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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.
Pages in category "Covering problems" The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes. * Covering problems; A.
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 ...
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.
An exact cover problem involves the relation contains between subsets and elements. But an exact cover problem can be represented by any heterogeneous relation between a set of choices and a set of constraints. For example, an exact cover problem is equivalent to an exact hitting set problem, an incidence matrix, or a bipartite graph.
Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given:
The problem was posed by Henri Lebesgue in a letter to Gyula Pál in 1914. It was published in a paper by Pál in 1920 along with Pál's analysis. [1] He showed that a cover for all curves of constant width one is also a cover for all sets of diameter one and that a cover can be constructed by taking a regular hexagon with an inscribed circle of diameter one and removing two corners from the ...
The maximum coverage problem is a classical question in computer science, computational complexity theory, and operations research. It is a problem that is widely taught in approximation algorithms. As input you are given several sets and a number . The sets may have some elements in common.