Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-08-04 , DOI: 10.1016/j.tcs.2020.07.038 Satyabrata Jana; Supantha Pandit
We study a class of geometric covering and packing problems for bounded closed regions on the plane. We are given a set of axis-parallel line segments that induce a planar subdivision with bounded (rectilinear) faces. We are interested in the following problems.
- (P1) Stabbing-Subdivision:
Stab all closed bounded faces of the planar subdivision by selecting a minimum number of points in the plane.
- (P2) Independent-Subdivision:
Select a maximum size collection of pairwise non-intersecting closed bounded faces of the planar subdivision.
- (P3) Dominating-Subdivision:
Select a minimum size collection of bounded faces of the planar subdivision such that every other face of the subdivision that is not selected has a non-empty intersection (i.e., sharing an edge or a vertex) with some selected face.