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.

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

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 edge’s SQL query¶

Where:

Description of the parameters of the signatures¶

Description of the return values¶

Returns set of (start_vid, end_vid, agg_cost)

See Also¶

• http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

Indices and tables

• Index
• Search Page