# pgRouting Manual (2.5)

## pgr_dijkstraVia - Proposed

## Name

`pgr_dijkstraVia` — Using dijkstra algorithm, it finds the route that goes through a list of vertices.

Boost Graph Inside

Availability: 2.2.0

## Synopsis

Given a list of vertices and a graph, this function is equivalent to finding the shortest path between \(vertex_i\) and \(vertex_{i+1}\) for all \(i < size\_of(vertex_via)\).

The paths represents the sections of the route.

Note

This is a proposed function

## Signatrue Summary

    pgr_dijkstraVia(edges_sql, via_vertices)
    pgr_dijkstraVia(edges_sql, via_vertices, directed, strict, U_turn_on_edge)

    RETURNS SET OF (seq, path_pid, path_seq, start_vid, end_vid,
        node, edge, cost, agg_cost, route_agg_cost) or EMPTY SET

## Signatures

### Minimal Signature

    pgr_dijkstraVia(edges_sql, via_vertices)
    RETURNS SET OF (seq, path_pid, path_seq, start_vid, end_vid,
        node, edge, cost, agg_cost, route_agg_cost) or EMPTY SET

Example: | Find the route that visits the vertices 1 3 9 in that order

    SELECT * FROM pgr_dijkstraVia(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id',
        ARRAY[1, 3, 9]
    );
     seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
    -----+---------+----------+-----------+---------+------+------+------+----------+----------------
       1 |       1 |        1 |         1 |       3 |    1 |    1 |    1 |        0 |              0
       2 |       1 |        2 |         1 |       3 |    2 |    4 |    1 |        1 |              1
       3 |       1 |        3 |         1 |       3 |    5 |    8 |    1 |        2 |              2
       4 |       1 |        4 |         1 |       3 |    6 |    9 |    1 |        3 |              3
       5 |       1 |        5 |         1 |       3 |    9 |   16 |    1 |        4 |              4
       6 |       1 |        6 |         1 |       3 |    4 |    3 |    1 |        5 |              5
       7 |       1 |        7 |         1 |       3 |    3 |   -1 |    0 |        6 |              6
       8 |       2 |        1 |         3 |       9 |    3 |    5 |    1 |        0 |              6
       9 |       2 |        2 |         3 |       9 |    6 |    9 |    1 |        1 |              7
      10 |       2 |        3 |         3 |       9 |    9 |   -2 |    0 |        2 |              8
    (10 rows)

### Complete Signature

    pgr_dijkstraVia(edges_sql, via_vertices, directed, strict, U_turn_on_edge)
    RETURNS SET OF (seq, path_pid, path_seq, start_vid, end_vid,
        node, edge, cost, agg_cost, route_agg_cost) or EMPTY SET

Example: | Find the route that visits the vertices 1 3 9 in that order on an undirected graph, avoiding U-turns when possible

    SELECT * FROM pgr_dijkstraVia(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id',
        ARRAY[1, 3, 9], false, strict:=true, U_turn_on_edge:=false
    );
     seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
    -----+---------+----------+-----------+---------+------+------+------+----------+----------------
       1 |       1 |        1 |         1 |       3 |    1 |    1 |    1 |        0 |              0
       2 |       1 |        2 |         1 |       3 |    2 |    2 |    1 |        1 |              1
       3 |       1 |        3 |         1 |       3 |    3 |   -1 |    0 |        2 |              2
       4 |       2 |        1 |         3 |       9 |    3 |    5 |    1 |        0 |              2
       5 |       2 |        2 |         3 |       9 |    6 |    9 |    1 |        1 |              3
       6 |       2 |        3 |         3 |       9 |    9 |   -2 |    0 |        2 |              4
    (6 rows)

## Description of the Signature

### Description of the edges_sql query for dijkstra like functions

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

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

### Description of the parameters of the signatures

Parameter | Type | Default | Description
--- | --- | --- | ---
edges_sql | `TEXT` |  | SQL query as described above.
via_vertices | `ARRAY[ANY-INTEGER]` |  | Array of ordered vertices identifiers that are going to be visited.

directed

`BOOLEAN`

`true`

- When `true` Graph is considered Directed
- When `false` the graph is considered as Undirected.

strict

`BOOLEAN`

`false`

- When `false` ignores missing paths returning all paths found
- When `true` if a path is missing stops and returns EMPTY SET

U_turn_on_edge

`BOOLEAN`

`true`

- When `true` departing from a visited vertex will not try to avoid using the edge used to reach it. In other words, U turn using the edge with same id is allowed.
- When `false` when a departing from a visited vertex tries to avoid using the edge used to reach it. In other words, U turn using the edge with same id is used when no other path is found.

### Description of the parameters of the signatures

Parameter | Type | Description
--- | --- | ---
edges_sql | `TEXT` | SQL query as described above.
via_vertices | `ARRAY[ANY-INTEGER]` | Array of vertices identifiers
directed | `BOOLEAN` | (optional) Default is true (is directed). When set to false the graph is considered as Undirected
strict | `BOOLEAN` | (optional) ignores if a subsection of the route is missing and returns everything it found Default is true (is directed). When set to false the graph is considered as Undirected
U_turn_on_edge | `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
--- | --- | ---
seq | `BIGINT` | Sequential value starting from 1.
path_pid | `BIGINT` | Identifier of the path.
path_seq | `BIGINT` | Sequential value starting from 1 for the path.
start_vid | `BIGINT` | Identifier of the starting vertex of the path.
end_vid | `BIGINT` | Identifier of the ending vertex of the path.
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. -2 for the last node of the route.
cost | `FLOAT` | Cost to traverse from `node` using `edge` to the next node in the route sequence.
agg_cost | `FLOAT` | Total cost from `start_vid` to `end_vid` of the path.
route_agg_cost | `FLOAT` | Total cost from `start_vid` of `path_pid = 1` to `end_vid` of the current `path_pid` .

## Examples

Example 1: | Find the route that visits the vertices 1 5 3 9 4 in that order

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

Example 2: | What’s the aggregate cost of the third path?

    SELECT agg_cost FROM  pgr_dijkstraVia(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id',
        ARRAY[1, 5, 3, 9, 4]
    )
    WHERE path_id = 3 AND edge <0;
     agg_cost
    ----------
            2
    (1 row)

Example 3: | What’s the route’s aggregate cost of the route at the end of the third path?

    SELECT route_agg_cost FROM  pgr_dijkstraVia(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id',
        ARRAY[1, 5, 3, 9, 4]
    )
    WHERE path_id = 3 AND edge < 0;
     route_agg_cost
    ----------------
                  8
    (1 row)

Example 4: | How are the nodes visited in the route?

    SELECT row_number() over () as node_seq, node
    FROM  pgr_dijkstraVia(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id',
        ARRAY[1, 5, 3, 9, 4]
    )
    WHERE edge <> -1 ORDER BY seq;
     node_seq | node
    ----------+------
            1 |    1
            2 |    2
            3 |    5
            4 |    6
            5 |    9
            6 |    4
            7 |    3
            8 |    6
            9 |    9
           10 |    4
    (10 rows)

Example 5: | What are the aggregate costs of the route when the visited vertices are reached?

    SELECT path_id, route_agg_cost FROM  pgr_dijkstraVia(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id',
        ARRAY[1, 5, 3, 9, 4]
    )
    WHERE edge < 0;
     path_id | route_agg_cost
    ---------+----------------
           1 |              2
           2 |              6
           3 |              8
           4 |              9
    (4 rows)

Example 6: | show the route’s seq and aggregate cost and a status of “passes in front” or “visits” node 9

    SELECT seq, route_agg_cost, node, agg_cost ,
    CASE WHEN edge = -1 THEN 'visits'
    ELSE 'passes in front'
    END as status
    FROM  pgr_dijkstraVia(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id',
        ARRAY[1, 5, 3, 9, 4])
    WHERE node = 9 and (agg_cost  <> 0 or seq = 1);
     seq | route_agg_cost | node | agg_cost |     status
    -----+----------------+------+----------+-----------------
       6 |              4 |    9 |        2 | passes in front
      11 |              8 |    9 |        2 | visits
    (2 rows)

    ROLLBACK;
    ROLLBACK

## See Also

- http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
- Sample Data network.

Indices and tables

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