pgRouting Manual (2.3)

pgr_dijkstraCost

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pgr_dijkstraCost

Synopsis

pgr_dijkstraCost

Using Dijkstra algorithm implemented by Boost.Graph, and extract only the aggregate cost of the shortest path(s) found, for the combination of vertices given.

../../../_images/boost-inside5.jpeg

Boost Graph Inside

The pgr_dijkstraCost algorithm, is a good choice to calculate the sum of the costs of the shortest path for a subset of pairs of nodes of the graph. We make use of the Boost’s implementation of dijkstra which runs in \(O(V \log V + E)\) time.

Characteristics

The main Characteristics are:
  • 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.
    • The returned values are in the form of a set of (start_vid, end_vid, agg_cost).
    • When the starting vertex and ending vertex are the same, there is no path.
      • The agg_cost int the non included values (v, v) is 0
    • When the starting vertex and ending vertex are the different and there is no path.
      • The agg_cost in the non included values (u, v) is \(\infty\)
  • Let be the case the values returned are stored in a table, so the unique index would be the pair: (start_vid, end_vid).
  • For undirected graphs, the results are symmetric.
    • The agg_cost of (u, v) is the same as for (v, u).
  • Any duplicated value in the start_vids or end_vids is ignored.
  • The returned values are ordered:
    • start_vid ascending
    • end_vid ascending
  • Running time: \(O(| start\_vids | * (V \log V + E))\)

Signature Summary

pgr_dijkstraCost(edges_sql, start_vid, end_vid);
pgr_dijkstraCost(edges_sql, start_vid, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vid, end_vids, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vids, directed);

    RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET

Signatures

Minimal signature

The minimal signature is for a directed graph from one start_vid to one end_vid:

pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
    RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET

Example

SELECT * FROM pgr_dijkstraCost(
    'select id, source, target, cost, reverse_cost from edge_table',
    2, 3);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         2 |       3 |        5
(1 row)

pgr_dijkstraCost One to One

This signature performs a Dijkstra from one start_vid to one end_vid:
  • on a directed graph when directed flag is missing or is set to true.
  • on an undirected graph when directed flag is set to false.
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
                     BOOLEAN directed:=true);
    RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Example:
SELECT * FROM pgr_dijkstraCost(
    'select id, source, target, cost, reverse_cost from edge_table',
    2, 3, false);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         2 |       3 |        1
(1 row)

pgr_dijkstraCost One to Many

pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, array[ANY_INTEGER] end_vids,
        BOOLEAN directed:=true);
    RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
This signature performs a Dijkstra from one start_vid to each end_vid in end_vids:
  • on a directed graph when directed flag is missing or is set to true.
  • on an undirected graph when directed flag is set to false.
Example:
SELECT * FROM pgr_dijkstraCost(
    'select id, source, target, cost, reverse_cost from edge_table',
    2, ARRAY[3, 11]);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         2 |       3 |        5
         2 |      11 |        3
(2 rows)

pgr_dijkstraCost Many to One

pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, BIGINT end_vid,
                     BOOLEAN directed:=true);
    RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
This signature performs a Dijkstra from each start_vid in start_vids to one end_vid:
  • on a directed graph when directed flag is missing or is set to true.
  • on an undirected graph when directed flag is set to false.
Example:
SELECT * FROM pgr_dijkstraCost(
    'select id, source, target, cost, reverse_cost from edge_table',
    ARRAY[2, 7], 3);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         2 |       3 |        5
         7 |       3 |        6
(2 rows)

pgr_dijkstraCost Many to Many

pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, array[ANY_INTEGER] end_vids,
        BOOLEAN directed:=true);
    RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
This signature performs a Dijkstra from each start_vid in start_vids to each end_vid in end_vids:
  • on a directed graph when directed flag is missing or is set to true.
  • on an undirected graph when directed flag is set to false.
Example:
SELECT * FROM pgr_dijkstraCost(
    'select id, source, target, cost, reverse_cost from edge_table',
    ARRAY[2, 7], ARRAY[3, 11]);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         2 |       3 |        5
         2 |      11 |        3
         7 |       3 |        6
         7 |      11 |        4
(4 rows)

Description of the Signatures

Description of the edges_sql query

edges_sql:an SQL query, 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.
cost ANY-NUMERICAL  
Weight of the edge (source, target)
  • When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
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

Description of the parameters of the signatures

Column Type Default Description
sql TEXT   SQL query as described above.
start_vid BIGINT   Identifier of the starting vertex of the path.
start_vids ARRAY[BIGINT]   Array of identifiers of starting vertices.
end_vid BIGINT   Identifier of the ending vertex of the path.
end_vids ARRAY[BIGINT]   Array of identifiers of ending vertices.
directed BOOLEAN true
  • When true Graph is considered Directed
  • When false the graph is considered as Undirected.

Description of the return values

Returns 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 of the shortest path from start_vid to end_vid.

Additional Examples

Example 1:Demonstration of repeated values are ignored, and result is sorted.
SELECT * FROM pgr_dijkstraCost(
        'select id, source, target, cost, reverse_cost from edge_table',
            ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         3 |       4 |        3
         3 |       5 |        2
         4 |       3 |        1
         4 |       5 |        3
         5 |       3 |        4
         5 |       4 |        3
(6 rows)
Example 2:Making start_vids the same as end_vids
SELECT * FROM pgr_dijkstraCost(
        'select id, source, target, cost, reverse_cost from edge_table',
            ARRAY[5, 3, 4], ARRAY[5, 3, 4]);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         3 |       4 |        3
         3 |       5 |        2
         4 |       3 |        1
         4 |       5 |        3
         5 |       3 |        4
         5 |       4 |        3
(6 rows)

History

  • New in version 2.2.0

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