# pgRouting Manual (3.1)

## pgr_dagShortestPath - Experimental

`pgr_dagShortestPath` — Returns the shortest path(s) for weighted directed acyclic graphs(DAG). In particular, the DAG shortest paths algorithm implemented by Boost.Graph.

Boost Graph Inside

Warning

Possible server crash

- These functions might create a server crash

Warning

Experimental functions

- They are not officially of the current release.

- They likely will not be officially be part of the next release:

  - The functions might not make use of ANY-INTEGER and ANY-NUMERICAL

  - Name might change.

  - Signature might change.

  - Functionality might change.

  - pgTap tests might be missing.

  - Might need c/c++ coding.

  - May lack documentation.

  - Documentation if any might need to be rewritten.

  - Documentation examples might need to be automatically generated.

  - Might need a lot of feedback from the comunity.

  - Might depend on a proposed function of pgRouting

  - Might depend on a deprecated function of pgRouting

Availability

- Version 3.0.0

  - New experimental function

Support

- Supported versions: current(3.1) 3.0

## Description

Shortest Path for Directed Acyclic Graph(DAG) is a graph search algorithm that solves the shortest path problem for weighted directed acyclic graph, producing a shortest path from a starting vertex (`start_vid`) to an ending vertex (`end_vid`).

This implementation can only be used with a directed graph with no cycles i.e. directed acyclic graph.

The algorithm relies on topological sorting the dag to impose a linear ordering on the vertices, and thus is more efficient for DAG’s than either the Dijkstra or Bellman-Ford algorithm.

The main characteristics are:

  - Process is valid for weighted directed acyclic graphs only. otherwise it will throw warnings.

  - Values are returned when there is a path.

    - When the starting vertex and ending vertex are the same, there is no path.

      - The agg_cost the non included values (v, v) is 0

    - When the starting vertex and ending vertex are the different and there is no path:

      - The agg_cost the non included values (u, v) is \(\infty\)

  - For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.

  - The returned values are ordered:

    - start_vid ascending

    - end_vid ascending

  - Running time: \(O(| start\_vids | * (V + E))\)

## Signatures

Summary

    pgr_dagShortestPath(edges_sql, from_vid,  to_vid)
    pgr_dagShortestPath(edges_sql, from_vid,  to_vids)
    pgr_dagShortestPath(edges_sql, from_vids, to_vid)
    pgr_dagShortestPath(edges_sql, from_vids, to_vids)

    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
    OR EMPTY SET

### One to One

    pgr_dagShortestPath(edges_sql, from_vid,  to_vid)
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
    OR EMPTY SET

Example

  From vertex \(1\) to vertex \(6\)

    SELECT * FROM pgr_dagShortestPath(
        'SELECT id, source, target, cost FROM edge_table',
        1, 6
    );
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    1 |    1 |    1 |        0
       2 |        2 |    2 |    4 |    1 |        1
       3 |        3 |    5 |    8 |    1 |        2
       4 |        4 |    6 |   -1 |    0 |        3
    (4 rows)

### One to Many

    pgr_dagShortestPath(edges_sql, from_vid,  to_vids)
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
    OR EMPTY SET

Example

  From vertex \(1\) to vertices \(\{ 5, 6\}\)

    SELECT * FROM pgr_dagShortestPath(
        'SELECT id, source, target, cost FROM edge_table',
        1, ARRAY[5,6]
    );
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    1 |    1 |    1 |        0
       2 |        2 |    2 |    4 |    1 |        1
       3 |        3 |    5 |   -1 |    0 |        2
       4 |        1 |    1 |    1 |    1 |        0
       5 |        2 |    2 |    4 |    1 |        1
       6 |        3 |    5 |    8 |    1 |        2
       7 |        4 |    6 |   -1 |    0 |        3
    (7 rows)

### Many to One

    pgr_dagShortestPath(edges_sql, from_vids, to_vid)
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
    OR EMPTY SET

Example

  From vertices \(\{1, 3\}\) to vertex \(6\)

    SELECT * FROM pgr_dagShortestPath(
        'SELECT id, source, target, cost FROM edge_table',
        ARRAY[1,3], 6
    );
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    1 |    1 |    1 |        0
       2 |        2 |    2 |    4 |    1 |        1
       3 |        3 |    5 |    8 |    1 |        2
       4 |        4 |    6 |   -1 |    0 |        3
       5 |        1 |    3 |    5 |    1 |        0
       6 |        2 |    6 |   -1 |    0 |        1
    (6 rows)

### Many to Many

    pgr_dagShortestPath(edges_sql, from_vids, to_vids)
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
    OR EMPTY SET

Example

  From vertices \(\{1, 4\}\) to vertices \(\{12, 6\}\)

    SELECT * FROM pgr_dagShortestPath(
        'SELECT id, source, target, cost FROM edge_table',
        ARRAY[1, 4],ARRAY[12,6]
    );
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    1 |    1 |    1 |        0
       2 |        2 |    2 |    4 |    1 |        1
       3 |        3 |    5 |    8 |    1 |        2
       4 |        4 |    6 |   -1 |    0 |        3
       5 |        1 |    1 |    1 |    1 |        0
       6 |        2 |    2 |    4 |    1 |        1
       7 |        3 |    5 |   10 |    1 |        2
       8 |        4 |   10 |   12 |    1 |        3
       9 |        5 |   11 |   13 |    1 |        4
      10 |        6 |   12 |   -1 |    0 |        5
      11 |        1 |    4 |   16 |    1 |        0
      12 |        2 |    9 |   15 |    1 |        1
      13 |        3 |   12 |   -1 |    0 |        2
    (13 rows)

## Parameters

Description of the parameters of the signatures

Parameter | Type | Default | Description
--- | --- | --- | ---
edges_sql | `TEXT` |  | SQL query as described above.
start_vid | `BIGINT` |  | Identifier of the starting vertex of the path.
start_vids | `ARRAY[BIGINT]` |  | Array of identifiers of starting vertices.
end_vid | `BIGINT` |  | Identifier of the ending vertex of the path.
end_vids | `ARRAY[BIGINT]` |  | Array of identifiers of ending vertices.

## Inner Query

Column | Type | Default | Description
--- | --- | --- | ---
id | `ANY-INTEGER` |  | Identifier of the edge.
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

## Results Columns

Returns set of `(seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)`

Column | Type | Description
--- | --- | ---
seq | `INT` | Sequential value starting from 1.
path_seq | `INT` | Relative position in the path. Has value 1 for the beginning of a path.

start_vid

`BIGINT`

Identifier of the starting vertex. Returned when multiple starting vetrices are in the query.

- Many to One

- Many to Many

end_vid

`BIGINT`

Identifier of the ending vertex. Returned when multiple ending vertices are in the query.

- One to Many

- Many to Many

node | `BIGINT` | Identifier of the node in the path from `start_vid` to `end_vid`.
edge | `BIGINT` | Identifier of the edge used to go from `node` to the next node in the path sequence. `-1` for the last node of the path.
cost | `FLOAT` | Cost to traverse from `node` using `edge` to the next node in the path sequence.
agg_cost | `FLOAT` | Aggregate cost from `start_v` to `node`.

## See Also

- https://en.wikipedia.org/wiki/Topological_sorting

- The queries use the Sample Data network.

Indices and tables

- Index

- Search Page