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AbstractWe consider the problems of finding optimal identifying codes, (open) locating dominating sets and resolving sets (denoted Identifying Code, (Open) Open Locating Dominating Set and Metric Dimension) of an interval or a permutation graph. In these problems, one asks to distinguish all vertices of a graph by a subset of the vertices steroids, using either the neighbourhood within the solution set or the distances to the solution vertices. Using a general reduction for this class of problems, we prove that the decision problems associated to these four notions are NP complete, even for interval graphs of diameter 2 and permutation graphs of diameter 2.

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