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  2. Vertex cover - Wikipedia

    en.wikipedia.org/wiki/Vertex_cover

    The minimum vertex cover problem is the optimization problem of ... we find a maximal matching M with a greedy algorithm and construct a vertex cover C that consists ...

  3. Covering problems - Wikipedia

    en.wikipedia.org/wiki/Covering_problems

    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.

  4. Matching (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Matching_(graph_theory)

    Via this result, the minimum vertex cover, maximum independent set, and maximum vertex biclique problems may be solved in polynomial time for bipartite graphs. Hall's marriage theorem provides a characterization of bipartite graphs which have a perfect matching and the Tutte theorem provides a characterization for arbitrary graphs.

  5. Set cover problem - Wikipedia

    en.wikipedia.org/wiki/Set_cover_problem

    Trevisan (2001) proves that set cover instances with sets of size at most cannot be approximated to a factor better than ⁡ (⁡ ⁡) unless P = NP, thus making the approximation of ⁡ + of the greedy algorithm essentially tight in this case.

  6. Independent set (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Independent_set_(graph_theory)

    The optimization problem of finding such a set is called the maximum independent set problem. It is a strongly NP-hard problem. [3] As such, it is unlikely that there exists an efficient algorithm for finding a maximum independent set of a graph. Every maximum independent set also is maximal, but the converse implication does not necessarily hold.

  7. Maximal independent set - Wikipedia

    en.wikipedia.org/wiki/Maximal_independent_set

    That is, the complement is a vertex cover, a set of vertices that includes at least one endpoint of each edge, and is minimal in the sense that none of its vertices can be removed while preserving the property that it is a cover. Minimal vertex covers have been studied in statistical mechanics in connection with the hard-sphere lattice gas ...

  8. Maximum coverage problem - Wikipedia

    en.wikipedia.org/wiki/Maximum_coverage_problem

    The algorithm has several stages. First, find a solution using greedy algorithm. In each iteration of the greedy algorithm the tentative solution is added the set which contains the maximum residual weight of elements divided by the residual cost of these elements along with the residual cost of the set.

  9. Matching in hypergraphs - Wikipedia

    en.wikipedia.org/wiki/Matching_in_hypergraphs

    The vertex-cover number of a hypergraph H is the smallest size of a vertex cover in H. It is often denoted by τ(H), [1]: 466 for transversal. A fractional vertex-cover is a function assigning a weight to each vertex in V, such that for every hyperedge e in E, the sum of fractions of vertices in e is at least 1. A vertex cover is a special case ...