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In the fractional set cover problem, it is allowed to select fractions of sets, rather than entire sets. A fractional set cover is an assignment of a fraction (a number in [0,1]) to each set in , such that for each element x in the universe, the sum of fractions of sets that contain x is at least 1. The goal is to find a fractional set cover in ...
The most prominent examples of covering problems are the set cover problem, which is equivalent to the hitting set problem, and its special cases, the vertex cover problem and the edge cover problem. Covering problems allow the covering primitives to overlap; the process of covering something with non-overlapping primitives is called decomposition.
The maximum set packing need not cover every possible element. In the exact cover problem, every element of should be contained in exactly one of the subsets. Finding such an exact cover is an NP-complete problem, even in the special case in which the size of all sets is 3 (this special case is called exact 3 cover or X3C).
The discrete unit disc cover problem is a geometric version of the general set cover problem which is NP-hard. [2] 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.
Download as PDF; Printable version; ... Pages in category "Covering problems" The following 10 pages are in this category, out of 10 total. ... Set cover problem; V ...
A polygon covering problem is a special case of the set cover problem. In general, the problem of finding a smallest set covering is NP-complete, but for special classes of polygons, a smallest polygon covering can be found in polynomial time. A covering of a polygon P is a collection of maximal units, possibly overlapping, whose union equals P.
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The set cover problem is a well-known NP-hard problem – the decision version of set covering was one of Karp's 21 NP-complete problems. There exist a pair of polynomial-time L-reductions between the minimum dominating set problem and the set cover problem. [10]