The minimum constraint removal problem seeks to find the minimum number of
constraints, i.e., obstacles, that need to be removed to connect a start to a
goal location with a collision-free path. This problem is NP-hard and has been
studied in robotics, wireless sensing, and computational geometry. This work
contributes to the existing literature by presenting and discussing two
results. The first result shows that the minimum constraint removal is NP-hard
for simply connected obstacles where each obstacle intersects a constant number
of other obstacles. The second result demonstrates that for n simply
connected obstacles in the plane, instances of the minimum constraint removal
problem with minimum removable obstacles lower than (n+1)/3 can be solved in
polynomial time. This result is also empirically validated using several
instances of randomly sampled axis-parallel rectangles.Comment: Accepted for presentation at the 18th international conference on
Intelligent Autonomous System 202