Geometric combinatorial optimization

I am interested in geometric combinatorial optimization, specially geometric Set Cover Problems (SCPs) or Hitting Set Problems (HSPs). Geometrically speaking, we want to pierce or stab a set of objects with the minimum number of points, or dually cover a set of points by a minimum number copy of a geometric shape.

Caption: Piercing a set of axis-parallel rectangles with red points (Minimum Set Cover). Getting an independent set of pairwise non-intersecting axis-parallel blue rectangles (Maximum Independent Set).
Dynamic geometric combinatorial optimization problems:

Those problems are NP-hard: For example, stabbing/piercing a set of isothetic boxes or finding maximum independent set of geometric graphs. A recent breakthrough was obtained by Joseph S. B. Mitchell here (2021). I am interested in Helly, Gallai, and Hadwiger numbers as well.

Interactive demo:
Mouse left-click + drag to input rectangles. Then click on pierce button

Related publications

Combinatorial optimization algorithms for radio network planning, Theor. Comput. Sci. 263(1-2): 235-245 (2001)
Fast stabbing of boxes in high dimensions, Theor. Comput. Sci. 246(1-2): 53-72 (2000)
On point covers of c-oriented polygons, Theor. Comput. Sci. 263(1-2): 17-29 (2001)
On the smallest enclosing information disk, Inf. Process. Lett. 105(3): 93-97 (2008)
Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry , GSI 2015: 586-594
Maintenance of a Piercing Set for Intervals with Applications, Algorithmica 36(1): 59-73 (2003)
Maintenance of a Percing Set for Intervals with Applications , ISAAC 2000: 552-563
On Piercing Sets of Objects, ACM Symposium on Computational Geometry, 1996: 113-121
Maintenance of a Piercing Set for Intervals with Applications, Algorithmica 36(1): 59-73 (2003)