The Parameterized Complexity of the Rectangle Stabbing Problem and Its Variants
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Parameterized Complexity of Stabbing Rectangles and Squares in the Plane
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Fixed-Parameter algorithms for cochromatic number and disjoint rectangle stabbing
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Information and Computation
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In the weighted rectangle stabbing problem we are given a grid in $\mathbb{R}^2$ consisting of columns and rows each having a positive integral weight, and a set of closed axis-parallel rectangles each having a positive integral demand. The rectangles are placed arbitrarily in the grid with the only assumption being that each rectangle is intersected by at least one column or row. The objective is to find a minimum-weight (multi)set of columns and rows of the grid so that for each rectangle the total multiplicity of selected columns and rows stabbing it is at least its demand. A special case of this problem, called the interval stabbing problem, arises when each rectangle is intersected by exactly one row. We describe an algorithm called STAB, which is shown to be a constant-factor approximation algorithm for different variants of this stabbing problem.