Package org.jgrapht.alg.shortestpath
Class AStarShortestPath<V,E>
- java.lang.Object
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- org.jgrapht.alg.shortestpath.BaseShortestPathAlgorithm<V,E>
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- org.jgrapht.alg.shortestpath.AStarShortestPath<V,E>
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- Type Parameters:
V
- the graph vertex typeE
- the graph edge type
- All Implemented Interfaces:
ShortestPathAlgorithm<V,E>
public class AStarShortestPath<V,E> extends BaseShortestPathAlgorithm<V,E>
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 thegetPath(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
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Nested Class Summary
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Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.ShortestPathAlgorithm
ShortestPathAlgorithm.SingleSourcePaths<V,E>
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Field Summary
Fields Modifier and Type Field Description protected AStarAdmissibleHeuristic<V>
admissibleHeuristic
protected java.util.Map<V,E>
cameFrom
protected java.util.Set<V>
closedList
protected java.util.Comparator<java.lang.Double>
comparator
protected java.util.Map<V,java.lang.Double>
gScoreMap
protected int
numberOfExpandedNodes
protected FibonacciHeap<V>
openList
protected java.util.Map<V,FibonacciHeapNode<V>>
vertexToHeapNodeMap
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Fields inherited from class org.jgrapht.alg.shortestpath.BaseShortestPathAlgorithm
graph
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Constructor Summary
Constructors Constructor Description AStarShortestPath(Graph<V,E> graph, AStarAdmissibleHeuristic<V> admissibleHeuristic)
Create a new instance of the A* shortest path algorithm.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description private GraphPath<V,E>
buildGraphPath(V startVertex, V targetVertex, double pathLength)
Builds the graph pathprivate void
expandNode(FibonacciHeapNode<V> currentNode, V endVertex)
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.private void
initialize(AStarAdmissibleHeuristic<V> admissibleHeuristic)
Initializes the data structuresboolean
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 org.jgrapht.alg.shortestpath.BaseShortestPathAlgorithm
createEmptyPath, getPaths, getPathWeight
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Field Detail
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openList
protected FibonacciHeap<V> openList
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vertexToHeapNodeMap
protected java.util.Map<V,FibonacciHeapNode<V>> vertexToHeapNodeMap
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closedList
protected java.util.Set<V> closedList
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gScoreMap
protected java.util.Map<V,java.lang.Double> gScoreMap
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admissibleHeuristic
protected AStarAdmissibleHeuristic<V> admissibleHeuristic
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numberOfExpandedNodes
protected int numberOfExpandedNodes
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comparator
protected java.util.Comparator<java.lang.Double> comparator
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Constructor Detail
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AStarShortestPath
public AStarShortestPath(Graph<V,E> graph, AStarAdmissibleHeuristic<V> admissibleHeuristic)
Create a new instance of the A* shortest path algorithm.- Parameters:
graph
- the input graphadmissibleHeuristic
- admissible heuristic which estimates the distance from a node to the target node. The heuristic must never overestimate the distance.
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Method Detail
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initialize
private void initialize(AStarAdmissibleHeuristic<V> admissibleHeuristic)
Initializes the data structures- Parameters:
admissibleHeuristic
- admissible heuristic
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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 vertextargetVertex
- target vertex- Returns:
- the shortest path from sourceVertex to targetVertex
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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
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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 iffh(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
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expandNode
private void expandNode(FibonacciHeapNode<V> currentNode, V endVertex)
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buildGraphPath
private GraphPath<V,E> buildGraphPath(V startVertex, V targetVertex, double pathLength)
Builds the graph path- Parameters:
startVertex
- starting vertex of the pathtargetVertex
- ending vertex of the pathpathLength
- length of the path- Returns:
- the shortest path from startVertex to endVertex
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