Graph Throughput Algorithm

Question

I have the task to calculate the maximum throughput in a graph.

The easiest way to describe the graph is as int[][]. The inner array is the nodes in graph and the outer array is the distance connecting each node in the graph, e.g.:

new int[][] {
    {0, 5, 0, 0}, // node 0 (the "source")
    {0, 0, 4, 0}, // node 1
    {0, 0, 0, 8}, // node 2
    {0, 0, 0, 0}  // node 3 (the "destination")
}

So to get from node 0 (the source) to node 3 (the destination the "maximum throughput" would be 4 per turn, because:

5 packets can go from node 0 to node 1
4 packets can go from node 1 to node 2
8 packets can go from node 2 to node 3

On a "per turn" basis, the bottleneck is between node 1 and node 2, where the maximum throughput capacity is 4.

Can someone point me to an algorithm that would solve this "maximum throughput" problem for any given graph defined in this way as int[][] and given source and destination nodes?

The example graph is to be extended with multiple "sources" and "destinations" where I will need to calculate the maximum throughput of the entire system on any given "turn".

I'd appreciate help in the form of algorithms to study or "pseudo-code".

I think that what you're describing is typically called maximum flow. There's probably plenty of easily searchable information when you have the name. — moreON, Jan 18 '17 at 01:38
if you're looking for one of the bottle necks, you can use minimum cut algorithm (which uses maximum flow and just searches for the first edges that are at capacity) — bigballer, Jan 18 '17 at 02:58
A typically good algorithm for maximum flow is Edmons-Karp. It's not terribly hard to implement. — Gene, Jan 18 '17 at 06:25
This is a homework question. A typical max-flow type questions. For OP even type of input is important. Voting to close. — Saeed Amiri, Jan 18 '17 at 08:02
I'm voting to close this question as off-topic because it is a homework question and OP didn't show any effort. — Saeed Amiri, Jan 18 '17 at 08:04

score 1 · Answer 1 · answered Sep 10 '17 at 04:21

Maximum flow problem is what you are looking for:

In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum.

Edmonds–Karp algorithm is a usual algorithm for finding the Maximum flow:

In computer science, the Edmonds–Karp algorithm is an implementation of the Ford–Fulkerson method for computing the maximum flow in a flow network in O(V E²) time.

As seen from the Pseudocode, it's not a complex algorithm when it comes to implementation. Here is a C++ implementation too.

Minimum cut can be combined with the Maximum flow problem, in order to find a bottleneck (there may be more than one):

The cut in a flow network that separates the source and sink vertices and minimizes the total weight on the edges that are directed from the source side of the cut to the sink side of the cut. As shown in the max-flow min-cut theorem, the weight of this cut equals the maximum amount of flow that can be sent from the source to the sink in the given network.

Minimum cut uses Maximum flow and looks for the first edges that are at capacity.

Graph Throughput Algorithm

1 Answers1