On optimal comparability editing with applications to molecular diagnostics

<p>Abstract</p> <p>Background</p> <p>The C<smcaps>OMPARABILITY</smcaps> E<smcaps>DITING</smcaps> problem appears in the context of hierarchical disease classification based on noisy data. We are given a directed graph <it>G </it>representing hierarchical relationships between patient subgroups. The task is to identify the minimum number of edge insertions or deletions to transform <it>G </it>into a transitive graph, that is, if edges (<it>u</it>, <it>v</it>) and (<it>v</it>, <it>w</it>) are present then edge (<it>u</it>, <it>w</it>) must be present, too.</p> <p>Results</p> <p>We present two new approaches for the problem based on fixed-parameter algorithmics and integer linear programming. In contrast to previously used heuristics, our approaches compute provably optimal solutions.</p> <p>Conclusion</p> <p>Our computational results demonstrate that our exact algorithms are by far more efficient in practice than a previously used heuristic approach. In addition to the superior running time performance, our algorithms are capable of enumerating all optimal solutions, and naturally solve the weighted version of the problem.</p