# pgr_maxFlow - Proposed¶

## Synopsis¶

pgr_maxFlow — Calculates the maximum flow in a directed graph from the source(s) to the targets(s) using the Push Relabel algorithm.

Availability: 2.4.0

Warning

Experimental functions

• They are not officially of the current release.
• They likely will not be officially be part of the next release:
• The functions might not make use of ANY-INTEGER and ANY-NUMERICAL
• Name might change.
• Signature might change.
• Functionality might change.
• pgTap tests might be missing.
• Might need c/c++ coding.
• May lack documentation.
• Documentation if any might need to be rewritten.
• Documentation examples might need to be automatically generated.
• Might need a lot of feedback from the comunity.
• Might depend on a proposed function of pgRouting
• Might depend on a deprecated function of pgRouting

Characteristics

• The graph is directed.
• When the maximum flow is 0 then there is no flow and 0 is returned.
• There is no flow when a source is the same as a target.
• Any duplicated value in the source(s) or target(s) are ignored.
• Uses the pgr_pushRelabel algorithm.
• Running time: $$O( V ^ 3)$$

## Signature Summary¶

pgr_maxFlow(edges_sql, source,  target)
pgr_maxFlow(edges_sql, sources,  target)
pgr_maxFlow(edges_sql, source,  targets)
pgr_maxFlow(edges_sql, sources,  targets)
RETURNS BIGINT


### One to One¶

Calculates the maximum flow from the source to the target.

pgr_maxFlow(edges_sql, source,  target)
RETURNS BIGINT

SELECT * FROM pgr_maxFlow(
'SELECT id,
source,
target,
capacity,
reverse_capacity
FROM edge_table'
, 6, 11
);
pgr_maxflow
-------------
230
(1 row)



### One to Many¶

Calculates the maximum flow from the source to all of the targets.

pgr_maxFlow(edges_sql, source,  targets)
RETURNS BIGINT

SELECT * FROM pgr_maxFlow(
'SELECT id,
source,
target,
capacity,
reverse_capacity
FROM edge_table'
, 6, ARRAY[11, 1, 13]
);
pgr_maxflow
-------------
340
(1 row)



### Many to One¶

Calculates the maximum flow from all the sources to the target.

pgr_maxFlow(edges_sql, sources,  target)
RETURNS BIGINT

SELECT * FROM pgr_maxFlow(
'SELECT id,
source,
target,
capacity,
reverse_capacity
FROM edge_table'
, ARRAY[6, 8, 12], 11
);
pgr_maxflow
-------------
230
(1 row)



### Many to Many¶

Calculates the maximum flow from all of the sources to all of the targets.

pgr_maxFlow(edges_sql, sources,  targets)
RETURNS BIGINT

SELECT * FROM pgr_maxFlow(
'SELECT id,
source,
target,
capacity,
reverse_capacity
FROM edge_table'
, ARRAY[6, 8, 12], ARRAY[1, 3, 11]
);
pgr_maxflow
-------------
360
(1 row)



## Description of the Signatures¶

### Description of the edges_sql query for Max-flow like functions¶

edges_sql: an SQL query, which should return a set of rows with the following columns:
Column Type Default Description
id ANY-INTEGER   Identifier of the edge.
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
capacity ANY-INTEGER

Weight of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_capacity ANY-INTEGER -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT

### Description of the Parameters of the Flow Signatures¶

Column Type Default Description
edges_sql TEXT   The edges SQL query as described above.
source BIGINT   Identifier of the starting vertex of the flow.
sources ARRAY[BIGINT]   Array of identifiers of the starting vertices of the flow.
target BIGINT   Identifier of the ending vertex of the flow.
targets ARRAY[BIGINT]   Array of identifiers of the ending vertices of the flow.

### Description of the return value¶

Type Description
BIGINT Maximum flow possible from the source(s) to the target(s)