Package org.jgrapht.alg.shortestpath

Class BellmanFordShortestPath<V,E>

java.lang.Object

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

Type Parameters:

V - the graph vertex type

E - the graph edge type

All Implemented Interfaces:

ShortestPathAlgorithm<V,E>

public class BellmanFordShortestPath<V,E>
extends Object

The Bellman-Ford algorithm.

Computes shortest paths from a single source vertex to all other vertices in a weighted graph. The Bellman-Ford algorithm supports negative edge weights.

Negative weight cycles are not allowed and will be reported by the algorithm. This implies that negative edge weights are not allowed in undirected graphs. In such cases the code will throw an exception of type NegativeCycleDetectedException which will contain the detected negative weight cycle. Note that the algorithm will not report or find negative weight cycles which are not reachable from the source vertex.

The running time is $O(|E||V|)$.

Author:

Dimitrios Michail

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	Description
protected Comparator<Double>	comparator
protected Graph<V,E>	graph	The underlying graph.
protected static String	GRAPH_CONTAINS_A_NEGATIVE_WEIGHT_CYCLE	Error message for reporting the existence of a negative-weight cycle.
protected static String	GRAPH_MUST_CONTAIN_THE_SINK_VERTEX	Error message for reporting that a sink vertex is missing.
protected static String	GRAPH_MUST_CONTAIN_THE_SOURCE_VERTEX	Error message for reporting that a source vertex is missing.
protected int	maxHops

Constructor Summary

Constructors

Constructor	Description
BellmanFordShortestPath(Graph<V,E> graph)	Construct a new instance.
BellmanFordShortestPath(Graph<V,E> graph, double epsilon)	Construct a new instance.
BellmanFordShortestPath(Graph<V,E> graph, double epsilon, int maxHops)	Construct a new instance.

Method Summary

Modifier and Type	Method	Description
protected GraphPath<V,E>	createEmptyPath(V source, V sink)	Create an empty path.
static <V,E> GraphPath<V,E>	findPathBetween(Graph<V,E> graph, V source, V sink)	Find a path between two vertices.
GraphPath<V,E>	getPath(V source, V sink)	Get a shortest path from a source vertex to a sink vertex.
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.

Methods inherited from class java.lang.Object

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

Field Detail

comparator

protected final Comparator<Double> comparator

maxHops

protected final int maxHops

GRAPH_CONTAINS_A_NEGATIVE_WEIGHT_CYCLE

protected static final String GRAPH_CONTAINS_A_NEGATIVE_WEIGHT_CYCLE

Error message for reporting the existence of a negative-weight cycle.

See Also:

Constant Field Values

GRAPH_MUST_CONTAIN_THE_SOURCE_VERTEX

protected static final String GRAPH_MUST_CONTAIN_THE_SOURCE_VERTEX

Error message for reporting that a source vertex is missing.

See Also:

Constant Field Values

GRAPH_MUST_CONTAIN_THE_SINK_VERTEX

protected static final String GRAPH_MUST_CONTAIN_THE_SINK_VERTEX

Error message for reporting that a sink vertex is missing.

See Also:

Constant Field Values

graph

protected final Graph<V,E> graph

The underlying graph.

Constructor Detail

BellmanFordShortestPath

public BellmanFordShortestPath(Graph<V,E> graph)

Construct a new instance.

Parameters:

graph - the input graph

BellmanFordShortestPath

public BellmanFordShortestPath(Graph<V,E> graph,
                               double epsilon)

Construct a new instance.

Parameters:

graph - the input graph

epsilon - tolerance when comparing floating point values

BellmanFordShortestPath

public BellmanFordShortestPath(Graph<V,E> graph,
                               double epsilon,
                               int maxHops)

Construct a new instance.

Parameters:

graph - the input graph

epsilon - tolerance when comparing floating point values

maxHops - execute the algorithm for at most this many iterations. If this is smaller than the number of vertices, then the negative cycle detection feature is disabled.

Throws:

IllegalArgumentException - if the number of maxHops is not positive

Method Detail

getPath

public GraphPath<V,E> getPath(V source,
                                    V sink)

Get a shortest path from a source vertex to a sink vertex.

Parameters:

source - the source vertex

sink - the target vertex

Returns:

a shortest path or null if no path exists

Throws:

NegativeCycleDetectedException - in case a negative weight cycle is detected

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

Throws:

NegativeCycleDetectedException - in case a negative weight cycle is detected

findPathBetween

public static <V,E> GraphPath<V,E> findPathBetween(Graph<V,E> graph,
                                                               V source,
                                                               V sink)

Find a path between two vertices.

Type Parameters:

V - the graph vertex type

E - the graph edge type

Parameters:

graph - the graph to be searched

source - the vertex at which the path should start

sink - the vertex at which the path should end

Returns:

a shortest path, or null if no path exists

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