The Maximum Flow Problem
نویسندگان
چکیده
منابع مشابه
The maximum flow problem
In this network we have two special vertices: a source vertex s and a sink vertex t. Our goal is to send the maximum amount of flow from s to t; flow can only travel along arcs in the right direction, and is constrained by the arc capacities. This “flow” could be many things: imagine sending water along pipes, with the capacity representing the size of the pipe; or traffic, with the capacity be...
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Recently, Goldberg proposed a new approach lo the maximum netv.ork flow problem. The approach yields a ver>' simple algorithm nmning in 0{n^) time on n-vertex networks. Incorporation of the dynamic tree data structure of Sleator and Tarjan yields a more complicated algorithm with a running time of 0{rvn log {n^ Im)) on m-arc networks. Ahuja and Orlin developed a variant of Goldberg's algorithm ...
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An interesting application of Cmfp is for the case when the capacities of the arcs in the network are not fixed but can be increased at certain costs per unit (see e.g. [Ful59, KNR98, SK98]). One is allowed to spend a certain budget for raising capacities and wishes to maximize the throughput. This network improvement problem can be formulated as an instance of Cmfp where the cost functions on ...
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We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive constraints force that for certain pairs of arcs at least one arc has to carry flow in a feasible solutio...
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6.1 The Maximum Flow Problem In this section we define a flow network and setup the problem we are trying to solve in this lecture: the maximum flow problem. Definition 1 A network is a directed graph G = (V,E) with a source vertex s ∈ V and a sink vertex t ∈ V . Each edge = (v, w) from v to w has a defined capacity, denoted by u(e) or u(v, w). It is useful to also define capacity for any pair ...
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ژورنال
عنوان ژورنال: International Journal of Engineering Research and Technology
سال: 2020
ISSN: 0974-3154
DOI: 10.37624/ijert/13.7.2020.1534-1545