# pgRouting Manual (3.6)

## pgr_floydWarshall

# `pgr_floydWarshall`

`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

- Version 2.2.0

  - Signature change

  - Old signature no longer supported

- Version 2.0.0

  - Official function

## Description

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,

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_floydWarshall(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_floydWarshall(
      'SELECT id, source, target, cost, reverse_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 |       5 |        1
             6 |       7 |        1
             7 |       5 |        2
             7 |       6 |        1
            10 |       5 |        2
            10 |       6 |        1
            10 |       7 |        2
            15 |       5 |        3
            15 |       6 |        2
            15 |       7 |        3
            15 |      10 |        1
    (13 rows)

## Parameters

Parameter | Type | Default | Description
--- | --- | --- | ---
Edges SQL | `TEXT` |  | Edges SQL as described below.

### Optional parameters

Column | Type | Default | Description
--- | --- | --- | ---

`directed`

`BOOLEAN`

`true`

- When `true` the graph is considered Directed

- When `false` the graph is considered as Undirected.

## 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 (`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

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`.

## See Also

- pgr_johnson

- Boost floyd-Warshall

- Queries uses the Sample Data network.

Indices and tables

- Index

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