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Finding Connected Dense \(k\)-Subgraphs

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Theory and Applications of Models of Computation (TAMC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9076))

Abstract

Given a connected graph \(G\) on \(n\) vertices and a positive integer \(k\le n\), a subgraph of \(G\) on \(k\) vertices is called a \(k\)-subgraph in \(G\). We design combinatorial approximation algorithms for finding a connected \(k\)-subgraph in \(G\) such that its density is at least a factor \(\varOmega (\max \{n^{-2/5},k^2/n^2\})\) of the density of the densest \(k\)-subgraph in \(G\) (which is not necessarily connected). These particularly provide the first non-trivial approximations for the densest connected \(k\)-subgraph problem on general graphs.

Research supported in part by by NNSF of China under Grant No. 11222109, 11021161 and 10928102, by 973 Project of China under Grant No. 2011CB80800, and by CAS Program for Cross & Cooperative Team of Science & Technology Innovation.

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Authors and Affiliations

  1. Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, China

    Xujin Chen, Xiaodong Hu & Changjun Wang

Authors
  1. Xujin Chen
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  2. Xiaodong Hu
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  3. Changjun Wang
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Corresponding author

Correspondence to Xujin Chen .

Editor information

Editors and Affiliations

  1. National University of Singapore, Singapore, Singapore

    Rahul Jain

  2. National University of Singapore, Singapore, Singapore

    Sanjay Jain

  3. National University of Singapore, Singapore, Singapore

    Frank Stephan

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Chen, X., Hu, X., Wang, C. (2015). Finding Connected Dense \(k\)-Subgraphs. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_22

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  • DOI: https://doi.org/10.1007/978-3-319-17142-5_22

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  • Online ISBN: 978-3-319-17142-5

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