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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 ...
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 ...
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 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.
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.
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.
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 cover is said to be an open cover if each of its members is an open set. That is, each is contained in , where is the topology on X). [1] A simple way to get a subcover is to omit the sets contained in another set in the cover. Consider specifically open covers.