Finding Connected Dense \(k\)-Subgraphs

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Densest \(k\)-subgraphs Connectivity Combinatorial approximation algorithms 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Applied Mathematics, AMSSChinese Academy of SciencesBeijingChina

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