# pgRouting Manual (3.6)

## 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 3.2.0

  - New experimental function:

    - pgr_dagShortestPath(Combinations)

- Version 3.0.0

  - New experimental function

## 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, start vid, end vid)
pgr_dagShortestPath(Edges SQL, start vid, end vids)
pgr_dagShortestPath(Edges SQL, start vids, end vid)
pgr_dagShortestPath(Edges SQL, start vids, end vids)
pgr_dagShortestPath(Edges SQL, Combinations SQL)
Returns set of `(seq, path_seq, node, edge, cost, agg_cost)`
OR EMPTY SET

### One to One

pgr_dagShortestPath(Edges SQL, start vid, end vid)
Returns set of `(seq, path_seq, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  From vertex \(5\) to vertex \(11\) on a directed graph

    SELECT * FROM pgr_dagShortestPath(
      'SELECT id, source, target, cost FROM edges',
      5, 11);
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    5 |    1 |    1 |        0
       2 |        2 |    6 |    4 |    1 |        1
       3 |        3 |    7 |    8 |    1 |        2
       4 |        4 |   11 |   -1 |    0 |        3
    (4 rows)

### One to Many

pgr_dagShortestPath(Edges SQL, start vid, end vids)
Returns set of `(seq, path_seq, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  From vertex \(5\) to vertices \(\{7, 11\}\)

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

### Many to One

pgr_dagShortestPath(Edges SQL, start vids, end vid)
Returns set of `(seq, path_seq, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  From vertices \(\{5, 10\}\) to vertex \(11\)

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

### Many to Many

pgr_dagShortestPath(Edges SQL, start vids, end vids)
Returns set of `(seq, path_seq, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  From vertices \(\{5, 15\}\) to vertices \(\{11, 17\}\) on an undirected graph

    SELECT * FROM pgr_dagShortestPath(
      'SELECT id, source, target, cost FROM edges',
      ARRAY[5, 15], ARRAY[11, 17]);
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    5 |    1 |    1 |        0
       2 |        2 |    6 |    4 |    1 |        1
       3 |        3 |    7 |    8 |    1 |        2
       4 |        4 |   11 |   -1 |    0 |        3
       5 |        1 |    5 |    1 |    1 |        0
       6 |        2 |    6 |    4 |    1 |        1
       7 |        3 |    7 |    8 |    1 |        2
       8 |        4 |   11 |    9 |    1 |        3
       9 |        5 |   16 |   15 |    1 |        4
      10 |        6 |   17 |   -1 |    0 |        5
      11 |        1 |   15 |   16 |    1 |        0
      12 |        2 |   16 |   15 |    1 |        1
      13 |        3 |   17 |   -1 |    0 |        2
    (13 rows)

### Combinations

pgr_dagShortestPath(Edges SQL, Combinations SQL)
Returns set of `(seq, path_seq, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  Using a combinations table on an undirected graph

The combinations table:

    SELECT source, target FROM combinations;
     source | target
    --------+--------
          5 |      6
          5 |     10
          6 |      5
          6 |     15
          6 |     14
    (5 rows)

The query:

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

## Parameters

Column | Type | Description
--- | --- | ---
Edges SQL | `TEXT` | Edges SQL as described below
Combinations SQL | `TEXT` | Combinations SQL as described below
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 Queries

### Edges SQL

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`)

`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`

### Combinations SQL

Parameter | Type | Description
--- | --- | ---
`source` | ANY-INTEGER | Identifier of the departure vertex.
`target` | ANY-INTEGER | Identifier of the arrival vertex.

Where:

ANY-INTEGER:

  `SMALLINT`, `INTEGER`, `BIGINT`

## Return columns

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

Column | Type | Description
--- | --- | ---
`seq` | `INTEGER` | Sequential value starting from 1.
`path_seq` | `INTEGER` | 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_vid` to `node`.

## Additional Examples

Example 1:

  Demonstration of repeated values are ignored, and result is sorted.

    SELECT * FROM pgr_dagShortestPath(
      'SELECT id, source, target, cost FROM edges',
      ARRAY[5, 10, 5, 10, 10, 5], ARRAY[11, 17, 17, 11]);
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    5 |    1 |    1 |        0
       2 |        2 |    6 |    4 |    1 |        1
       3 |        3 |    7 |    8 |    1 |        2
       4 |        4 |   11 |   -1 |    0 |        3
       5 |        1 |    5 |    1 |    1 |        0
       6 |        2 |    6 |    4 |    1 |        1
       7 |        3 |    7 |    8 |    1 |        2
       8 |        4 |   11 |    9 |    1 |        3
       9 |        5 |   16 |   15 |    1 |        4
      10 |        6 |   17 |   -1 |    0 |        5
      11 |        1 |   10 |    5 |    1 |        0
      12 |        2 |   11 |   -1 |    0 |        1
      13 |        1 |   10 |    5 |    1 |        0
      14 |        2 |   11 |    9 |    1 |        1
      15 |        3 |   16 |   15 |    1 |        2
      16 |        4 |   17 |   -1 |    0 |        3
    (16 rows)

Example 2:

  Making start_vids the same as end_vids

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

Example 3:

  Manually assigned vertex combinations.

    SELECT * FROM pgr_dagShortestPath(
      'SELECT id, source, target, cost FROM edges',
      'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    6 |    4 |    1 |        0
       2 |        2 |    7 |   -1 |    0 |        1
    (2 rows)

## See Also

- Sample Data

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

Indices and tables

- Index

- Search Page