2-Approximation algorithm for finding a clique with minimum weight of vertices and edges

The problem of finding a minimum clique (with respect to the total weight of its vertices and edges) of fixed size in a complete undirected weighted graph is considered along with some of its important subclasses. Approximability issues are analyzed. The inapproximability of the problem is proved fo...

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Vydané v:Proceedings of the Steklov Institute of Mathematics Ročník 284; číslo Suppl 1; s. 87 - 95
Hlavní autori: Eremin, I. I., Gimadi, E. Kh, Kel’manov, A. V., Pyatkin, A. V., Khachai, M. Yu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Moscow Pleiades Publishing 01.04.2014
Predmet:
Mathematics
Mathematics and Statistics
approximation guarantee
minimum weight of vertices and edges
subset search
time complexity
clique of fixed size
complete undirected graph
polynomial time approximation algorithm
approximability
ISSN:0081-5438, 1531-8605
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Abstract The problem of finding a minimum clique (with respect to the total weight of its vertices and edges) of fixed size in a complete undirected weighted graph is considered along with some of its important subclasses. Approximability issues are analyzed. The inapproximability of the problem is proved for the general case. A 2-approximation efficient algorithm with time complexity O ( n 2 ) is suggested for the cases when vertex weights are nonnegative and edge weights either satisfy the triangle inequality or are squared pairwise distances for some point configuration of Euclidean space.
AbstractList The problem of finding a minimum clique (with respect to the total weight of its vertices and edges) of fixed size in a complete undirected weighted graph is considered along with some of its important subclasses. Approximability issues are analyzed. The inapproximability of the problem is proved for the general case. A 2-approximation efficient algorithm with time complexity O ( n 2 ) is suggested for the cases when vertex weights are nonnegative and edge weights either satisfy the triangle inequality or are squared pairwise distances for some point configuration of Euclidean space.
Author Gimadi, E. Kh
Khachai, M. Yu
Pyatkin, A. V.
Eremin, I. I.
Kel’manov, A. V.
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Issue Suppl 1
Keywords approximation guarantee
minimum weight of vertices and edges
subset search
time complexity
clique of fixed size
complete undirected graph
polynomial time approximation algorithm
approximability
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AhoAHopcroftJUllmanJThe Design and Analysis of Computer Algorithms1974Reading, MAAddison-Wesley0326.68005
Kel’manovA VPyatkinA VNP-completeness of some problems of choosing a vector subsetJ. Appl. Ind. Math.20115335235710.1134/S19904789110300692779350
HåstadJClique is hard to approximate within n1-ɛActa Math.1999182110514210.1007/BF023928250989.680601687331
ParkKLeeKParkSAn extended formulation approach to the edge-weighted maximal clique problemEurop. J. Oper. Res.199695367168210.1016/0377-2217(95)00299-50926.90086
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A V Kel’manov (6719_CR5) 2011; 5
A Aho (6719_CR4) 1974
M R Garey (6719_CR1) 1979
J Håstad (6719_CR2) 1999; 182
A V Kel’manov (6719_CR6) 2012; 6
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– reference: Kel’manovA VRomanchenkoS MAn approximation algorithm for solving a problem of search for a vector subsetJ. Appl. Ind. Math.201264909610.1134/S19904789120100972847829
– reference: HåstadJClique is hard to approximate within n1-ɛActa Math.1999182110514210.1007/BF023928250989.680601687331
– reference: Kel’manovA VPyatkinA VNP-completeness of some problems of choosing a vector subsetJ. Appl. Ind. Math.20115335235710.1134/S19904789110300692779350
– reference: ParkKLeeKParkSAn extended formulation approach to the edge-weighted maximal clique problemEurop. J. Oper. Res.199695367168210.1016/0377-2217(95)00299-50926.90086
– reference: AhoAHopcroftJUllmanJThe Design and Analysis of Computer Algorithms1974Reading, MAAddison-Wesley0326.68005
– volume-title: Computers and Intractability: A Guide to the Theory of NP-Completeness
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Title 2-Approximation algorithm for finding a clique with minimum weight of vertices and edges
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