pgRouting Manual (2.2)

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-inside2.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 symetric.
    • 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
  • Runing 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 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 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 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 edge’s SQL query

edges_sql:is a TEXT that containes an SQL query, which should return a set of rows with the following columns:
Column Type 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), if negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_cost ANY-NUMERICAL (optional) Weight of the edge (target, source), if 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 Description
edges_sql TEXT SQL query as decribed above.
start_vid BIGINT Identifier of the starting vertex of the path.
end_vid BIGINT Identifier of the ending vertex of the path.
start_vids array[ANY-INTEGER] Array of identifiers of starting vertices.
end_vids array[ANY-INTEGER] Array of identifiers of ending vertices.
directed BOOLEAN (optional). When false the graph is considered as Undirected. Default is true which considers the graph as Directed.

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.

Examples

Example 1:

Repeated values are ignored, and arrays are 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:

start_vids are 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)

The queries use the Sample Data network.

History

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