Abstract
Given a simple undirected graph G = (V, E) and an integer k < |V|, the Sparsest k -Subgraph problem asks for a set of k vertices which induces the minimum number of edges. As a generalization of the classical independent set problem, Sparsest k -Subgraph is \(\mathcal{NP}\)-hard and even not approximable unless \(\mathcal{P} = \mathcal{NP}\) in general graphs. Thus, we investigate Sparsest k -Subgraph in graph classes where independent set is polynomial-time solvable, such as subclasses of perfect graphs. Our two main results are the \(\mathcal{NP}\)-hardness of Sparsest k -Subgraph on chordal graphs, and a greedy 2-approximation algorithm. Finally, we also show how to derive a PTAS for Sparsest k -Subgraph on proper interval graphs.
This work has been funded by grant ANR 2010 BLAN 021902.
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Watrigant, R., Bougeret, M., Giroudeau, R. (2014). Approximating the Sparsest k-Subgraph in Chordal Graphs. In: Kaklamanis, C., Pruhs, K. (eds) Approximation and Online Algorithms. WAOA 2013. Lecture Notes in Computer Science, vol 8447. Springer, Cham. https://doi.org/10.1007/978-3-319-08001-7_7
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DOI: https://doi.org/10.1007/978-3-319-08001-7_7
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