Blocking Flow
Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) time and is similar to the Edmonds–Karp algorithm, which runs in O(VE^2) time, in that it uses shortest augmenting paths. The introduction of the concepts of the ''level graph'' and ''blocking flow'' enable Dinic's algorithm to achieve its performance. History Yefim Dinitz invented this algorithm in response to a pre-class exercise in Adelson-Velsky's algorithms class. At the time he was not aware of the basic facts regarding the Ford–Fulkerson algorithm. Dinitz mentions inventing his algorithm in January 1969, which was published in 1970 in the journal ''Doklady Akademii Nauk SSSR''. In 1974, Shimon Even and (his then Ph.D. student) Alon Itai at the Technion in Haifa were very curious and intrigued by Dinitz's algorithm as well as A ...
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Strongly Polynomial
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed ...
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Hopcroft–Karp Algorithm
In computer science, the Hopcroft–Karp algorithm (sometimes more accurately called the Hopcroft–Karp–Karzanov algorithm) is an algorithm that takes a bipartite graph as input and produces a maximum cardinality matching as output – a set of as many edges as possible with the property that no two edges share an endpoint. It runs in O(, E, \sqrt) time in the worst case, where E is set of edges in the graph, V is set of vertices of the graph, and it is assumed that , E, =\Omega(, V, ). In the case of dense graphs the time bound becomes O(, V, ^), and for sparse random graphs it runs in time O(, E, \log , V, ) with high probability. The algorithm was discovered by and independently by . As in previous methods for matching such as the Hungarian algorithm and the work of , the Hopcroft–Karp algorithm repeatedly increases the size of a partial matching by finding ''augmenting paths''. These paths are sequences of edges of the graph, which alternate between edges in the matching ...
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Maximum Flow Problem
In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. 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. History The maximum flow problem was first formulated in 1954 by T. E. Harris and F. S. Ross as a simplified model of Soviet railway traffic flow. In 1955, Lester R. Ford, Jr. and Delbert R. Fulkerson created the first known algorithm, the Ford–Fulkerson algorithm.Ford, L.R., Jr.; Fulkerson, D.R., ''Flows in Networks'', Princeton University Press (1962). In their 1955 paper, Ford and Fulkerson wrote that the problem of Harris and Ross is formulated as follows (see p. 5):Consider a rail network conn ...
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Dinic Algorithm GL3
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...

Dinic Algorithm Gf3
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...

Dinic Algorithm G3
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...

Dinic Algorithm GL2
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...

Dinic Algorithm Gf2
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...

Dinic Algorithm G2
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...

Dinic Algorithm GL1
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...

Dinic Algorithm Gf1
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...

Dinic Algorithm G1
Dinic may refer to: *Dinić, a surname * Dinič, a surname *DiNic, a surname *Dinic's algorithm Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim (Chaim) A. Dinitz. The algorithm runs in O(V^2 E) ti ...