Solves a maximum flow problem.
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
// 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)))
}Type Details
- yfiles module
- view-layout-bridge
- yfiles-umd modules
- view-layout-bridge
- Legacy UMD name
- yfiles.analysis.MaximumFlow
See Also
Constructors
Creates a new MaximumFlow instance.
Parameters
A map of options to pass to the method.
- capacities - ItemMapping<IEdge,number>
A mapping for capacities of edges. This option sets the capacities property on the created object.
- sources - ItemCollection<INode>
A collection of source nodes. This option sets the sources property on the created object.
- sinks - ItemCollection<INode>
A collection of sink nodes. This option sets the sinks property on the created object.
- subgraphNodes - ItemCollection<INode>
The collection of nodes which define a subset of the graph for the algorithms to work on. This option sets the subgraphNodes property on the created object.
- subgraphEdges - ItemCollection<IEdge>
The collection of edges which define a subset of the graph for the algorithms to work on. This option sets the subgraphEdges property on the created object.
Properties
Gets or sets a mapping for capacities of edges.
Remarks
0x7FFFFFFF as an edge's capacity signifies an infinite capacity for that edge.Gets or sets a collection of sink nodes.
Gets or sets a collection of source nodes.
Gets or sets the collection of edges which define a subset of the graph for the algorithms to work on.
Remarks
If nothing is set, all edges of the graph will be processed.
If only the excludes are set all edges in the graph except those provided in the 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.
Examples
// prepare the maximum flow algorithm
const algorithm = new MaximumFlow({
sources,
sinks,
capacities,
// Ignore edges without target arrow heads
subgraphEdges: {
excludes: (edge) =>
edge.style instanceof PolylineEdgeStyle &&
edge.style.targetArrow === IArrow.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)))
}// 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 === IArrow.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)))
}Gets or sets the collection of nodes which define a subset of the graph for the algorithms to work on.
Remarks
If nothing is set, all nodes of the graph will be processed.
If only the excludes are set all nodes in the graph except those provided in the excludes are processed.
ItemCollection<T> instances may be shared among algorithm instances and will be (re-)evaluated upon (re-)execution of the algorithm.
Examples
// prepare the maximum flow algorithm
const algorithm = new MaximumFlow({
sources,
sinks,
capacities,
subgraphNodes: {
// only consider elliptical nodes in the graph
includes: (node) =>
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)))
}// 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
Solves a maximum flow problem.
Parameters
A map of options to pass to the method.
- graph - IGraph
- The input graph to run the algorithm on.
Returns
- ↪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.