Computing Coverage Kernels Under Restricted Settings

We consider the Minimum Coverage Kernel problem: given a set B of d-dimensional boxes, find a subset of B of minimum size covering the same region as B. This problem is NP -hard, but as for many NP -hard problems on graphs, the problem becomes solvable in polynomial time under restrictions on the graph induced by B. We consider various classes of graphs, show that Minimum Coverage Kernel remains NP -hard even for severely restricted instances, and provide two polynomial time approximation algorithms for this problem. © 2018, Springer International Publishing AG, part of Springer Nature.