properties and generalizations

A. N. Subochev

State University, Higher School of Economics, Moscow, Russia

Abstract: We consider the problem of collective choice in a tournament, i.e., when the majority relation, which plays the role of the collective preference system on this set of alternatives, can be represented by a complete asymmetric oriented graph. We compare three solutions of the collective choice problem: minimal dominating, uncovered, and minimal weakly stable sets. We construct generalizations of the minimal dominating set and find out, with their help, how the system of dominating sets looks like in the general case. We formulate a criterion that determines whether an alternative belongs to a minimal weakly stable set. We find out how minimal weakly stable sets relate to uncovered sets. Based on the notion of stability of an alternative and the set of alternatives we construct generalizations for the notions of uncovered and weakly stable sets – the classes of $k$-stable alternatives and $k$-stable sets. We prove inclusion relations between these classes.

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English version:
Automation and Remote Control, 2010, 71:1, 116–127

Bibliographic databases:

PACS: 02.50.Le
Presented by the member of Editorial Board: Ф. Т. Алескеров

Received: 15.07.2008

Citation: A. N. Subochev, “Dominating, weakly stable, and uncovered sets: Properties and generalizations”, Avtomat. i Telemekh., 2010, no. 1, 130–143; Autom. Remote Control, 71:1 (2010), 116–127

Citation in format AMSBIB
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\jour Autom. Remote Control
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\pages 116--127
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Aleskerov F., Meshcheryakova N., Shvydun S., Yakuba V., “Centrality Measures in Large and Sparse Networks”, 2016 6Th International Conference on Computers Communications and Control (Icccc), eds. Dzitac I., Filip F., Manolescu M., IEEE, 2016, 118–123  crossref  isi
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