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Diskretnyi Analiz i Issledovanie Operatsii, 2013, Volume 20, Issue 6, Pages 59–76 (Mi da753)  
This article is cited in 19 scientific papers (total in 19 papers)

Critical graph classes for the edge list-ranking problem

D. S. Malyshevab

a Nizhniy Novgorod Higher School of Economics, 25/12 B. Pecherskaya St., 603155 Nizhniy Novgorod, Russia
b Nizhniy Novgorod State University, 23 Gagarin Ave., 603950 Nizhniy Novgorod, Russia
Full-text PDF (290 kB) Citations (19)
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Abstract: The edge list-ranking problem is a model for some parallel processes. We study the computational complexity of this problem for graph sets closed under isomorphism and deletion of vertices (hereditary classes). We describe all finitely defined and minor-closed cases for which the problem is polynomial-time solvable. We find the whole set of “critical” graph classes, the inclusion of which in a finitely defined class is equivalent to intractability of the edge list-ranking problem in this class. It seems to be the first result on a complete description for non-artificial NP-complete graph problems. For this problem, we constructively prove that among minimal under inclusion NP-complete hereditary cases there are exactly 5 finitely defined classes and exactly 1 minor-closed class. Ill. 1, bibliogr. 13.
Keywords: computational complexity, hereditary class, boundary class, minimal hard class, polynomial algorithm, edge list-ranking problem.
Received: 06.08.2012
Revised: 14.03.2013
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 2, Pages 245–255
DOI: https://doi.org/10.1134/S1990478914020112
Bibliographic databases:
Document Type: Article
UDC: 519.178
Language: Russian
Citation: D. S. Malyshev, “Critical graph classes for the edge list-ranking problem”, Diskretn. Anal. Issled. Oper., 20:6 (2013), 59–76; J. Appl. Industr. Math., 8:2 (2014), 245–255
Citation in format AMSBIB
\Bibitem{Mal13}
\by D.~S.~Malyshev
\paper Critical graph classes for the edge list-ranking problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 6
\pages 59--76
\mathnet{http://mi.mathnet.ru/da753}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3185264}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 2
\pages 245--255
\crossref{https://doi.org/10.1134/S1990478914020112}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902132811}
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретный анализ и исследование операций
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