Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Art gallery theorems and algorithms
Art gallery theorems and algorithms
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Hardness of Set Cover with Intersection 1
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Worst-case-optimal algorithms for guarding planar graphs and polyhedral surfaces
Computational Geometry: Theory and Applications
Experimental study on approximation algorithms for guarding sets of line segments
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
Guarding a set of line segments in the plane
Theoretical Computer Science
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Given a finite set of straight line segments S in R^2 and some k@?N, is there a subset V of points on segments in S with |V|@?k such that each segment of S contains at least one point in V? This is a special case of the set covering problem where the family of subsets given can be taken as a set of intersections of the straight line segments in S. Requiring that the given subsets can be interpreted geometrically this way is a major restriction on the input, yet we have shown that the problem is still strongly NP-complete [5]. In light of this result, we studied the accuracy of two polynomial-time approximation algorithms along with a third heuristic based algorithm which return segment coverings. We obtain certain theoretical results, and in particular we show that the performance ratio for each of these algorithms is unbounded, in general. Despite this, our experimental results suggest that the cases where this ratio exceeds 2 are rare for ''reasonable'' methods of placing segments. This is evidence that these polynomial-time algorithms solve the problem accurately in practice.