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# single_pair_short_path(+Graph, +DistanceArg, +SourceNode, +SinkNode, +Tolerance, -Path)

Computes short paths from a source to a sink node
*Graph*
- a graph structure
*DistanceArg*
- which argument of EdgeData to use as distance: integer
*SourceNode*
- source node number (integer)
*SinkNode*
- sink node number (integer)
*Tolerance*
- tolerable deviation from minimal length (non-negative number)
*Path*
- Length-EdgeList structure

## Description

Computes shortest (or sufficiently short) paths from SourceNode to
SinkNode. Alternative paths are generated on backtracking.
Fails if there is no path at all.

DistanceArg refers to the graph's EdgeData information that was
specified when the graph was constructed. If EdgeData is a simple
number, then DistanceArg should be 0 and EdgeData will be taken
as the length of the edge. If EdgeData is a compound data structure,
DistanceArg should be a number between 1 and the arity of that
structure and determines which argument of the EdgeData structure
will be interpreted as the edge's length. Important: the distance
information in EdgeData must be a non-negative number.

If DistanceArg is given as -1, then any EdgeData is ignored and
the length of every edge is assumed to be equal to 1.

If Tolerance is given as zero, all paths returned will have the same
length and will be shortest paths from SourceNode to SinkNode.
If Tolerance is nonzero, additional paths will be returned with
lengths up to the length of the shortest path plus the tolerance.
Note that the solutions are not generated in any specific order.

A resulting path is returned as a Length-EdgeList structure where
Length is the length of the path and EdgeList is the path in
reverse order, i.e. starting with the edge reaching SinkNode and
ending with the edge starting from SourceNode.

### Modes and Determinism

- single_pair_short_path(+, +, +, +, +, -) is nondet

### Fail Conditions

There is no path from SourceNode to SinkNode
## Examples

?- sample_graph(G), single_pair_short_path(G, 0, 1, 3, P).
P = 2 - [e(2, 3, 1), e(1, 2, 1)]

## See Also

shortest_paths / 4, single_pair_shortest_path / 5, all_short_paths_as_edges / 6, all_short_paths_as_graph / 6, single_pair_all_short_paths_as_graph / 7, possible_path / 7