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) -- Experimental on v3.2
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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