Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs
نویسندگان
چکیده
We study the problems Locating-Dominating Set and Metric Dimension, which consist in determining a minimum-size set of vertices that distinguishes the vertices of a graph using either neighbourhoods or distances. We consider these problems when restricted to interval graphs and permutation graphs. We prove that both decision problems are NP-complete, even for graphs that are at the same time interval graphs and permutation graphs and have diameter 2. While Locating-Dominating Set parameterized by solution size is trivially fixed-parameter-tractable, it is known that Metric Dimension is W [2]hard. We show that for interval graphs, this parameterization of Metric Dimension is fixed-parameter-tractable.
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