Cost Matrix - Category

proposed

Warning

Proposed functions for next mayor release.

  • They are not officially in the current release.

  • They will likely officially be part of the next mayor release:

    • The functions make use of ANY-INTEGER and ANY-NUMERICAL

    • Name might not change. (But still can)

    • Signature might not change. (But still can)

    • Functionality might not change. (But still can)

    • pgTap tests have being done. But might need more.

    • Documentation might need refinement.

General Information

Synopsis

Traveling Sales Person - Family of functions needs as input a symmetric cost matrix and no edge (u, v) must value \(\infty\).

This collection of functions will return a cost matrix in form of a table.

Characteristics

The main Characteristics are:

  • Can be used as input to pgr_TSP.

    • Use directly when the resulting matrix is symmetric and there is no \(\infty\) value.

    • It will be the users responsibility to make the matrix symmetric.

      • By using geometric or harmonic average of the non symmetric values.

      • By using max or min the non symmetric values.

      • By setting the upper triangle to be the mirror image of the lower triangle.

      • By setting the lower triangle to be the mirror image of the upper triangle.

    • It is also the users responsibility to fix an \(\infty\) value.

  • Each function works as part of the family it belongs to.

  • It does not return a path.

  • Returns the sum of the costs of the shortest path for pair combination of nodes in the graph.

  • Process is done only on edges with positive costs.

  • Values are returned when there is a path.

    • When the starting vertex and ending vertex are the same, there is no path.

      • The aggregate cost in the non included values (v, v) is 0.

    • When the starting vertex and ending vertex are the different and there is no path.

      • The aggregate cost in the non included values (u, v) is \(\infty\).

  • Let be the case the values returned are stored in a table:

    • The unique index would be the pair: (start_vid, end_vid).

  • Depending on the function and its parameters, the results can be symmetric.

    • The aggregate cost of (u, v) is the same as for (v, u).

  • Any duplicated value in the start vids are ignored.

  • The returned values are ordered:

    • start_vid ascending

    • end_vid ascending

Parameters

Used in:

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

start vids

ARRAY[BIGINT]

Array of identifiers of starting vertices.

Used in:

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

Points SQL

TEXT

Points SQL as described below

start vids

ARRAY[BIGINT]

Array of identifiers of starting vertices.

Optional parameters

Column

Type

default

Description

directed

BOOLEAN

true

  • When true the graph is considered Directed

  • When false the graph is considered as Undirected.

Inner query

Edges SQL

Used in:

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.

cost

ANY-NUMERICAL

Weight of the edge (source, target)

reverse_cost

ANY-NUMERICAL

-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

ANY-NUMERICAL

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Points SQL

Parameter

Type

Default

Description

pid

ANY-INTEGER

value

Identifier of the point.

  • Use with positive value, as internally will be converted to negative value

  • If column is present, it can not be NULL.

  • If column is not present, a sequential negative value will be given automatically.

edge_id

ANY-INTEGER

Identifier of the “closest” edge to the point.

fraction

ANY-NUMERICAL

Value in <0,1> that indicates the relative postition from the first end point of the edge.

side

CHAR

b

Value in [b, r, l, NULL] indicating if the point is:

  • In the right r,

  • In the left l,

  • In both sides b, NULL

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Return Columns

Set of (start_vid, end_vid, agg_cost)

Column

Type

Description

start_vid

BIGINT

Identifier of the starting vertex.

end_vid

BIGINT

Identifier of the ending vertex.

agg_cost

FLOAT

Aggregate cost from start_vid to end_vid.

See Also

Indices and tables