# pgRouting Manual (3.1)

## 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.

Boost Graph Inside

Availability

- Version 2.2.0

  - Signature change

  - Old signature no longer supported

- Version 2.0.0

  - Official function

Support

- Supported versions: current(3.1) 3.0 2.6

- Unsupported versions: 2.5 2.4 2.3 2.2 2.1 2.0

## 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.

## Signatures

Summary

    pgr_johnson(edges_sql)
    pgr johnson(edges_sql [, directed])
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Using default

    pgr_johnson(edges_sql)
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example 1

  For vertices \(\{1, 2, 3, 4\}\) 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)

### Complete Signature

    pgr_johnson(edges_sql[, directed])
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example 2

  For vertices \(\{1, 2, 3, 4\}\) 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)

## Parameters

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

## Inner query

Description of the edges_sql query (id is not necessary)

edges_sql

  an SQL query, which should return a set of rows with the following columns:

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)

- When negative: edge (source, target) does not exist, therefore it’s not part of the graph.

reverse_cost

`ANY-NUMERICAL`

-1

Weight of the edge (target, source),

- When 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

## Result Columns

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`.

## See Also

- pgr_floydWarshall

- Boost Johnson algorithm implementation.

- Queries uses the Sample Data network.

Indices and tables

- Index

- Search Page