# pgRouting Manual (2.1.0)

## pgr_trsp - Turn Restriction Shortest Path (TRSP)

## Name

`pgr_trsp` — Returns the shortest path with support for turn restrictions.

## Synopsis

The turn restricted shorthest path (TRSP) is a shortest path algorithm that can optionally take into account complicated turn restrictions like those found in real work navigable road networks. Performamnce wise it is nearly as fast as the A* search but has many additional features like it works with edges rather than the nodes of the network. Returns a set of pgr_costResult (seq, id1, id2, cost) rows, that make up a path.

    pgr_costResult[] pgr_trsp(sql text, source integer, target integer,
                directed boolean, has_rcost boolean [,restrict_sql text]);

    pgr_costResult[] pgr_trsp(sql text, source_edge integer, source_pos float8,
                    target_edge integer, target_pos float8,
                directed boolean, has_rcost boolean [,restrict_sql text]);

    pgr_costResult3[] pgr_trspViaVertices(sql text, vids integer[],
                    directed boolean, has_reverse_cost boolean
                    [, turn_restrict_sql text]);

    pgr_costResult3[] pgr_trspViaEdges(sql text, eids integer[], pcts float8[],
                   directed boolean, has_reverse_cost boolean
                   [, turn_restrict_sql text]);

## Description

The Turn Restricted Shortest Path algorithm (TRSP) is similar to the Shooting Star algorithm in that you can specify turn restrictions.

The TRSP setup is mostly the same as Dijkstra shortest path with the addition of an optional turn restriction table. This provides an easy way of adding turn restrictions to a road network by placing them in a separate table.

sql:

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

    SELECT id, source, target, cost, [,reverse_cost] FROM edge_table

id: | `int4` identifier of the edge
source: | `int4` identifier of the source vertex
target: | `int4` identifier of the target vertex
cost: | `float8` value, of the edge traversal cost. A negative cost will prevent the edge from being inserted in the graph.
reverse_cost: | (optional) the cost for the reverse traversal of the edge. This is only used when the `directed` and `has_rcost` parameters are `true` (see the above remark about negative costs).

source: | `int4` NODE id of the start point
target: | `int4` NODE id of the end point
directed: | `true` if the graph is directed
has_rcost: | if `true`, the `reverse_cost` column of the SQL generated set of rows will be used for the cost of the traversal of the edge in the opposite direction.

restrict_sql:

(optional) a SQL query, which should return a set of rows with the following columns:

    SELECT to_cost, target_id, via_path FROM restrictions

to_cost: | `float8` turn restriction cost
target_id: | `int4` target id
via_path: | `text` commar seperated list of edges in the reverse order of `rule`

Another variant of TRSP allows to specify EDGE id of source and target together with a fraction to interpolate the position:

source_edge: | `int4` EDGE id of the start edge
source_pos: | `float8` fraction of 1 defines the position on the start edge
target_edge: | `int4` EDGE id of the end edge
target_pos: | `float8` fraction of 1 defines the position on the end edge

Returns set of pgr_costResult[]:

seq: | row sequence
id1: | node ID
id2: | edge ID (`-1` for the last row)
cost: | cost to traverse from `id1` using `id2`

History

- New in version 2.0.0

## Support for Vias

Warning

The Support for Vias functions are prototypes. Not all corner cases are being considered.

We also have support for vias where you can say generate a from A to B to C, etc. We support both methods above only you pass an array of vertices or and array of edges and percentage position along the edge in two arrays.

sql:

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

    SELECT id, source, target, cost, [,reverse_cost] FROM edge_table

id: | `int4` identifier of the edge
source: | `int4` identifier of the source vertex
target: | `int4` identifier of the target vertex
cost: | `float8` value, of the edge traversal cost. A negative cost will prevent the edge from being inserted in the graph.
reverse_cost: | (optional) the cost for the reverse traversal of the edge. This is only used when the `directed` and `has_rcost` parameters are `true` (see the above remark about negative costs).

vids: | `int4[]` An ordered array of NODE id the path will go through from start to end.
directed: | `true` if the graph is directed
has_rcost: | if `true`, the `reverse_cost` column of the SQL generated set of rows will be used for the cost of the traversal of the edge in the opposite direction.

restrict_sql:

(optional) a SQL query, which should return a set of rows with the following columns:

    SELECT to_cost, target_id, via_path FROM restrictions

to_cost: | `float8` turn restriction cost
target_id: | `int4` target id
via_path: | `text` commar seperated list of edges in the reverse order of `rule`

Another variant of TRSP allows to specify EDGE id together with a fraction to interpolate the position:

eids: | `int4` An ordered array of EDGE id that the path has to traverse
pcts: | `float8` An array of fractional positions along the respective edges in `eids`, where 0.0 is the start of the edge and 1.0 is the end of the eadge.

Returns set of pgr_costResult[]:

seq: | row sequence
id1: | route ID
id2: | node ID
id3: | edge ID (`-1` for the last row)
cost: | cost to traverse from `id2` using `id3`

History

- Via Support prototypes new in version 2.1.0

## Examples

- Without turn restrictions

    SELECT seq, id1 AS node, id2 AS edge, cost
            FROM pgr_trsp(
                    'SELECT id, source, target, cost FROM edge_table',
                    7, 12, false, false
            );

    seq | node | edge | cost
    ----+------+------+------
      0 |    7 |    6 |    1
      1 |    8 |    7 |    1
      2 |    5 |    8 |    1
      3 |    6 |   11 |    1
      4 |   11 |   13 |    1
      5 |   12 |   -1 |    0
    (6 rows)

- With turn restrictions

Turn restrictions require additional information, which can be stored in a separate table:

    CREATE TABLE restrictions (
        rid serial,
        to_cost double precision,
        to_edge integer,
        from_edge integer,
        via text
    );

    INSERT INTO restrictions VALUES (1,100,7,4,null);
    INSERT INTO restrictions VALUES (2,4,8,3,5);
    INSERT INTO restrictions VALUES (3,100,9,16,null);

Then a query with turn restrictions is created as:

    SELECT seq, id1 AS node, id2 AS edge, cost
            FROM pgr_trsp(
                    'SELECT id, source, target, cost FROM edge_table',
                    7, 12, false, false,
                    'SELECT to_cost, to_edge AS target_id,
               from_edge || coalesce('','' || via, '''') AS via_path
           FROM restrictions'
            );

     seq | node | edge | cost
    -----+------+------+------
       0 |    7 |    6 |    1
       1 |    8 |    7 |    1
       2 |    5 |    8 |    1
       3 |    6 |   11 |    1
       4 |   11 |   13 |    1
       5 |   12 |   -1 |    0
    (6 rows)

An example query using vertex ids and via points:

    SELECT * FROM pgr_trspViaVertices(
        'SELECT id, source::INTEGER, target::INTEGER, cost,
            reverse_cost FROM edge_table',
        ARRAY[1,8,13,5]::INTEGER[],
        true,
        true,

        'SELECT to_cost, to_edge AS target_id, FROM_edge ||
            coalesce('',''||via,'''') AS via_path FROM restrictions');

     seq | id1 | id2 | id3 | cost
    -----+-----+-----+-----+------
       1 |   1 |   1 |   1 |    1
       2 |   1 |   2 |   4 |    1
       3 |   1 |   5 |   8 |    1
       4 |   1 |   6 |   9 |    1
       5 |   1 |   9 |  16 |    1
       6 |   1 |   4 |   3 |    1
       7 |   1 |   3 |   5 |    1
       8 |   1 |   6 |   8 |    1
       9 |   1 |   5 |   7 |    1
      10 |   2 |   8 |   7 |    1
      11 |   2 |   5 |  10 |    1
      12 |   2 |  10 |  14 |    1
      13 |   3 |  13 |  14 |    1
      14 |   3 |  10 |  10 |    1
      15 |   3 |   5 |  -1 |    0
    (15 rows)

An example query using edge ids and vias:

    SELECT * FROM pgr_trspViaEdges(
        'SELECT id, source::INTEGER, target::INTEGER,cost,
             reverse_cost FROM edge_table',
        ARRAY[1,11,6]::INTEGER[],
        ARRAY[0.5, 0.5, 0.5]::FLOAT8[],
        true,
        true,

        'SELECT to_cost, to_edge AS target_id, FROM_edge ||
            coalesce('',''||via,'''') AS via_path FROM restrictions');

     seq | id1 | id2 | id3 | cost
    -----+-----+-----+-----+------
       1 |   1 |  -1 |   1 |  0.5
       2 |   1 |   2 |   4 |    1
       3 |   1 |   5 |   8 |    1
       4 |   1 |   6 |  11 |    1
       5 |   2 |  11 |  13 |    1
       6 |   2 |  12 |  15 |    1
       7 |   2 |   9 |   9 |    1
       8 |   2 |   6 |   8 |    1
       9 |   2 |   5 |   7 |    1
      10 |   2 |   8 |   6 |  0.5
    (10 rows)

The queries use the Sample Data network.

## See Also

- pgr_costResult[]