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.

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, [options])

options: [directed, driving_side]

Returns set of (start_vid, end_vid, agg_cost)

OR EMPTY SET

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

• withPoints - Family of functions

• Cost Matrix - Category

• Traveling Sales Person - Family of functions

• Sample Data

Indices and tables

• Index

• Search Page