pgr_withPointsCostMatrix - proposed

pgr_withPointsCostMatrix - Calculates a cost matrix using pgr_withPoints - 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.

_images/boost-inside.jpeg

Boost Graph Inside

Availability

  • Version 2.2.0

    • New proposed function

Description

Using Dijkstra algorithm, calculate and return a cost matrix.

Dijkstra’s algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956. It is a graph search algorithm that solves the shortest path problem for a graph with non-negative edge path costs, producing a shortest path from a starting vertex to an ending vertex. This implementation can be used with a directed graph and an undirected graph.

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

Signatures

Summary

pgr_withPointsCostMatrix(Edges SQL, Points SQL, start vids
  [, directed] [, driving_side])
RETURNS SET OF (start_vid, end_vid, agg_cost)

Note

There is no details flag, unlike the other members of the withPoints family of functions.

Example:

Cost matrix for points \(\{1, 6\}\) and vertices \(\{10, 11\}\) on an undirected graph

  • Returning a symmetrical cost matrix

  • Using the default side value on the points_sql query

  • Using the default driving_side value

SELECT * FROM pgr_withPointsCostMatrix(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction from pointsOfInterest',
  array[-1, 10, 11, -6], directed := false);
 start_vid | end_vid | agg_cost
-----------+---------+----------
        -6 |      -1 |      1.3
        -6 |      10 |      1.7
        -6 |      11 |      1.3
        -1 |      -6 |      1.3
        -1 |      10 |      1.6
        -1 |      11 |      2.6
        10 |      -6 |      1.7
        10 |      -1 |      1.6
        10 |      11 |        1
        11 |      -6 |      1.3
        11 |      -1 |      2.6
        11 |      10 |        1
(12 rows)

Parameters

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.

With points optional parameters

Parameter

Type

Default

Description

driving_side

CHAR

b

Value in [r, l, b] indicating if the driving side is:

  • r for right driving side.

  • l for left driving side.

  • b for both.

Inner Queries

Edges SQL

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.

Note

When start_vid or end_vid columns have negative values, the identifier is for a Point.

Additional Examples

Use pgr_findCloseEdges in the Points SQL.

Find the matrix cost of the routes from vertex \(1\) and the two closest locations on the graph of point (2.9, 1.8).

SELECT * FROM pgr_withPointsCostMatrix(
  $e$ SELECT * FROM edges $e$,
  $p$ SELECT edge_id, round(fraction::numeric, 2) AS fraction, side
      FROM pgr_findCloseEdges(
        $$SELECT id, geom FROM edges$$,
        (SELECT ST_POINT(2.9, 1.8)),
        0.5, cap => 2)
  $p$,
  ARRAY[5, 10, -1, -2]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
        -2 |      -1 |      3.9
        -2 |       5 |      2.9
        -2 |      10 |      3.1
        -1 |      -2 |      0.3
        -1 |       5 |      3.2
        -1 |      10 |      3.2
         5 |      -2 |      2.9
         5 |      -1 |      6.8
         5 |      10 |        6
        10 |      -2 |      1.1
        10 |      -1 |      0.8
        10 |       5 |        2
(12 rows)

  • Point \(-1\) corresponds to the closest edge from point (2.9,1.8).

  • Point \(-2\) corresponds to the next close edge from point (2.9,1.8).

Use with pgr_TSP.

SELECT * FROM pgr_TSP(
  $$
  SELECT * FROM pgr_withPointsCostMatrix(
    'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
    'SELECT pid, edge_id, fraction from pointsOfInterest',
    array[-1, 10, 11, -6], directed := false);
  $$
);
NOTICE:  pgr_TSP no longer solving with simulated annaeling
HINT:  Ignoring annaeling parameters
 seq | node | cost | agg_cost
-----+------+------+----------
   1 |   -6 |    0 |        0
   2 |   -1 |  1.3 |      1.3
   3 |   10 |  1.6 |      2.9
   4 |   11 |    1 |      3.9
   5 |   -6 |  1.3 |      5.2
(5 rows)

See Also

Indices and tables