Search results
Results from the WOW.Com Content Network
In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical capacities on its edges), and the goal is to construct a flow, numerical values on each edge that respect the capacity constraints and that have incoming flow equal to outgoing flow at all vertices except for certain designated terminals.
A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or ...
The "current-arc" data structure is a mechanism for visiting the in- and out-neighbors of a node in the flow network in a static circular order. If a singly linked list of neighbors is created for a node, the data structure can be as simple as a pointer into the list that steps through the list and rewinds to the head when it runs off the end.
The Ford–Fulkerson method or Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network.It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a residual graph is not fully specified [1] or it is specified in several implementations with different running times. [2]
Network problems that involve finding an optimal way of doing something are studied as combinatorial optimization.Examples include network flow, shortest path problem, transport problem, transshipment problem, location problem, matching problem, assignment problem, packing problem, routing problem, critical path analysis, and program evaluation and review technique.
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 a flow network.A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some capacity and cost associated.
The maximum flow problem can be seen as a special case of more complex 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 of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem .
A network flow problem typically involves a directed graph where each edge represents a pipe, wire, or road, and each edge has a capacity, which is the maximum amount that can flow through it. The goal is to find a feasible flow that maximizes the flow from a source node to a sink node.