Computing Densest k-Subgraph with Structural Parameters

07/20/2022

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by   Tesshu Hanaka, et al.

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Densest k-Subgraph is the problem to find a vertex subset S of size k such that the number of edges in the subgraph induced by S is maximized. In this paper, we show that Densest k-Subgraph is fixed parameter tractable when parameterized by neighborhood diversity, block deletion number, distance-hereditary deletion number, and cograph deletion number, respectively. Furthermore, we give a 2-approximation 2^(G)/2n^O(1)-time algorithm where (G) is the twin cover number of an input graph G.