Ulam k-center is FPT for k+d but admits no polynomial kernel unless NP is in coNP/poly; k-median is W[1]-hard for d yet FPT for k+d via a polynomial kernel.
30 ClusteringPermutationsundertheUlamMetric: AParameterizedComplexityStudy 17 Luís Cunha, Ignasi Sau, and Uéverton S
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Clustering Permutations under the Ulam Metric: A Parameterized Complexity Study
Ulam k-center is FPT for k+d but admits no polynomial kernel unless NP is in coNP/poly; k-median is W[1]-hard for d yet FPT for k+d via a polynomial kernel.