BACKGROUND: The COMPARABILITY EDITING problem appears in the context of hierarchical disease classification based on noisy data. We are given a directed graph G representing hierarchical relationships between patient subgroups. The task is to identify the minimum number of edge insertions or deletions to transform G into a transitive graph, that is, if edges (u, v) and (v, w) are present then edge (u, w) must be present, too. RESULTS: 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. CONCLUSION: 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.
BACKGROUND: The COMPARABILITY EDITING problem appears in the context of hierarchical disease classification based on noisy data. We are given a directed graph G representing hierarchical relationships between patient subgroups. The task is to identify the minimum number of edge insertions or deletions to transform G into a transitive graph, that is, if edges (u, v) and (v, w) are present then edge (u, w) must be present, too. RESULTS: 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. CONCLUSION: 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.
Authors: Michael Hummel; Stefan Bentink; Hilmar Berger; Wolfram Klapper; Swen Wessendorf; Thomas F E Barth; Heinz-Wolfram Bernd; Sergio B Cogliatti; Judith Dierlamm; Alfred C Feller; Martin-Leo Hansmann; Eugenia Haralambieva; Lana Harder; Dirk Hasenclever; Michael Kühn; Dido Lenze; Peter Lichter; Jose Ignacio Martin-Subero; Peter Möller; Hans-Konrad Müller-Hermelink; German Ott; Reza M Parwaresch; Christiane Pott; Andreas Rosenwald; Maciej Rosolowski; Carsten Schwaenen; Benjamin Stürzenhofecker; Monika Szczepanowski; Heiko Trautmann; Hans-Heinrich Wacker; Rainer Spang; Markus Loeffler; Lorenz Trümper; Harald Stein; Reiner Siebert Journal: N Engl J Med Date: 2006-06-08 Impact factor: 91.245