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 Queries

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

Result 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.