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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]
If there are multiple maximum cliques, one of them may be chosen arbitrarily. [14] In the weighted maximum clique problem, the input is an undirected graph with weights on its vertices (or, less frequently, edges) and the output is a clique with maximum total weight. The maximum clique problem is the special case in which all weights are equal ...
Level 3: a node for each task. There is an arc from each agent i to each task j, with the corresponding cost, and capacity 1. Level 4: One sink-node t. There is an arc from each task to t, with cost 0 and capacity d j. An integral maximum flow of minimum cost can be found in polynomial time; see network flow problem.
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 ...
An arborescence of graph G is a directed tree of G which contains a directed path from a specified node L to each node of a subset V′ of V \{L}. Node L is called the root of arborescence. An arborescence is a spanning arborescence if V′ = V \{L}. MBST in this case is a spanning arborescence with the minimum bottleneck edge.
In this graph, the widest path from Maldon to Feering has bandwidth 29, and passes through Clacton, Tiptree, Harwich, and Blaxhall. In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight of the minimum-weight edge in the path.
Prim's algorithm starting at vertex A. In the third step, edges BD and AB both have weight 2, so BD is chosen arbitrarily. After that step, AB is no longer a candidate for addition to the tree because it links two nodes that are already in the tree.
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.