pgRouting Manual (2.2)

pgr_johnson

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pgr_johnson

Synopsis

pgr_johnson - Returns the sum of the costs of the shortest path for each pair of nodes in the graph using Johnson’s algorithm.

../../../_images/boost-inside1.jpeg

Boost Graph Inside

The Johnson algorithm, is a good choice to calculate the sum of the costs of the shortest path for each pair of nodes in the graph, for sparse graphs. We make use of the Boost’s implementation which runs in \(O(V E \log V)\) time,

Signature

pgr_johnson(edges_sql, directed:=true)
     RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET

Example

pgr_johnson(
   'SELECT source, target, cost, reverse_cost FROM edge_table WHERE city_code = 304'
);

Characteristics:

The main Characteristics are:
  • It does not return a path.
  • Returns the sum of the costs of the shortest path for each pair of nodes in the graph.
  • Process is done only on edges with positive costs.
  • Boost returns a \(V \times V\) matrix, where the infinity values. Represent the distance between vertices for which there is no path.
    • We return only the non infinity values in form of a set of (start_vid, end_vid, agg_cost).
  • 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 the undirected graph, the results are symmetric.
    • The agg_cost of (u, v) is the same as for (v, u).
  • When start_vid = end_vid, the agg_cost = 0.

Description of the Signature

Description of the SQL query

edges_sql:is an SQL query, which should return a set of rows with the following columns:
Column Type Description
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

Receives (edges_sql, directed)

Parameter Type Description
edges_sql TEXT SQL query as described above.
directed BOOLEAN (optional) Default is true (is directed). When set to 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 Total cost from start_vid to end_vid.

Examples

Example 1:On a directed graph.
SELECT * FROM pgr_johnson(
    'SELECT source, target, cost FROM edge_table WHERE id < 5
         ORDER BY id'
);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         1 |       2 |        1
         1 |       5 |        2
         2 |       5 |        1
(3 rows)
Example 2:On an undirected graph.
SELECT * FROM pgr_johnson(
    'SELECT source, target, cost FROM edge_table WHERE id < 5
         ORDER BY id',
    false
);
 start_vid | end_vid | agg_cost 
-----------+---------+----------
         1 |       2 |        1
         1 |       5 |        2
         2 |       1 |        1
         2 |       5 |        1
         5 |       1 |        2
         5 |       2 |        1
(6 rows)

These queries uses the Sample Data network.

History

See Also

Indices and tables

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