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:file: This file is part of the pgRouting project.
:copyright: Copyright (c) 2016-2026 pgRouting developers
:license: Creative Commons Attribution-Share Alike 3.0 https://creativecommons.org/licenses/by-sa/3.0
.. index::
single: Flow Family ; pgr_pushRelabel
single: pushRelabel
|
``pgr_pushRelabel``
===============================================================================
``pgr_pushRelabel`` — Calculates the flow on the graph edges that maximizes the
flow from the sources to the targets using Push Relabel Algorithm.
.. rubric:: Availability
.. rubric:: Version 4.0.0
* Combinations signature promoted to official.
.. rubric:: Version 3.2.0
* New proposed signature:
* pgr_pushRelabel(Combinations)
.. rubric:: Version 3.0.0
* Function promoted to official.
.. rubric:: Version 2.5.0
* Renamed from ``pgr_maxFlowPushRelabel``
* Function promoted to proposed.
.. rubric:: Version 2.3.0
* New experimental function.
Description
-------------------------------------------------------------------------------
.. include:: flow-family.rst
:start-after: characteristics_start
:end-before: characteristics_end
* Running time: :math:`O( V ^ 3)`
|Boost| Boost Graph Inside
Signatures
-------------------------------------------------------------------------------
.. rubric:: Summary
.. admonition:: \ \
:class: signatures
| pgr_pushRelabel(`Edges SQL`_, **start vid**, **end vid**)
| pgr_pushRelabel(`Edges SQL`_, **start vid**, **end vids**)
| pgr_pushRelabel(`Edges SQL`_, **start vids**, **end vid**)
| pgr_pushRelabel(`Edges SQL`_, **start vids**, **end vids**)
| pgr_pushRelabel(`Edges SQL`_, `Combinations SQL`_)
| Returns set of |result-flow|
| OR EMPTY SET
.. index::
single: pushRelabel ; One to One
One to One
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_pushRelabel(`Edges SQL`_, **start vid**, **end vid**)
| Returns set of |result-flow|
| OR EMPTY SET
:Example: From vertex :math:`11` to vertex :math:`12`
.. literalinclude:: pushRelabel.queries
:start-after: -- q1
:end-before: -- q2
.. index::
single: pushRelabel ; One to Many
One to Many
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_pushRelabel(`Edges SQL`_, **start vid**, **end vids**)
| Returns set of |result-flow|
| OR EMPTY SET
:Example: From vertex :math:`11` to vertices :math:`\{5, 10, 12\}`
.. literalinclude:: pushRelabel.queries
:start-after: -- q2
:end-before: -- q3
.. index::
single: pushRelabel ; Many to One
Many to One
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_pushRelabel(`Edges SQL`_, **start vids**, **end vid**)
| Returns set of |result-flow|
| OR EMPTY SET
:Example: From vertices :math:`\{11, 3, 17\}` to vertex :math:`12`
.. literalinclude:: pushRelabel.queries
:start-after: -- q3
:end-before: -- q4
.. index::
single: pushRelabel ; Many to Many
Many to Many
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_pushRelabel(`Edges SQL`_, **start vids**, **end vids**)
| Returns set of |result-flow|
| OR EMPTY SET
:Example: From vertices :math:`\{11, 3, 17\}` to vertices :math:`\{5, 10, 12\}`
.. literalinclude:: pushRelabel.queries
:start-after: -- q4
:end-before: -- q5
.. index::
single: pushRelabel ; Combinations
Combinations
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_pushRelabel(`Edges SQL`_, `Combinations SQL`_)
| Returns set of |result-flow|
| OR EMPTY SET
:Example: Using a combinations table, equivalent to calculating result from
vertices :math:`\{5, 6\}` to vertices :math:`\{10, 15, 14\}`.
The combinations table:
.. literalinclude:: pushRelabel.queries
:start-after: -- q5
:end-before: -- q51
The query:
.. literalinclude:: pushRelabel.queries
:start-after: -- q51
: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: flow_edges_sql_start
:end-before: flow_edges_sql_end
Combinations SQL
...............................................................................
.. include:: pgRouting-concepts.rst
:start-after: basic_combinations_sql_start
:end-before: basic_combinations_sql_end
Result columns
-------------------------------------------------------------------------------
.. include:: flow-family.rst
:start-after: result_flow_start
:end-before: result_flow_end
Additional Examples
-------------------------------------------------------------------------------
:Example: Manually assigned vertex combinations.
.. literalinclude:: pushRelabel.queries
:start-after: -- q6
:end-before: -- q7
See Also
-------------------------------------------------------------------------------
* :doc:`flow-family`
* :doc:`pgr_boykovKolmogorov`
* :doc:`pgr_edmondsKarp`
* `Boost: push relabel max flow
<https://www.boost.org/libs/graph/doc/push_relabel_max_flow.html>`__
* https://en.wikipedia.org/wiki/Push%E2%80%93relabel_maximum_flow_algorithm
.. rubric:: Indices and tables
* :ref:`genindex`
* :ref:`search`
|
