On 2-Clubs in Graph-Based Data Clustering: Theory and Algorithm Engineering

Editing a graph into disjoint union of clusters is standard optimization task in graph-based data clustering. Here, complementing classic work where the shall be cliques, we focus on that 2-clubs, is, subgraphs diameter two. This naturally leads to two NP-hard problems 2-Club Cluster (the allowed editing operations are edge insertion and deletion) Vertex Deletion vertex deletions). Answering an open question from literature, show W[2]-hard with respect number modifications, thus contrasting fixed-parameter tractability result for problem (considering cliques instead 2-clubs). Then focusing Deletion, which easily seen tractable, under complexity-theoretic assumptions it does not have polynomial-size kernel when parameterized by deletions. Nevertheless, develop several effective reduction pruning rules, resulting competitive solver, clearly outperforming CPLEX solver most instances established biological test set.