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  2. Matching (graph theory) - Wikipedia

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

    A maximum matching (also known as maximum-cardinality matching [2]) is a matching that contains the largest possible number of edges. There may be many maximum matchings. The matching number of a graph G is the size of a maximum matching. Every maximum matching is maximal, but not every maximal matching is a maximum matching.

  3. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Remains NP-complete for 3-sets. Solvable in polynomial time for 2-sets (this is a matching). [2] [3]: SP2 Finding the global minimum solution of a Hartree-Fock problem [37] Upward planarity testing [8] Hospitals-and-residents problem with couples; Knot genus [38]

  4. Gap penalty - Wikipedia

    en.wikipedia.org/wiki/Gap_penalty

    A Gap penalty is a method of scoring alignments of two or more sequences. When aligning sequences, introducing gaps in the sequences can allow an alignment algorithm to match more terms than a gap-less alignment can. However, minimizing gaps in an alignment is important to create a useful alignment.

  5. Stable roommates problem - Wikipedia

    en.wikipedia.org/wiki/Stable_roommates_problem

    In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separation of the set into disjoint pairs ("roommates

  6. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...

  7. NP-completeness - Wikipedia

    en.wikipedia.org/wiki/NP-completeness

    Nobody has yet been able to determine conclusively whether NP-complete problems are in fact solvable in polynomial time, making this one of the great unsolved problems of mathematics. The Clay Mathematics Institute is offering a US$1 million reward ( Millennium Prize ) to anyone who has a formal proof that P=NP or that P≠NP.

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  9. Vertex cover - Wikipedia

    en.wikipedia.org/wiki/Vertex_cover

    In the following figure, a maximal matching M is marked with red, and the vertex cover C is marked with blue. The set C constructed this way is a vertex cover: suppose that an edge e is not covered by C; then M ∪ {e} is a matching and e ∉ M, which is a contradiction with the assumption that M is maximal.

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