Abstract
We consider the following problem. Given a graph and a rational number \(\mu \), \(0 < \mu \le 1\), find a connected subgraph of density at least \(\mu \) with the largest number of vertices. Here, the density of an \(n\)-vertex graph with \(m\) edges is \(m/\left( {\begin{array}{c}n\\ 2\end{array}}\right) \). This problem arises in many application contexts such as community detection in social networks. We implement a branch and bound algorithm and tune it for efficiency on sparse real-world graphs for the case \(\mu \ge 1/2\). Central issues for the implementation are the choice of branching candidates, two new upper bounding procedures, and several data reduction and early termination rules.
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Komusiewicz, C., Sorge, M., Stahl, K. (2015). Finding Connected Subgraphs of Fixed Minimum Density: Implementation and Experiments. In: Bampis, E. (eds) Experimental Algorithms. SEA 2015. Lecture Notes in Computer Science(), vol 9125. Springer, Cham. https://doi.org/10.1007/978-3-319-20086-6_7
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DOI: https://doi.org/10.1007/978-3-319-20086-6_7
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