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.
Complexity
- O(|E| + |V| ⋅ log(|E|)) when
are provided - O(|E| + |V|) otherwise
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)
}See Also
Developer's Guide
API
- findCycleEdges, findCycleEdgesDfs
Members
Constructors
Properties
Gets or sets a mapping for edge costs.
When specifying costs, the algorithm will try to minimize the total cost of edges that have to be removed or reversed to make the graph acyclic.
Costs must not be negative.
See Also
Developer's Guide
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 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: 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 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.
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: 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.
Parameters
- graph: IGraph
- The input graph to run the algorithm on.
Return Value
- 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.