A Fixed-Parameter Approach for Weighted Cluster Editing

Clustering objects with respect to a given similarity or distance measure is a problem often encountered in computational biology. Several well-known clustering algorithms are based on transforming the input matrix into a weighted graph although the resulting WEIGHTED CLUSTER EDITING problem is computationally hard: here, we transform the input graph into a disjoint union of cliques such that the sum of weights of all modified edges is minimized. We present fixed-parameter algorithms for this problem which guarantee to find an optimal solution in provable worst-case running time. We introduce a new data reduction operation (merging vertices) that has no counterpart in the unweighted case and strongly cuts down running times in practice. We have applied our algorithms to both artificial and biological data. Despite the complexity of the problem, our method often allows exact computation of optimal solutions in reasonable running time.