1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
|
: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_maxFlow
single: maxFlow
|
``pgr_maxFlow``
===============================================================================
``pgr_maxFlow`` — Calculates the maximum flow in a directed graph from the
source(s) to the targets(s) using the Push Relabel algorithm.
.. rubric:: Availability
.. rubric:: Version 4.0.0
* Combinations signature promoted to official.
.. rubric:: Version 3.2.0
* New proposed signature:
* pgr_maxFlow(Combinations)
.. rubric:: Version 3.0.0
* Function promoted to official.
.. rubric:: Version 2.4.0
* New proposed function.
Description
-------------------------------------------------------------------------------
**The main characteristics are:**
- The graph is **directed**.
- Calculates the maximum flow from the sources to the targets.
- When the maximum flow is **0** then there is no flow and **0** is returned.
- There is no flow when source has the same value as target.
- Any duplicated values in source or target are ignored.
- Uses the :doc:`pgr_pushRelabel <pgr_pushRelabel>` algorithm.
* Running time: :math:`O( V ^ 3)`
|Boost| Boost Graph Inside
Signatures
-------------------------------------------------------------------------------
.. rubric:: Summary
.. admonition:: \ \
:class: signatures
| pgr_maxFlow(`Edges SQL`_, **start vid**, **end vid**)
| pgr_maxFlow(`Edges SQL`_, **start vid**, **end vids**)
| pgr_maxFlow(`Edges SQL`_, **start vids**, **end vid**)
| pgr_maxFlow(`Edges SQL`_, **start vids**, **end vids**)
| pgr_maxFlow(`Edges SQL`_, `Combinations SQL`_)
| RETURNS ``BIGINT``
.. index::
single: maxFlow ; One to One
One to One
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_maxFlow(`Edges SQL`_, **start vid**, **end vid**)
| RETURNS ``BIGINT``
:Example: From vertex :math:`11` to vertex :math:`12`
.. literalinclude:: maxFlow.queries
:start-after: -- q1
:end-before: -- q2
.. index::
single: maxFlow ; One to Many
One to Many
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_maxFlow(`Edges SQL`_, **start vid**, **end vids**)
| RETURNS ``BIGINT``
:Example: From vertex :math:`11` to vertices :math:`\{5, 10, 12\}`
.. literalinclude:: maxFlow.queries
:start-after: -- q2
:end-before: -- q3
.. index::
single: maxFlow ; Many to One
Many to One
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_maxFlow(`Edges SQL`_, **start vids**, **end vid**)
| RETURNS ``BIGINT``
:Example: From vertices :math:`\{11, 3, 17\}` to vertex :math:`12`
.. literalinclude:: maxFlow.queries
:start-after: -- q3
:end-before: -- q4
.. index::
single: maxFlow ; Many to Many
Many to Many
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_maxFlow(`Edges SQL`_, **start vids**, **end vids**)
| RETURNS ``BIGINT``
:Example: From vertices :math:`\{11, 3, 17\}` to vertices :math:`\{5, 10, 12\}`
.. literalinclude:: maxFlow.queries
:start-after: -- q4
:end-before: -- q5
.. index::
single: maxFlow ; Combinations
Combinations
...............................................................................
.. admonition:: \ \
:class: signatures
| pgr_maxFlow(`Edges SQL`_, `Combinations SQL`_)
| RETURNS ``BIGINT``
:Example: Using a combinations table, equivalent to calculating result from
vertices :math:`\{5, 6\}` to vertices :math:`\{10, 15, 14\}`.
The combinations table:
.. literalinclude:: maxFlow.queries
:start-after: -- q5
:end-before: -- q51
The query:
.. literalinclude:: maxFlow.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
-------------------------------------------------------------------------------
====================== =================================================
Type Description
====================== =================================================
``BIGINT`` Maximum flow possible from the source(s) to the target(s)
====================== =================================================
Additional Examples
-------------------------------------------------------------------------------
:Example: Manually assigned vertex combinations.
.. literalinclude:: maxFlow.queries
:start-after: -- q6
:end-before: -- q7
See Also
-------------------------------------------------------------------------------
* :doc:`flow-family`
* :doc:`pgr_pushRelabel`
* `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`
|
