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).

images/boost-inside.jpeg

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

Indices and tables