C

MaximumFlow

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Solves a maximum flow problem.
Inheritance Hierarchy

Remarks

The maximum flow problem is an optimization problem that involves finding the maximum flow from source to sink nodes through a network of edges, each with a specified maximum capacity.

The algorithm is an implementation of the preflow-push algorithm (also known as push-relabel algorithm) and is based on

  • Mehlhorn, Naeher: LEDA: a platform for combinatorial and geometric computing, Cambridge University Press, 2000, pp. 443–488.

Other Flow Algorithms

yFiles for HTML supports another algorithm related to network flow:

  • MinimumCostFlow – Solves a minimum-cost flow problem where a given flow should be routed as cheaply as possible through a graph

Examples

Calculating a maximum flow of the graph
// prepare the maximum flow algorithm
const algorithm = new MaximumFlow({
  sources,
  sinks,
  capacities,
})
// run the algorithm
const result = algorithm.run(graph)

// highlight the partitions and the cut edges
for (const node of result.sourcePartition) {
  graph.setStyle(node, sourcePartitionStyle)
}
for (const node of result.sinkPartition) {
  graph.setStyle(node, sinkPartitionStyle)
}
for (const edge of result.minimumCut) {
  graph.setStyle(edge, cutEdgeStyle)
}
// add labels indicating the actual flow
for (const edge of graph.edges) {
  graph.addLabel(edge, String(result.flow.get(edge)))
}

See Also

Developer's Guide

API

maximumFlow

Members

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Constructors

MaximumFlow

()

Parameters

Properties

capacities

: ItemMapping<IEdge, number>
Gets or sets a mapping for capacities of edges.
The capacity of an edge is the maximum possible flow over that edge. 0x7FFFFFFF as an edge's capacity signifies an infinite capacity for that edge.
conversionfinal

sinks

: ItemCollection<INode>
Gets or sets a collection of sink nodes.
The sink nodes must not be contained in the source node at the same time.
conversionfinal

See Also

Developer's Guide

sources

: ItemCollection<INode>
Gets or sets a collection of source nodes.
The source nodes must not be contained in the sink nodes at the same time.
conversionfinal

See Also

Developer's Guide

subgraphEdges

: ItemCollection<IEdge>
Gets or sets the collection of edges which define a subset of the graph for the algorithms to work on.

If nothing is set, all edges of the graph will be processed.

If only the ItemCollection<TItem>.excludes are set, all edges in the graph except those provided in the ItemCollection<TItem>.excludes are processed.

Note that edges which start or end at nodes which are not in the subgraphNodes are automatically not considered by the algorithm.

ItemCollection<T> instances may be shared among algorithm instances and will be (re-)evaluated upon (re-)execution of the algorithm.

The edges provided here must be part of the graph which is passed to the run method.
conversionfinal

Examples

Calculating a maximum flow of a subset of the graph
// prepare the maximum flow algorithm
const algorithm = new MaximumFlow({
  sources,
  sinks,
  capacities,
  // Ignore edges without target arrow heads
  subgraphEdges: {
    excludes: (edge: IEdge): boolean =>
      edge.style instanceof PolylineEdgeStyle &&
      edge.style.targetArrow instanceof Arrow &&
      edge.style.targetArrow.type === ArrowType.NONE,
  },
})
// run the algorithm
const result = algorithm.run(graph)

// highlight the partitions and the cut edges
for (const node of result.sourcePartition) {
  graph.setStyle(node, sourcePartitionStyle)
}
for (const node of result.sinkPartition) {
  graph.setStyle(node, sinkPartitionStyle)
}
for (const edge of result.minimumCut) {
  graph.setStyle(edge, cutEdgeStyle)
}
// add labels indicating the actual flow
for (const edge of graph.edges) {
  graph.addLabel(edge, String(result.flow.get(edge)))
}

subgraphNodes

: ItemCollection<INode>
Gets or sets the collection of nodes which define a subset of the graph for the algorithms to work on.

If nothing is set, all nodes of the graph will be processed.

If only the ItemCollection<TItem>.excludes are set, all nodes in the graph except those provided in the ItemCollection<TItem>.excludes are processed.

ItemCollection<T> instances may be shared among algorithm instances and will be (re-)evaluated upon (re-)execution of the algorithm.

The nodes provided here must be part of the graph which is passed to the run method.
conversionfinal

Examples

Calculating a maximum flow of a subset of the graph
// prepare the maximum flow algorithm
const algorithm = new MaximumFlow({
  sources,
  sinks,
  capacities,
  subgraphNodes: {
    // only consider elliptical nodes in the graph
    includes: (node: INode): boolean =>
      node.style instanceof ShapeNodeStyle &&
      node.style.shape === ShapeNodeShape.ELLIPSE,
    // but ignore the first node, regardless of its shape
    excludes: graph.nodes.first()!,
  },
})
// run the algorithm
const result = algorithm.run(graph)

// highlight the partitions and the cut edges
for (const node of result.sourcePartition) {
  graph.setStyle(node, sourcePartitionStyle)
}
for (const node of result.sinkPartition) {
  graph.setStyle(node, sinkPartitionStyle)
}
for (const edge of result.minimumCut) {
  graph.setStyle(edge, cutEdgeStyle)
}
// add labels indicating the actual flow
for (const edge of graph.edges) {
  graph.addLabel(edge, String(result.flow.get(edge)))
}

Methods

run

(graph: IGraph): MaximumFlowResult
Solves a maximum flow problem.
The result obtained from this algorithm is a snapshot which is no longer valid once the graph has changed, e.g. by adding or removing nodes or edges.
final

Parameters

graph: IGraph
The input graph to run the algorithm on.

Return Value

MaximumFlowResult
A MaximumFlowResult containing the computed flows as well as a cut between sources and sinks.

Throws

Exception ({ name: 'InvalidOperationError' })
If the algorithm can't create a valid result due to an invalid graph structure or wrongly configured properties.