Several works have recently investigated the parameterized complexity of data completion problems,
motivated by their applications in machine learning, and clustering in particular. Interestingly, these
problems can be equivalently formulated as classical graph problems on induced subgraphs of powers
of partially-defined hypercubes.
In this paper, we follow up on this recent direction by investigating the Independent Set problem
on this graph class, which has been studied in the data science setting under the name Diversity.
We obtain a comprehensive picture of the problem’s parameterized complexity and establish its
fixed-parameter tractability w.r.t. the solution size plus the power of the hypercube.
Given that several such FO-definable problems have been shown to be fixed-parameter tractable
on the considered graph class, one may ask whether fixed-parameter tractability could be extended
to capture all FO-definable problems. We answer this question in the negative by showing that FO
model checking on induced subgraphs of hypercubes is as difficult as FO model checking on general
graphs.
CORE (COnnecting REpositories)
CORE (COnnecting REpositories)