Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Worst-case-optimal algorithms for guarding planar graphs and polyhedral surfaces
Computational Geometry: Theory and Applications
Guarding a set of line segments in the plane
Theoretical Computer Science
Complexity and approximability issues in combinatorial image analysis
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Approximation algorithms for a geometric set cover problem
Discrete Applied Mathematics
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Consider any real structure that can be modeled by a set of straight line segments. This can be a network of streets in a city, tunnels in a mine, corridors in a building, pipes in a factory, etc. We want to approximate a minimal number of locations where to place "guards" (either men or machines), in a way that any point of the network can be "seen" by at least one guard. A guard can see all points on segments it is on (and nothing more). As the problem is known to be NP-hard, we consider three greedy-type algorithms for finding approximate solutions. We show that for each of these, theoretically the ratio of the approximate to the optimal solution can increase without bound with the increase of the number of segments. Nevertheless, our extensive experiments show that on randomly generated instances, the approximate solutions are always very close to the optimal ones and often are, in fact, optimal.