Consensus Strings with Small Maximum Distance and Small Distance Sum

The parameterised complexity of various consensus string problems ( Closest String , Closest Substring , Closest String with Outliers ) is investigated in a more general setting, i. e., with a bound on the maximum Hamming distance and a bound on the sum of Hamming distances between solution and input strings. We completely settle the parameterised complexity of these generalised variants of Closest String and Closest Substring , and partly for Closest String with Outliers ; in addition, we answer some open questions from the literature regarding the classical problem variants with only one distance bound. Finally, we investigate the question of polynomial kernels and respective lower bounds.