pgr_floydWarshall¶

Synopsis¶

pgr_floydWarshall - Returns the sum of the costs of the shortest path for each pair of nodes in the graph using Floyd-Warshall algorithm.

Boost Graph Inside

The Floyd-Warshall algorithm, also known as Floyd’s 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 dense graphs. We make use of the Boost’s implementation which runs in \(\Theta(V^3)\) time,

Signature¶

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

Example¶

pgr_floydWarshall(
   '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.
Recomended, use a bounding box of no more than 3500 edges.

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_floydWarshall(
    'SELECT id, source, target, cost FROM edge_table where id < 5'
);
 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_floydWarshall(
    'SELECT id, source, target, cost FROM edge_table where id < 5',
    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

Re-design of pgr_apspWarshall in Version 2.2.0

pgRouting Manual (2.2)