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 Diskretn. Anal. Issled. Oper., 2011, Volume 18, Number 3, Pages 84–88 (Mi da656)

Analysis of the number of the edges effect on the complexity of the independent set problem solvability

D. S. Malyshevab

a Nizhniy Novgorod Branch of Higher School of Economics, Nizhny Novgorod, Russia
b Nizhniy Novgorod State University, Nizhniy Novgorod, Russia

Abstract: We consider classes of connected graphs, defined by functional constraints of the number of the edges depending on the vertex quantity. We show that for any fixed $C$ this problem is polynomially solvable in the class $\bigcup_{n=1}^\infty\{G\colon|V(G)|=n, |E(G)|\leq n+C[\log_2(n)]\}$. From the other hand, we prove that this problem isn't polynomial in the class $\bigcup_{n=1}^\infty\{G\colon|V(G)|=n, |E(G)|\leq n+f^2(n)\}$, providing $f(n)\colon\mathbb N\to\mathbb N$ is unbounded and nondecreasing and an exponent of $f(n)$ grows faster than a polynomial of $n$. The last result holds if there is no subexponential algorithms for solving of the independent set problem. Bibliogr. 3.

Keywords: computational complexity, independent set problem.

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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:1, 97–99

Bibliographic databases:

UDC: 519.178
Revised: 22.02.2011

Citation: D. S. Malyshev, “Analysis of the number of the edges effect on the complexity of the independent set problem solvability”, Diskretn. Anal. Issled. Oper., 18:3 (2011), 84–88; J. Appl. Industr. Math., 6:1 (2012), 97–99

Citation in format AMSBIB
\Bibitem{Mal11} \by D.~S.~Malyshev \paper Analysis of the number of the edges effect on the complexity of the independent set problem solvability \jour Diskretn. Anal. Issled. Oper. \yr 2011 \vol 18 \issue 3 \pages 84--88 \mathnet{http://mi.mathnet.ru/da656} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2883750} \zmath{https://zbmath.org/?q=an:1249.68089} \transl \jour J. Appl. Industr. Math. \yr 2012 \vol 6 \issue 1 \pages 97--99 \crossref{https://doi.org/10.1134/S1990478912010103} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857672145} 

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This publication is cited in the following articles:
1. D. S. Malyshev, “The impact of the growth rate of the packing number of graphs on the computational complexity of the independent set problem”, Discrete Math. Appl., 23:3-4 (2013), 245–249
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