- Type Parameters:
V
- the graph vertex typeE
- the graph edge type
- All Implemented Interfaces:
ShortestPathAlgorithm<V,
E>
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 PairingHeap data structure by default 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. Custom heap implementation
can be specified during the construction time. 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 PairingHeap, 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
AStarAdmissibleHeuristic.isConsistent(Graph)
. 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!
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Nested Class Summary
Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.ShortestPathAlgorithm
ShortestPathAlgorithm.SingleSourcePaths<V,
E> -
Field Summary
FieldsModifier and TypeFieldDescriptionprotected AStarAdmissibleHeuristic
<V> protected Comparator
<Double> protected int
Fields inherited from class org.jgrapht.alg.shortestpath.BaseShortestPathAlgorithm
graph, GRAPH_CONTAINS_A_NEGATIVE_WEIGHT_CYCLE, GRAPH_MUST_CONTAIN_THE_SINK_VERTEX, GRAPH_MUST_CONTAIN_THE_SOURCE_VERTEX
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Constructor Summary
ConstructorsConstructorDescriptionAStarShortestPath
(Graph<V, E> graph, AStarAdmissibleHeuristic<V> admissibleHeuristic) Create a new instance of the A* shortest path algorithm.AStarShortestPath
(Graph<V, E> graph, AStarAdmissibleHeuristic<V> admissibleHeuristic, Supplier<org.jheaps.AddressableHeap<Double, V>> heapSupplier) Create a new instance of the A* shortest path algorithm. -
Method Summary
Modifier and TypeMethodDescriptionbuildGraphPath
(V startVertex, V targetVertex, double pathLength) Builds the graph pathprivate void
expandNode
(org.jheaps.AddressableHeap.Handle<Double, V> currentNode, V endVertex) int
Returns how many nodes have been expanded in the A* search procedure in its last invocation.Calculates (and returns) the shortest path from the sourceVertex to the targetVertex.private void
initialize
(AStarAdmissibleHeuristic<V> admissibleHeuristic) Initializes the data structures.Methods inherited from class org.jgrapht.alg.shortestpath.BaseShortestPathAlgorithm
createEmptyPath, getPaths, getPathWeight
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Field Details
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heapSupplier
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openList
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vertexToHeapNodeMap
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closedList
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gScoreMap
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cameFrom
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admissibleHeuristic
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numberOfExpandedNodes
protected int numberOfExpandedNodes -
comparator
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Constructor Details
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AStarShortestPath
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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AStarShortestPath
public AStarShortestPath(Graph<V, E> graph, AStarAdmissibleHeuristic<V> admissibleHeuristic, Supplier<org.jheaps.AddressableHeap<Double, V>> heapSupplier) 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.heapSupplier
- supplier of the preferable heap implementation
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Method Details
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initialize
Initializes the data structures.- Parameters:
admissibleHeuristic
- admissible heuristic
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getPath
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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expandNode
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buildGraphPath
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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