# pgRouting Manual (2.5)

## 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

Availability: 2.0.0

- Renamed on 2.2.0, previous name pgr_apspWarshall

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 use Boost’s implementation which runs in \(\Theta(V^3)\) time,

## 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.
  - Recommended, use a bounding box of no more than 3500 edges.

## Signature Summary

    pgr_floydWarshall(edges_sql)
    pgr floydWarshall(edges_sql, directed)
    RETURNS SET OF (start_vid, end_vid,  agg_cost) or EMPTY SET

## Signatures

### Minimal Signature

    pgr_floydWarshall(edges_sql)
    RETURNS SET OF (start_vid, end_vid,  agg_cost) or EMPTY SET

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)

### Complete Signature

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

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)

## Description of the Signatures

### 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

### 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`.

History

- Re-design of pgr_apspWarshall in Version 2.2.0

## See Also

- pgr_johnson
- Boost floyd-Warshall algorithm
- Queries uses the Sample Data network.

Indices and tables

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