Roman Domination and Independent Roman Domination are solvable in 4^k n^{O(1)} time when parameterized by distance to cluster, with SETH and kernel lower bounds showing this is nearly optimal.
Downey and Michael R
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(Independent) Roman Domination Parameterized by Distance to Cluster
Roman Domination and Independent Roman Domination are solvable in 4^k n^{O(1)} time when parameterized by distance to cluster, with SETH and kernel lower bounds showing this is nearly optimal.