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Finding large "cliquish" subgraphs is a classic NP-hard graph problem. Inthis work, we focus on finding maximum $s$-clubs and $s$-plexes, i.e., graphsof diameter $s$ and graphs where each vertex is adjacent to all but $s$vertices. Preprocessing based on Turing kernelization is a standard tool totackle these problems, especially on sparse graphs. We provide a newparameterized analysis for the Turing kernelization and demonstrate theirusefulness in practice. Moreover, we provide evidence that the new theoreticalbounds indeed better explain the observed running times than the existingtheoretical running time bounds. To this end, we suggest a general method tocompare how well theoretical running time bounds fit to measured running times.

Correlating Theory and Practice in Finding Clubs and Plexes