# pgRouting Manual (3.3)

## pgr_maxFlowMinCost_Cost - Experimental

- Supported versions: Latest (3.3) 3.2 3.1 3.0

# pgr_maxFlowMinCost_Cost - Experimental

`pgr_maxFlowMinCost_Cost` — Calculates the minmum cost maximum flow in a directed graph from the source(s) to the targets(s).

Boost Graph Inside

Warning

Possible server crash

- These functions might create a server crash

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

Availability

- Version 3.2.0

  - New experimental function:

    - pgr_maxFlowMinCost_Cost(Combinations)

- Version 3.0.0

  - New experimental function

## Description

The main characteristics are:

- The graph is directed.

- The cost value of all input edges must be nonnegative.

- 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_maxFlowMinCost algorithm.

- Running time: \(O(U * (E + V * logV))\), where \(U\) is the value of the max flow. \(U\) is upper bound on number of iteration. In many real world cases number of iterations is much smaller than \(U\).

## Signatures

Summary

    pgr_maxFlowMinCost_Cost(Edges SQL, source, target)
    pgr_maxFlowMinCost_Cost(Edges SQL, sources, target)
    pgr_maxFlowMinCost_Cost(Edges SQL, source, targets)
    pgr_maxFlowMinCost_Cost(Edges SQL, sources, targets)
    pgr_maxFlowMinCost_Cost(Edges SQL, Combinations SQL)
    RETURNS FLOAT

### One to One

    pgr_maxFlowMinCost_Cost(Edges SQL, source, target)
    RETURNS FLOAT

Example

  From vertex \(2\) to vertex \(3\)

    SELECT * FROM pgr_MaxFlowMinCost_Cost(
        'SELECT id,
         source, target,
         capacity, reverse_capacity,
         cost, reverse_cost FROM edge_table',
        2, 3
    );
     pgr_maxflowmincost_cost
    -------------------------
                         400
    (1 row)

### One to Many

    pgr_maxFlowMinCost_Cost(Edges SQL, source, targets)
    RETURNS FLOAT

Example

  From vertex \(13\) to vertices \(\{7, 1, 4\}\)

    SELECT * FROM pgr_MaxFlowMinCost_Cost(
        'SELECT id,
         source, target,
         capacity, reverse_capacity,
         cost, reverse_cost FROM edge_table',
        13, ARRAY[7, 1, 4]
    );
     pgr_maxflowmincost_cost
    -------------------------
                         450
    (1 row)

### Many to One

    pgr_maxFlowMinCost_Cost(Edges SQL, sources, target)
    RETURNS FLOAT

Example

  From vertices \(\{1, 7, 14\}\) to vertex \(12\)

    SELECT * FROM pgr_MaxFlowMinCost_Cost(
        'SELECT id,
         source, target,
         capacity, reverse_capacity,
         cost, reverse_cost FROM edge_table',
        ARRAY[1, 7, 14], 12
    );
     pgr_maxflowmincost_cost
    -------------------------
                         650
    (1 row)

### Many to Many

    pgr_maxFlowMinCost_Cost(Edges SQL, sources, targets)
    RETURNS FLOAT

Example

  From vertices \(\{7, 13\}\) to vertices \(\{3, 9\}\)

    SELECT * FROM pgr_MaxFlowMinCost_Cost(
        'SELECT id,
         source, target,
         capacity, reverse_capacity,
         cost, reverse_cost FROM edge_table',
        ARRAY[7, 13], ARRAY[3, 9]
    );
     pgr_maxflowmincost_cost
    -------------------------
                         600
    (1 row)

### Combinations

    pgr_maxFlowMinCost_Cost(Edges SQL, Combinations SQL)
    RETURNS FLOAT

Example

  Using a combinations table, equivalent to calculating result from vertices \(\{7, 13\}\) to vertices \(\{3, 9\}\).

    SELECT * FROM pgr_MaxFlowMinCost_Cost(
        'SELECT id,
         source, target,
         capacity, reverse_capacity,
         cost, reverse_cost FROM edge_table',
        'SELECT * FROM ( VALUES (7, 3), (13, 9) ) AS t(source, target)'
    );
     pgr_maxflowmincost_cost
    -------------------------
                         600
    (1 row)

## Parameters

Column | Type | Default | Description
--- | --- | --- | ---
Edges SQL | `TEXT` |  | Edges query as described in Inner Queries.
Combinations SQL | `TEXT` |  | Combinations query as described in Inner Queries.
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.

## Inner queries

Edges SQL

  an SQL query of a directed graph of capacities, 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`

Capacity 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

Capacity of the edge (target, source),

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

cost | `ANY-NUMERICAL` |  | Weight of the edge (source, target) if it exists.
reverse_cost | `ANY-NUMERICAL` | 0 | Weight of the edge (target, source) if it exists.

Where:

ANY-INTEGER

  SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL

  smallint, int, bigint, real, float

Combinations SQL

  an SQL query which should return a set of rows with the following columns:

Column | Type | Default | Description
--- | --- | --- | ---
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.

Where:

ANY-INTEGER

  SMALLINT, INTEGER, BIGINT

The function aggregates the sources and the targets, removes the duplicates, and then it calculates the result from the resultant source vertices to the target vertices.

## Result Columns

Type | Description
--- | ---
`FLOAT` | Minimum Cost Maximum Flow possible from the source(s) to the target(s)

## See Also

- Flow - Family of functions

- https://www.boost.org/libs/graph/doc/successive_shortest_path_nonnegative_weights.html

Indices and tables

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