Computing Coverage Kernels Under Restricted Settings

We consider the Minimum Coverage Kernel problem: given a set \(\mathcal {B}\) of d-dimensional boxes, find a subset of \(\mathcal {B}\) of minimum size covering the same region as \(\mathcal {B}\). This problem is \(\mathsf {NP}\)-hard, but as for many \(\mathsf {NP}\)-hard problems on graphs, the problem becomes solvable in polynomial time under restrictions on the graph induced by \(\mathcal {B}\). We consider various classes of graphs, show that Minimum Coverage Kernel remains \(\mathsf {NP}\)-hard even for severely restricted instances, and provide two polynomial time approximation algorithms for this problem.

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