Closest 4-leaf power is fixed-parameter tractable |
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Authors: | Michael Dom Jiong Guo Rolf Niedermeier |
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Institution: | Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany |
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Abstract: | The NP-complete Closest 4-Leaf Power problem asks, given an undirected graph, whether it can be modified by at most r edge insertions or deletions such that it becomes a 4-leaf power. Herein, a 4-leaf power is a graph that can be constructed by considering an unrooted tree—the 4-leaf root—with leaves one-to-one labeled by the graph vertices, where we connect two graph vertices by an edge iff their corresponding leaves are at distance at most 4 in the tree. Complementing previous work on Closest 2-Leaf Power and Closest 3-Leaf Power, we give the first algorithmic result for Closest 4-Leaf Power, showing that Closest 4-Leaf Power is fixed-parameter tractable with respect to the parameter r. |
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Keywords: | Fixed-parameter tractability Graph algorithm Graph modification Graph power Leaf power Forbidden subgraph characterization |
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