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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 problem remains NP-complete even if a prime factorization of is provided. Serializability of database histories [3]: SR33 Set cover (also called "minimum cover" problem). This is equivalent, by transposing the incidence matrix, to the hitting set problem. [2] [3]: SP5, SP8 Set packing [2] [3]: SP3
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.
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
Set cover problem; Set packing; Set splitting problem; Set TSP problem; Shakashaka; Shared risk resource group; Shikaku; Shortest common supersequence; Single-machine scheduling; Skew-symmetric graph; Slitherlink; Slope number; Smallest grammar problem; Sokoban; Star coloring; Steiner tree problem; String graph; String-to-string correction ...
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 ...
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[15] In the set cover problem formed from a metric dimension problem, the elements to be covered are the () pairs of vertices to be distinguished, and the sets that can cover them are the sets of pairs that can be distinguished by a single chosen vertex. The approximation bound then follows by applying standard approximation algorithms for set ...