org.jgrapht.alg.shortestpath

Class AStarShortestPath<V,E>

java.lang.Object

org.jgrapht.alg.shortestpath.AStarShortestPath<V,E>

Type Parameters:

V - the graph vertex type

E - the graph edge type

All Implemented Interfaces:

ShortestPathAlgorithm<V,E>

public class AStarShortestPath<V,E>
extends Object

A* shortest path. An implementation of A* shortest path algorithm. This class works for directed and undirected graphs, as well as multi-graphs and mixed-graphs. The graph can also change between invocations of the getPath(Object, Object) method; no new instance of this class has to be created. The heuristic is implemented using a FibonacciHeap data structure to maintain the set of open nodes. However, there still exist several approaches in literature to improve the performance of this heuristic which one could consider to implement. Another issue to take into consideration is the following: given two candidate nodes, $i$, $j$ to expand, where $f(i)=f(j)$, $g(i)$ > $g(j)$, $h(i)$ < $g(j)$, $f(i)=g(i)+h(i)$, $g(i)$ is the actual distance from the source node to $i$, $h(i)$ is the estimated distance from $i$ to the target node. Usually a depth-first search is desired, so ideally we would expand node $i$ first. Using the FibonacciHeap, this is not necessarily the case though. This could be improved in a later version.

Note: This implementation works with both consistent and inconsistent admissible heuristics. For details on consistency, refer to the description of the method isConsistentHeuristic(AStarAdmissibleHeuristic). However, this class is not optimized for inconsistent heuristics. Several opportunities to improve both worst case and average runtime complexities for A* with inconsistent heuristics described in literature can be used to improve this implementation!

Since:

Aug, 2015

Author:

Joris Kinable, Jon Robison, Thomas Breitbart

Nested Class Summary

Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.ShortestPathAlgorithm

ShortestPathAlgorithm.SingleSourcePaths<V,E>

Field Summary

Fields

Modifier and Type	Field and Description
protected AStarAdmissibleHeuristic<V>	admissibleHeuristic
protected Map<V,E>	cameFrom
protected Set<V>	closedList
protected Comparator<Double>	comparator
protected Graph<V,E>	graph The underlying graph.
protected Map<V,Double>	gScoreMap
protected int	numberOfExpandedNodes
protected FibonacciHeap<V>	openList
protected Map<V,FibonacciHeapNode<V>>	vertexToHeapNodeMap

Constructor Summary

Constructors

Constructor and Description
AStarShortestPath(Graph<V,E> graph, AStarAdmissibleHeuristic<V> admissibleHeuristic) Create a new instance of the A* shortest path algorithm.

Method Summary

Modifier and Type	Method and Description
protected GraphPath<V,E>	createEmptyPath(V source, V sink) Create an empty path.
int	getNumberOfExpandedNodes() Returns how many nodes have been expanded in the A* search procedure in its last invocation.
GraphPath<V,E>	getPath(V sourceVertex, V targetVertex) Calculates (and returns) the shortest path from the sourceVertex to the targetVertex.
ShortestPathAlgorithm.SingleSourcePaths<V,E>	getPaths(V source) Compute all shortest paths starting from a single source vertex.
double	getPathWeight(V source, V sink) Get the weight of the shortest path from a source vertex to a sink vertex.
boolean	isConsistentHeuristic(AStarAdmissibleHeuristic<V> admissibleHeuristic) Returns true if the provided heuristic is a consistent or monotone heuristic wrt the graph provided at construction time.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

openList

protected FibonacciHeap<V> openList

vertexToHeapNodeMap

protected Map<V,FibonacciHeapNode<V>> vertexToHeapNodeMap

closedList

protected Set<V> closedList

gScoreMap

protected Map<V,Double> gScoreMap

cameFrom

protected Map<V,E> cameFrom

admissibleHeuristic

protected AStarAdmissibleHeuristic<V> admissibleHeuristic

numberOfExpandedNodes

protected int numberOfExpandedNodes

comparator

protected Comparator<Double> comparator

graph

protected final Graph<V,E> graph

The underlying graph.

Constructor Detail

AStarShortestPath

public AStarShortestPath(Graph<V,E> graph,
                         AStarAdmissibleHeuristic<V> admissibleHeuristic)

Create a new instance of the A* shortest path algorithm.

Parameters:

graph - the input graph

admissibleHeuristic - admissible heuristic which estimates the distance from a node to the target node. The heuristic must never overestimate the distance.

Method Detail

getPath

public GraphPath<V,E> getPath(V sourceVertex,
                              V targetVertex)

Calculates (and returns) the shortest path from the sourceVertex to the targetVertex. Note: each time you invoke this method, the path gets recomputed.

Parameters:

sourceVertex - source vertex

targetVertex - target vertex

Returns:

the shortest path from sourceVertex to targetVertex

getNumberOfExpandedNodes

public int getNumberOfExpandedNodes()

Returns how many nodes have been expanded in the A* search procedure in its last invocation. A node is expanded if it is removed from the open list.

Returns:

number of expanded nodes

isConsistentHeuristic

public boolean isConsistentHeuristic(AStarAdmissibleHeuristic<V> admissibleHeuristic)

Returns true if the provided heuristic is a consistent or monotone heuristic wrt the graph provided at construction time. A heuristic is monotonic if its estimate is always less than or equal to the estimated distance from any neighboring vertex to the goal, plus the step cost of reaching that neighbor. For details, refer to https://en.wikipedia.org/wiki/Consistent_heuristic. In short, a heuristic is consistent iff h(u)≤ d(u,v)+h(v), for every edge $(u,v)$, where $d(u,v)$ is the weight of edge $(u,v)$ and $h(u)$ is the estimated cost to reach the target node from vertex u. Most natural admissible heuristics, such as Manhattan or Euclidean distance, are consistent heuristics.

Parameters:

admissibleHeuristic - admissible heuristic

Returns:

true is the heuristic is consistent, false otherwise

getPaths

public ShortestPathAlgorithm.SingleSourcePaths<V,E> getPaths(V source)

Compute all shortest paths starting from a single source vertex.

Specified by:

getPaths in interface ShortestPathAlgorithm<V,E>

Parameters:

source - the source vertex

Returns:

the shortest paths

getPathWeight

public double getPathWeight(V source,
                            V sink)

Get the weight of the shortest path from a source vertex to a sink vertex. Returns Double.POSITIVE_INFINITY if no path exists.

Specified by:

getPathWeight in interface ShortestPathAlgorithm<V,E>

Parameters:

source - the source vertex

sink - the sink vertex

Returns:

the weight of the shortest path from a source vertex to a sink vertex, or Double.POSITIVE_INFINITY if no path exists

createEmptyPath

protected final GraphPath<V,E> createEmptyPath(V source,
                                               V sink)

Create an empty path. Returns null if the source vertex is different than the target vertex.

Parameters:

source - the source vertex

sink - the sink vertex

Returns:

an empty path or null null if the source vertex is different than the target vertex