The proposed (2+ε) and (7+ε) FPT algorithms for colorful sum of radii are not proven: the sampling argument misses small clusters and the residual-instance lemma uses one center too few.
A technique for obtaining true approximations for k-center with covering constraints
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FPT Constant Approximation Algorithms for Colorful Sum of Radii
The proposed (2+ε) and (7+ε) FPT algorithms for colorful sum of radii are not proven: the sampling argument misses small clusters and the residual-instance lemma uses one center too few.