We study a novel generalization of the
problem which is motivated by, e.g., error correction in the inference of chemical mixtures by their observable reaction products. We focus on the important case of deciding on one of two candidate substances. This problem has nice graph-theoretic formulations situated between
. In order to characterize their parameterized complexity we devise parameter-preserving reductions, and we show that some minimum solution can be computed faster than by solving
in general. More explicitly, we introduce the
problem: In a hypergraph with red and blue vertices, edit the colors so that the red set becomes the union of some hyperedges. The case of degree 2 is equivalent to
: In a graph with red and blue edges, edit the colors so that the red set becomes the union of some stars, i.e., vertices with
their incident edges.