The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through...

network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity...

_{i=1}^{k}d_{i}} The minimum cost variant of the multi-commodity flow problem is a generalization of the minimum cost flow problem (in which there is merely...

minimum-cost flow problem, in which the edges have costs as well as capacities and the goal is to achieve a given amount of flow (or a maximum flow)...

equivalent in the single-terminal case to the maximum flow problem), and approximating the minimum-cost weighted perfect matching. Other practical applications...

minimum cost flow problem, each edge u , v {\displaystyle u,v} has a given cost k ( u , v ) {\displaystyle k(u,v)} , and the cost of sending the flow...

n. The assignment problem is a special case of the transportation problem, which is a special case of the minimum cost flow problem, which in turn is...

Minimum cost multi-commodity flow problem - As above, but minimize the cost. Minimum cost flow problem - As above, with 1 commodity. Maximum flow problem...

second path. The problem of finding two disjoint paths of minimum weight can be seen as a special case of a minimum cost flow problem, where in this case...

reformulation as an assignment problem. Moreover, the preflow-push algorithm for the linear minimum cost flow problem is mathematically equivalent to...

equal to its out-degree. This can be solved as an instance of the minimum-cost flow problem in which there is one unit of supply for every unit of excess...

algorithm. The algorithm is usually formulated in terms of a minimum-cost flow problem. The network simplex method works very well in practice, typically...

theorem. The theorem equates two quantities: the maximum flow through a network, and the minimum capacity of a cut of the network. To state the theorem...

computed by solving an instance of transportation problem, using any algorithm for minimum-cost flow problem, e.g. the network simplex algorithm. The Hungarian...

the minimum-cost flow problem in a flow network. It was published in 1961 by D. R. Fulkerson  and is described here. The analog of steady state flow in...

{\displaystyle A_{2}} at zero cost. To satisfy the demands s i {\displaystyle s_{i}} of all the vertices, solve a minimum cost flow problem in the graph ( V , A...

flow is a general class of optimization problems that includes as special cases the minimum-cost flow problem, matroid intersection, and the problem of...

the minimum-cost flow problem. Dinitz also stayed in touch with his classmate Aleksandr Karzanov, publishing a paper on the minimum-cost flow problem with...

instead formulated as a set partitioning problem which asks what is the collection of circuits with minimum cost that satisfy the VRP constraints. This...

optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such...

Augment the Flow: Find the minimum capacity along the shortest path. Increase the flow on the edges of the shortest path by this minimum capacity. Decrease...

planar directed flow graphs, the definition of reducibility does not require the graph to be planar. When the minimum feedback arc set problem is restricted...

financial accounting, free cash flow (FCF) or free cash flow to firm (FCFF) is the amount by which a business's operating cash flow exceeds its working capital...

movement of traffic and minimal traffic congestion problems. The foundation for modern traffic flow analysis dates back to the 1920s with Frank Knight's...

maximum flow and minimum cost flow problems yield a coefficient matrix with these properties (and with empty C). Thus, such network flow problems with bounded...

Finding a matching in a bipartite graph can be treated as a network flow problem. Given a graph G = (V, E), a matching M in G is a set of pairwise non-adjacent...

feasible elements), it is also the global minimum, but a nonconvex problem may have more than one local minimum not all of which need be global minima....

"Minimum-cost flow - Successive shortest path algorithm". Algorithms for Competitive Programming. Retrieved 14 May 2023. "Solving assignment problem using...

By the max-flow min-cut theorem, a minimum cut, and the optimal closure derived from it, can be found by solving a maximum flow problem. Alternative...

introduced minimum wage legislation by the end of the 20th century. Because minimum wages increase the cost of labor, companies often try to avoid minimum wage...