Finds edges of a given graph whose removal or reversal would make the graph acyclic (also called Feedback Arc Set).
Remarks
This minimization is performed heuristically, since it is a well known hard problem to come up with an optimal solution.
If costs are provided the algorithm tries to minimize the cost associated with the marked edges. Otherwise, a faster algorithm based on a depth-first search is used. This approach also provides more stable results when edges are added or removed over time.
Other Tree-Related Algorithms
yFiles for HTML supports a number of other algorithms and helpers related to trees:
- SpanningTree – calculates a (minimum) spanning tree for a graph
- TreeAnalysis – analyzes directed trees and provides access to tree properties, for example, the root node, the set of leaf nodes or the depth of a node.
Examples
// prepare the feedback set detection algorithm
const algorithm = new FeedbackEdgeSet()
// run the algorithm
const result = algorithm.run(graph)
// highlight the cycle
for (const edge of result.feedbackEdgeSet) {
graph.setStyle(edge, highlightFeedbackEdgeSetStyle)
}Type Details
- yfiles module
- view-layout-bridge
- yfiles-umd modules
- view-layout-bridge
- Legacy UMD name
- yfiles.analysis.FeedbackEdgeSet
See Also
Constructors
Creates a new FeedbackEdgeSet instance.
Parameters
A map of options to pass to the method.
- costs - ItemMapping<IEdge,number>
A mapping for edge costs. This option sets the costs 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 edge costs.
Remarks
When specifying costs the algorithm will try minimizing the total cost of edges that have to be removed or reversed to make the graph acyclic.
Costs must not be negative.
See Also
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 feedback set detection algorithm
const algorithm = new FeedbackEdgeSet({
// 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 cycle
for (const edge of result.feedbackEdgeSet) {
graph.setStyle(edge, highlightFeedbackEdgeSetStyle)
}// prepare the feedback set detection algorithm
const algorithm = new FeedbackEdgeSet({
// 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 cycle
for (const edge of result.feedbackEdgeSet) {
graph.setStyle(edge, highlightFeedbackEdgeSetStyle)
}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 feedback set detection algorithm
const algorithm = new FeedbackEdgeSet({
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 cycle
for (const edge of result.feedbackEdgeSet) {
graph.setStyle(edge, highlightFeedbackEdgeSetStyle)
}// prepare the feedback set detection algorithm
const algorithm = new FeedbackEdgeSet({
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 cycle
for (const edge of result.feedbackEdgeSet) {
graph.setStyle(edge, highlightFeedbackEdgeSetStyle)
}Methods
Finds the edges of a given graph whose removal or reversal would make the graph acyclic.
Complexity
O(|E| + |V| ⋅ log(|E|))
Parameters
A map of options to pass to the method.
- graph - IGraph
- The input graph to run the algorithm on.
Returns
- ↪FeedbackEdgeSetResult
- A FeedbackEdgeSetResult containing the edges whose removal or reversal would make the graph acyclic.
Throws
- Exception({ name: 'InvalidOperationError' })
- If the algorithm can't create a valid result due to an invalid graph structure or wrongly configured properties.