2/24/40/30/50/1s12t Goldberg Tarjan Push Relabel Algorithm Technische Universität München
2/24/41/35/51/1s12t

The maximum s-t flow has a value of 6

The maximum flow problem

Suppose that we have a communication network, in which certain pairs of nodes are linked by connections; each connection has a limit to the rate at which data can be sent. Given two nodes on the network, what is the maximum rate at which one can send data to the other, assuming no other pair of nodes are attempting to communicate? (source)

This is a typical instance of a maximum flow problem: given an underlying network, where the edge weights denote the maximum possible capacity per edge, one wants to find out how much can be transerred over the edges from the source node s to the target node t.

This applet presents Goldberg Tarjan's Push Relabel algorithm with the FIFO selection rule which calculates the maximum s-t flow on a directed, weighted graph in O(|V|3). This is much faster than the older Edmonds-Karp or Dinic's algorithm, which are based on the Ford-Fulkerson method.

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