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2. Maximum weight matching - Wikipedia

   en.wikipedia.org/wiki/Maximum_weight_matching

   In computer science and graph theory, the maximum weight matching problem is the problem of finding, in a weighted graph, a matching in which the sum of weights is maximized. A special case of it is the assignment problem , in which the input is restricted to be a bipartite graph , and the matching constrained to be have cardinality that of the ...

3. Matching (graph theory) - Wikipedia

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

   The following figure shows examples of maximal matchings (red) in three graphs. 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 ...

4. Blossom algorithm - Wikipedia

   en.wikipedia.org/wiki/Blossom_algorithm

   The matching problem can be generalized by assigning weights to edges in G and asking for a set M that produces a matching of maximum (minimum) total weight: this is the maximum weight matching problem. This problem can be solved by a combinatorial algorithm that uses the unweighted Edmonds's algorithm as a subroutine. [6]

5. Assignment problem - Wikipedia

   en.wikipedia.org/wiki/Assignment_problem

   The corresponding problem, of finding a matching in a weighted graph where the sum of weights is maximized, is called the maximum weight matching problem. Another generalization of the assignment problem is extending the number of sets to be matched from two to many.

6. Auction algorithm - Wikipedia

   en.wikipedia.org/wiki/Auction_algorithm

   The original form of the auction algorithm is an iterative method to find the optimal prices and an assignment that maximizes the net benefit in a bipartite graph, the maximum weight matching problem (MWM). [2] [3] This algorithm was first proposed by Dimitri Bertsekas in 1979.

7. Kőnig's theorem (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Kőnig's_theorem_(graph...

   An example of a bipartite graph, with a maximum matching (blue) and minimum vertex cover (red) both of size six. In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (), describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs.

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9. Secretary problem - Wikipedia

   en.wikipedia.org/wiki/Secretary_problem

   The objective is to find an assignment where the sum of qualifications is as big as possible. This problem is identical to finding a maximum-weight matching in an edge-weighted bipartite graph where the nodes of one side arrive online in random order. Thus, it is a special case of the online bipartite matching problem.