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..
****************************************************************************
pgRouting Manual
Copyright(c) pgRouting Contributors
This documentation is licensed under a Creative Commons Attribution-Share
Alike 3.0 License: https://creativecommons.org/licenses/by-sa/3.0/
****************************************************************************
|
* **Supported versions:**
`Latest <https://docs.pgrouting.org/latest/en/pgr_dagShortestPath.html>`__
(`3.4 <https://docs.pgrouting.org/3.4/en/pgr_dagShortestPath.html>`__)
`3.3 <https://docs.pgrouting.org/3.3/en/pgr_dagShortestPath.html>`__
`3.2 <https://docs.pgrouting.org/3.2/en/pgr_dagShortestPath.html>`__
`3.1 <https://docs.pgrouting.org/3.1/en/pgr_dagShortestPath.html>`__
`3.0 <https://docs.pgrouting.org/3.0/en/pgr_dagShortestPath.html>`__
pgr_dagShortestPath - Experimental
===============================================================================
``pgr_dagShortestPath`` — Returns the shortest path(s) for weighted directed
acyclic graphs(DAG).
In particular, the DAG shortest paths algorithm implemented by Boost.Graph.
.. figure:: images/boost-inside.jpeg
:target: https://www.boost.org/libs/graph/doc/dag_shortest_paths.html
Boost Graph Inside
.. include:: experimental.rst
:start-after: begin-warn-expr
:end-before: end-warn-expr
.. rubric:: Availability
* Version 3.2.0
* New **experimental** function:
* pgr_dagShortestPath(Combinations)
* Version 3.0.0
* New **experimental** function
Description
-------------------------------------------------------------------------------
Shortest Path for Directed Acyclic Graph(DAG) is a graph search algorithm that
solves the shortest path problem for weighted directed acyclic graph, producing
a shortest path from a starting vertex (``start_vid``) to an ending vertex
(``end_vid``).
This implementation can only be used with a **directed** graph with no cycles
i.e. directed acyclic graph.
The algorithm relies on topological sorting the dag to impose a linear ordering
on the vertices, and thus is more efficient for DAG's than either the Dijkstra
or Bellman-Ford algorithm.
The main characteristics are:
- Process is valid for weighted directed acyclic graphs only. otherwise it
will throw warnings.
- Values are returned when there is a path.
- When the starting vertex and ending vertex are the same, there is no path.
- The `agg_cost` the non included values `(v, v)` is `0`
- When the starting vertex and ending vertex are the different and there is
no path:
- The `agg_cost` the non included values `(u, v)` is :math:`\infty`
- For optimization purposes, any duplicated value in the `start_vids` or
`end_vids` are ignored.
- The returned values are ordered:
- `start_vid` ascending
- `end_vid` ascending
* Running time: :math:`O(| start\_vids | * (V + E))`
Signatures
-------------------------------------------------------------------------------
.. rubric:: Summary
.. admonition:: \ \
:class: signatures
| pgr_dagShortestPath(`Edges SQL`_, **start vid**, **end vid**)
| pgr_dagShortestPath(`Edges SQL`_, **start vid**, **end vids**)
| pgr_dagShortestPath(`Edges SQL`_, **start vids**, **end vid**)
| pgr_dagShortestPath(`Edges SQL`_, **start vids**, **end vids**)
| pgr_dagShortestPath(`Edges SQL`_, `Combinations SQL`_)
| RETURNS SET OF |result-1-1|
| OR EMPTY SET
.. index::
single: dagShortestPath(One to One) - Experimental on v3.0
One to One
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_dagShortestPath(`Edges SQL`_, **start vid**, **end vid**)
| RETURNS SET OF |result-1-1|
| OR EMPTY SET
:Example: From vertex :math:`5` to vertex :math:`11` on a **directed** graph
.. literalinclude:: doc-pgr_dagShortestPath.queries
:start-after: -- q2
:end-before: -- q3
.. index::
single: dagShortestPath(One to Many) - Experimental on v3.0
One to Many
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_dagShortestPath(`Edges SQL`_, **start vid**, **end vids**)
| RETURNS SET OF |result-1-1|
| OR EMPTY SET
:Example: From vertex :math:`5` to vertices :math:`\{7, 11\}`
.. literalinclude:: doc-pgr_dagShortestPath.queries
:start-after: -- q3
:end-before: -- q4
.. index::
single: dagShortestPath(Many to One) - Experimental on v3.0
Many to One
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_dagShortestPath(`Edges SQL`_, **start vids**, **end vid**)
| RETURNS SET OF |result-1-1|
| OR EMPTY SET
:Example: From vertices :math:`\{5, 10\}` to vertex :math:`11`
.. literalinclude:: doc-pgr_dagShortestPath.queries
:start-after: -- q4
:end-before: -- q5
.. index::
single: dagShortestPath(Many to Many) - Experimental on v3.0
Many to Many
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_dagShortestPath(`Edges SQL`_, **start vids**, **end vids**)
| RETURNS SET OF |result-1-1|
| OR EMPTY SET
:Example: From vertices :math:`\{5, 15\}` to vertices :math:`\{11, 17\}` on an
**undirected** graph
.. literalinclude:: doc-pgr_dagShortestPath.queries
:start-after: -- q5
:end-before: -- q51
.. index::
single: dagShortestPath(Combinations) - Experimental on v3.2
Combinations
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_dagShortestPath(`Edges SQL`_, `Combinations SQL`_)
| RETURNS SET OF |result-1-1|
| OR EMPTY SET
:Example: Using a combinations table on an **undirected** graph
The combinations table:
.. literalinclude:: doc-pgr_dijkstraCost.queries
:start-after: -- q51
:end-before: -- q52
The query:
.. literalinclude:: doc-pgr_dagShortestPath.queries
:start-after: -- q52
:end-before: -- q6
Parameters
-------------------------------------------------------------------------------
.. include:: dijkstra-family.rst
:start-after: dijkstra_parameters_start
:end-before: dijkstra_parameters_end
Inner Queries
-------------------------------------------------------------------------------
Edges SQL
...............................................................................
.. include:: pgRouting-concepts.rst
:start-after: basic_edges_sql_start
:end-before: basic_edges_sql_end
Combinations SQL
...............................................................................
.. include:: pgRouting-concepts.rst
:start-after: basic_combinations_sql_start
:end-before: basic_combinations_sql_end
Resturn Columns
-------------------------------------------------------------------------------
.. include:: pgRouting-concepts.rst
:start-after: return_path_short_start
:end-before: return_path_short_end
Additional Examples
-------------------------------------------------------------------------------
:Example 1: Demonstration of repeated values are ignored, and result is sorted.
.. literalinclude:: doc-pgr_dagShortestPath.queries
:start-after: -- q6
:end-before: -- q7
:Example 2: Making **start_vids** the same as **end_vids**
.. literalinclude:: doc-pgr_dagShortestPath.queries
:start-after: -- q7
:end-before: -- q8
:Example 3: Manually assigned vertex combinations.
.. literalinclude:: doc-pgr_dagShortestPath.queries
:start-after: -- q8
:end-before: -- q9
See Also
-------------------------------------------------------------------------------
* :doc:`sampledata`
* https://en.wikipedia.org/wiki/Topological_sorting
.. rubric:: Indices and tables
* :ref:`genindex`
* :ref:`search`
|
