TL;DR
This paper establishes the computational complexity of the convex transversal problem, proving NP-hardness for stabbing disjoint bends and APX-hardness for line segments, highlighting the problem's difficulty in geometric optimization.
Contribution
It proves the NP-hardness and APX-hardness of convex transversal problems for disjoint bends and line segments, respectively, advancing understanding of their computational complexity.
Findings
Convex transversal for disjoint bends is NP-hard.
Optimization of convex stabbers for line segments is APX-hard.
Highlights the computational difficulty of geometric stabbing problems.
Abstract
In this paper, we prove the problem of stabbing a set of disjoint bends by a convex stabber to be NP-hard. We also consider the optimization version of the convex stabber problem and prove this problem to be APX-hard for sets of line segments.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Optimization and Packing Problems · Complexity and Algorithms in Graphs