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Our main results are 2-approximation algorithms for five versions of this problem involving reversals and transpositions. We also give bounds for the diameters concerning these problems and provide an improved approximation factor for simple permutations considering transpositions.As a rule, receptor-ligand assay data are fitted by logistic functions (4PL model, 5PL model, Feldman's model). The preparation of the initial estimates for parameters of these functions is an important problem for processing receptor-ligand interaction data. T
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