The Complexity of Physical Mapping with Strict Chimerism

Abstract

We analyze the algorithmic complexity of physical mapping by hybridization in situations of restricted forms of chimeric errors, which is motivated by typical experimental conditions. The constituents of a chimeric probe always occur in pure form in the data base, too. This problem can be modelled by a variant of the k-consecutive ones problem. We show that even under this restriction the corresponding decision problem is $\mathcal{N}\mathcal{P}$-complete. Considering the most important situation of strict 2-chimerism, for the related optimization problem a complete separation between efficiently solvable and $\mathcal{N}\mathcal{P}$-hard cases is given based on the sparseness parameters of the clone library. For the favourable case we present a fast algorithm and a data structure that provides an effective description of all optimal solutions to the problem.