  We consider the problems of finding optimal identifying codes, (open)
locating-dominating sets and resolving sets of an interval or a permutation
graph. In these problems, one asks to find a subset of vertices, normally
called a \emph{solution} set, using which all vertices of the graph are
distinguished. The identification can be done by considering the neighborhood
within the solution set, or by employing the distances to the solution
vertices. Normally the goal is to minimize the size of the solution set then.
Here we study the case of interval graphs, unit interval graphs, (bipartite)
permutation graphs and cographs. For these classes of graphs we give tight
lower bounds for the size of such solution sets depending on the order of the
input graph. While such lower bounds for the general class of graphs are in
logarithmic order, the improved bounds in these special classes are of the
order of either quadratic root or linear in terms of number of vertices.
Moreover, the results for cographs lead to linear-time algorithms to solve the
considered problems on inputs that are cographs.
