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- The geometric set cover problem is the special case of the set cover problem in geometric settings. The input is a range space where is a universe of points in and is a family of subsets of called ranges, defined by the intersection of and geometric shapes such as disks and axis-parallel rectangles. The goal is to select a minimum-size subset of ranges such that every point in the universe is covered by some range in . Given the same range space , a closely related problem is the geometric hitting set problem, where the goal is to select a minimum-size subset of points such that every range of has nonempty intersection with , i.e., is hit by . In the one-dimensional case, where contains points on the real line and is defined by intervals, both the geometric set cover and hitting set problems can be solved in polynomial time using a simple greedy algorithm. However, in higher dimensions, they are known to be NP-complete even for simple shapes, i.e., when is induced by unit disks or unit squares. The discrete unit disc cover problem is a geometric version of the general set cover problem which is NP-hard. Many approximation algorithms have been devised for these problems. Due to the geometric nature, the approximation ratios for these problems can be much better than the general set cover/hitting set problems. Moreover, these approximate solutions can even be computed in near-linear time. (en)
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- 6025 (xsd:nonNegativeInteger)
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- The geometric set cover problem is the special case of the set cover problem in geometric settings. The input is a range space where is a universe of points in and is a family of subsets of called ranges, defined by the intersection of and geometric shapes such as disks and axis-parallel rectangles. The goal is to select a minimum-size subset of ranges such that every point in the universe is covered by some range in . (en)
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- Geometric set cover problem (en)
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