C

ShortestPath

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Finds the shortest path between two nodes (also known as the single-source single-sink shortest path problem).
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Remarks

The shortest path will be determined either by Dijkstra's algorithm, or an implementation of A*, depending on whether a heuristic exists for estimating the remaining distance between a node and the sink node.

Other Shortest Path Algorithms

yFiles for HTML supports a number of other algorithms that compute shortest paths in a graph:

Other Path-Related Algorithms

yFiles for HTML also supports a number of other algorithms related to paths in a graph:

  • Paths – finds all paths between a set of source and a set of target nodes
  • Chains – finds all chains, that is, sequences of nodes that are each connected with just an edge without branches
  • Cycle – finds a cycle if one exists
  • LongestPath – finds the longest path in the graph

Examples

Highligthing the shortest path edges between a start and an end node
// configure the shortest path algorithm
const algorithm = new ShortestPath({
  // single source - single sink
  source: startNode,
  sink: endNode,
  // add edge cost mapping which returns the actual length of the edge
  costs: (edge) =>
    edge.style.renderer
      .getPathGeometry(edge, edge.style)
      .getPath()!
      .getLength(),
})
// run the algorithm
const result = algorithm.run(graph)
// highlight the edge path
for (const edge of result.edges) {
  graph.setStyle(edge, highlightPathStyle)
}

See Also

Developer's Guide

API

shortestPath

Members

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Constructors

ShortestPath

()

Parameters

Properties

costs

: ItemMapping<IEdge, number>
Gets or sets a mapping for the cost for traversing an edge.

For the shortest path algorithm, this is a measure of the edge's length, so more expensive (higher cost) edges are considered longer and avoided if there's a shorter (cheaper) path elsewhere in the graph.

The costs must not be negative.

When no costs are provided, uniform costs of 1 are assumed for all edges. This makes the shortest path the path with the fewest edges.

conversionfinal

Examples

Mapping a value to some edges
// setting the cost for traversing e1 and e2 to 1.0
algorithm.costs.mapper.set(e1, 1.0)
algorithm.costs.mapper.set(e2, 1.0)
// all other edges are not set and return 0
Using a delegate to determine the cost
// returns the length of the actual edge path as cost
algorithm.costs = (edge) =>
  edge.style.renderer
    .getPathGeometry(edge, edge.style)
    .getPath()!
    .getLength()

directed

: boolean
Gets or sets a value indicating whether edge direction should be considered.
Default is true.
final

Property Value

true if the graph should be considered as directed, false otherwise.

heuristic

: function(INode, INode): number
Gets or sets a function that estimates the distance between two nodes.

This can be used to speed up the shortest path search by internally switching to an A* implementation which can skip large parts of the graph that would lead further away from the target node.

A heuristic must be admissible, that is, it must never overestimate the remaining distance to the target. Otherwise the found path may not be the shortest one.

The heuristic ties closely into the costs, as both should use the same, or similar measures. For example, if the costs are defined by the actual visual length of an edge, the heuristic can be Euclidean distance between the two nodes because that's a useful estimate of the remaining distance when the costs are defined that way.

Don't use a heuristic if there is no useful and quick way of estimating the remaining distance.

The second node passed to the function is always the sink node as the remaining distance is only ever estimated towards the sink node.

final

sink

: ItemCollection<INode>
Gets or sets the sink (end, target) node of the path.
If multiple nodes are provided, the first valid sink node is used.
conversionfinal

Examples

// the item is the explicitly set item (the end node)
algorithm = new ShortestPath({
  sink: endNode,
})

// the item is the first item in the source (the first selected node)
algorithm = new ShortestPath({
  sink: graphComponent.selection.nodes,
})

// the item is the first in the graph for which the predicate returns true
// (the first node in the graph with "sink" as tag)
algorithm = new ShortestPath({
  sink: (node) => node.tag === 'sink',
})

source

: ItemCollection<INode>
Gets or sets the source (start) node of the path.
If multiple nodes are provided, the first valid source node is used.
conversionfinal

Examples

// the item is the explicitly set item (the start node)
algorithm = new ShortestPath({
  source: startNode,
})

// the item is the first item in the source (the first selected node)
algorithm = new ShortestPath({
  source: graphComponent.selection.nodes,
})

// the item is the first in the graph for which the predicate returns true
// (the first node in the graph with "source" as tag)
algorithm = new ShortestPath({
  source: (node) => node.tag === 'source',
})

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 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.

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

Examples

Calculating shortest paths on a subset of the graph
// configure the shortest path algorithm
const algorithm = new ShortestPath({
  // single source - single sink
  source: startNode,
  sink: endNode,
  // 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 edge path
for (const edge of result.edges) {
  graph.setStyle(edge, highlightPathStyle)
}

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 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.

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

Examples

Calculating shortest paths on a subset of the graph
// configure the shortest path algorithm
const algorithm = new ShortestPath({
  // single source - single sink
  source: startNode,
  sink: endNode,
  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 edge path
for (const edge of result.edges) {
  graph.setStyle(edge, highlightPathStyle)
}
Considering only selected nodes
algorithm.subgraphNodes = graphComponent.selection.nodes
Ignoring all group nodes
algorithm.subgraphNodes.excludes = (n) => graph.isGroupNode(n)
Considering selected nodes but ignoring group nodes
algorithm.subgraphNodes = graphComponent.selection.nodes
algorithm.subgraphNodes.excludes = (n) => graph.isGroupNode(n)

Methods

run

(graph: IGraph): ShortestPathResult
Finds the shortest path between source and sink.
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

ShortestPathResult
A ShortestPathResult containing the shortest path between source and sink if one exists.

Throws

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

Examples

Highlighting the shortest path edges between a start and an end node
// configure the shortest path algorithm
const algorithm = new ShortestPath({
  // single source - single sink
  source: startNode,
  sink: endNode,
  // add edge cost mapping which returns the actual length of the edge
  costs: (edge) =>
    edge.style.renderer
      .getPathGeometry(edge, edge.style)
      .getPath()!
      .getLength(),
})
// run the algorithm
const result = algorithm.run(graph)
// highlight the edge path
for (const edge of result.edges) {
  graph.setStyle(edge, highlightPathStyle)
}