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 Diskretn. Anal. Issled. Oper., Ser. 2, 2006, Volume 13, Number 2, Pages 3–20 (Mi da2)

An approximate algorithm for finding a maximum-weight $d$-homogeneous connected spanning subgraph in a complete graph with random edge weights

A. E. Baburin, E. Kh. Gimadi

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: An approximation algorithm is suggested for the problem of finding a $d$-regular spanning connected subgraph of maximum weight in a complete undirected weighted $n$-vertex graph. Probabilistic analysis of the algorithm is carried out for the problem with random input data (some weights of edges) in the case of a uniform distribution of the weights of edges and in the case of a minorized type distribution. It is shown that the algorithm finds an asymptotically optimal solution with time complexity $O(n^2)$ when $d=o(n)$. For the minimization version of the problem, an additional restriction on the dispersion of weights of the graph edges is added to the condition of the asymptotical optimality of the modified algorithm.

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English version:
Journal of Applied and Industrial Mathematics, 2008, 2:2, 155–166

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Citation: A. E. Baburin, E. Kh. Gimadi, “An approximate algorithm for finding a maximum-weight $d$-homogeneous connected spanning subgraph in a complete graph with random edge weights”, Diskretn. Anal. Issled. Oper., Ser. 2, 13:2 (2006), 3–20; J. Appl. Industr. Math., 2:2 (2008), 155–166

Citation in format AMSBIB
\Bibitem{BabGim06} \by A.~E.~Baburin, E.~Kh.~Gimadi \paper An approximate algorithm for finding a maximum-weight $d$-homogeneous connected spanning subgraph in a~complete graph with random edge weights \jour Diskretn. Anal. Issled. Oper., Ser.~2 \yr 2006 \vol 13 \issue 2 \pages 3--20 \mathnet{http://mi.mathnet.ru/da2} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2310924} \zmath{https://zbmath.org/?q=an:1249.90210} \transl \jour J. Appl. Industr. Math. \yr 2008 \vol 2 \issue 2 \pages 155--166 \crossref{https://doi.org/10.1134/S1990478908020026} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-44849132851} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. Kh. Gimadi, “O veroyatnostnom analize priblizhënnogo algoritma resheniya zadachi o $p$-mediane”, Diskretn. analiz i issled. oper., 17:3 (2010), 19–31
2. E. Kh. Gimadi, V. T. Dementev, “Veroyatnostnyi analiz detsentralizovannoi versii odnogo obobscheniya zadachi o naznacheniyakh”, Diskretn. analiz i issled. oper., 18:3 (2011), 11–20
3. E. Kh. Gimadi, A. V. Shakhshneyder, “Approximate algorithms with estimates for routing problems on random inputs with a bounded number of customers per route”, Autom. Remote Control, 73:2 (2012), 323–335
4. Cornelissen K., Hoeksma R., Manthey B., Narayanaswamy N.S., Rahul C.S., “Approximability of Connected Factors”, Approximation and Online Algorithms, Waoa 2013, Lecture Notes in Computer Science, 8447, eds. Kaklamanis C., Pruhs K., Springer-Verlag Berlin, 2014, 120–131
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