pgr_johnson
¶
pgr_johnson
- Returns the sum of the costs of the shortest path for each
pair of nodes in the graph using Floyd-Warshall algorithm.
Availability
- Version 2.2.0
- Signature change
- Old signature no longer supported
- Version 2.0.0
- Official function
Description¶
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. It usees the Boost’s implementation which runs in \(O(V E \log V)\) time,
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.
- Recommended, use a bounding box of no more than 3500 edges.
Signatures¶
Summary
pgr johnson(Edges SQL [, directed]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
Example: | For a directed subgraph with edges \(\{1, 2, 3, 4\}\). |
---|
SELECT * FROM pgr_johnson(
'SELECT source, target, cost FROM edges
WHERE id < 5'
) ORDER BY start_vid, end_vid;
start_vid | end_vid | agg_cost
-----------+---------+----------
5 | 6 | 1
5 | 7 | 2
6 | 7 | 1
(3 rows)
Parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
Edges SQL | TEXT |
Edges SQL as described below. |
Optional parameters¶
Column | Type | Default | Description |
---|---|---|---|
directed |
BOOLEAN |
true |
|
Inner Queries¶
Edges SQL¶
Column | Type | Default | 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 ) |
|
reverse_cost |
ANY-NUMERICAL | -1 | Weight of the edge (
|
Where:
ANY-INTEGER: | SMALLINT , INTEGER , BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT , INTEGER , BIGINT , REAL , FLOAT |
Result Columns¶
Returns set of (start_vid, end_vid, agg_cost)
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 from start_vid to end_vid . |