# pgr_trsp - Proposed¶

pgr_trsp - routing vertices with restrictions.

Warning

Proposed functions for next mayor release.

• They are not officially in the current release.

• They will likely officially be part of the next mayor release:

• The functions make use of ANY-INTEGER and ANY-NUMERICAL

• Name might not change. (But still can)

• Signature might not change. (But still can)

• Functionality might not change. (But still can)

• pgTap tests have being done. But might need more.

• Documentation might need refinement.

Availability

• Version 3.4.0

• New proposed signatures:

• Deprecated signatures:

• pgr_trsp(text,integer,integer,boolean,boolean,text)

• pgr_trsp(text,integer,float,integer,float,boolean,boolean,text)

• pgr_trspViaVertices(text,anyarray,boolean,boolean,text)

• pgr_trspviaedges(text,integer[],double precision[],boolean,boolean,text)

• Version 2.1.0

• New prototypes:

• pgr_trspViaVertices

• pgr_trspViaEdges

• Version 2.0.0

• Official function

## Description¶

Turn restricted shortest path (TRSP) is an algorithm that receives turn restrictions in form of a query like those found in real world navigable road networks.

The main characteristics are:

• It does no guarantee the shortest path as it might contain restriction paths.

The general algorithm is as follows:

• Execute a Dijkstra.

• If the solution passes thru a restriction then.

• Execute the TRSP algorithm with restrictions.

## Signatures¶

Proposed

pgr_trsp(Edges SQL, Restrictions SQL, start vid, end vid, [directed])
pgr_trsp(Edges SQL, Restrictions SQL, start vid, end vids, [directed])
pgr_trsp(Edges SQL, Restrictions SQL, start vids, end vid, [directed])
pgr_trsp(Edges SQL, Restrictions SQL, start vids, end vids, [directed])
pgr_trsp(Edges SQL, Restrictions SQL, Combinations SQL, [directed])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

### One to One¶

pgr_trsp(Edges SQL, Restrictions SQL, start vid, end vid, [directed])

RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertex $$6$$ to vertex $$10$$ on an undirected graph.

SELECT * FROM pgr_trsp(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
6, 10,
false);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         6 |      10 |    6 |    2 |    1 |        0
2 |        2 |         6 |      10 |   10 |   -1 |    0 |        1
(2 rows)



### One to Many¶

pgr_trsp(Edges SQL, Restrictions SQL, start vid, end vids, [directed])

RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertex $$6$$ to vertices $$\{10, 1\}$$ on an undirected graph.

SELECT * FROM pgr_trsp(
$$SELECT id, source, target, cost FROM edges$$,
$$SELECT * FROM restrictions$$,
6, ARRAY[10, 1],
false);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         6 |       1 |    6 |    4 |    1 |        0
2 |        2 |         6 |       1 |    7 |   10 |    1 |        1
3 |        3 |         6 |       1 |    8 |   12 |    1 |        2
4 |        4 |         6 |       1 |   12 |   11 |    1 |        3
5 |        5 |         6 |       1 |   11 |    8 |    1 |        4
6 |        6 |         6 |       1 |    7 |    7 |    1 |        5
7 |        7 |         6 |       1 |    3 |    6 |    1 |        6
8 |        8 |         6 |       1 |    1 |   -1 |    0 |        7
9 |        1 |         6 |      10 |    6 |    4 |    1 |        0
10 |        2 |         6 |      10 |    7 |    8 |    1 |        1
11 |        3 |         6 |      10 |   11 |    5 |    1 |        2
12 |        4 |         6 |      10 |   10 |   -1 |    0 |        3
(12 rows)



### Many to One¶

pgr_trsp(Edges SQL, Restrictions SQL, start vids, end vid, [directed])

RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertices $$\{6, 1\}$$ to vertex $$8$$ on a directed graph.

SELECT * FROM pgr_trsp(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[6, 1], 8);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         1 |       8 |    1 |    6 |    1 |        0
2 |        2 |         1 |       8 |    3 |    7 |    1 |        1
3 |        3 |         1 |       8 |    7 |   10 |  101 |        2
4 |        4 |         1 |       8 |    8 |   -1 |    0 |      103
5 |        1 |         6 |       8 |    6 |    4 |    1 |        0
6 |        2 |         6 |       8 |    7 |   10 |    1 |        1
7 |        3 |         6 |       8 |    8 |   -1 |    0 |        2
(7 rows)



### Many to Many¶

pgr_trsp(Edges SQL, Restrictions SQL, start vids, end vids, [directed])

RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertices $$\{6, 1\}$$ to vertices $$\{10, 8\}$$ on an undirected graph.

SELECT * FROM pgr_trsp(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[6, 1], ARRAY[10, 8],
false);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         1 |       8 |    1 |    6 |    1 |        0
2 |        2 |         1 |       8 |    3 |    7 |    1 |        1
3 |        3 |         1 |       8 |    7 |    4 |    1 |        2
4 |        4 |         1 |       8 |    6 |    2 |    1 |        3
5 |        5 |         1 |       8 |   10 |    5 |    1 |        4
6 |        6 |         1 |       8 |   11 |   11 |    1 |        5
7 |        7 |         1 |       8 |   12 |   12 |    1 |        6
8 |        8 |         1 |       8 |    8 |   -1 |    0 |        7
9 |        1 |         1 |      10 |    1 |    6 |    1 |        0
10 |        2 |         1 |      10 |    3 |    7 |    1 |        1
11 |        3 |         1 |      10 |    7 |    4 |    1 |        2
12 |        4 |         1 |      10 |    6 |    2 |    1 |        3
13 |        5 |         1 |      10 |   10 |   -1 |    0 |        4
14 |        1 |         6 |       8 |    6 |    4 |    1 |        0
15 |        2 |         6 |       8 |    7 |   10 |    1 |        1
16 |        3 |         6 |       8 |    8 |   -1 |    0 |        2
17 |        1 |         6 |      10 |    6 |    2 |    1 |        0
18 |        2 |         6 |      10 |   10 |   -1 |    0 |        1
(18 rows)



### Combinations¶

pgr_trsp(Edges SQL, Restrictions SQL, Combinations SQL, [directed])

RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

Using a combinations table on an undirected graph.

SELECT * FROM pgr_trsp(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT * FROM (VALUES (6, 10), (6, 1), (6, 8), (1, 8)) AS combinations (source, target)$$);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         1 |       8 |    1 |    6 |    1 |        0
2 |        2 |         1 |       8 |    3 |    7 |    1 |        1
3 |        3 |         1 |       8 |    7 |   10 |  101 |        2
4 |        4 |         1 |       8 |    8 |   -1 |    0 |      103
5 |        1 |         6 |       1 |    6 |    4 |    1 |        0
6 |        2 |         6 |       1 |    7 |   10 |    1 |        1
7 |        3 |         6 |       1 |    8 |   12 |    1 |        2
8 |        4 |         6 |       1 |   12 |   13 |    1 |        3
9 |        5 |         6 |       1 |   17 |   15 |    1 |        4
10 |        6 |         6 |       1 |   16 |    9 |    1 |        5
11 |        7 |         6 |       1 |   11 |    8 |    1 |        6
12 |        8 |         6 |       1 |    7 |    7 |    1 |        7
13 |        9 |         6 |       1 |    3 |    6 |    1 |        8
14 |       10 |         6 |       1 |    1 |   -1 |    0 |        9
15 |        1 |         6 |       8 |    6 |    4 |    1 |        0
16 |        2 |         6 |       8 |    7 |   10 |    1 |        1
17 |        3 |         6 |       8 |    8 |   -1 |    0 |        2
18 |        1 |         6 |      10 |    6 |    4 |    1 |        0
19 |        2 |         6 |      10 |    7 |   10 |    1 |        1
20 |        3 |         6 |      10 |    8 |   12 |    1 |        2
21 |        4 |         6 |      10 |   12 |   13 |    1 |        3
22 |        5 |         6 |      10 |   17 |   15 |    1 |        4
23 |        6 |         6 |      10 |   16 |   16 |    1 |        5
24 |        7 |         6 |      10 |   15 |    3 |    1 |        6
25 |        8 |         6 |      10 |   10 |   -1 |    0 |        7
(25 rows)



## Parameters¶

Column

Type

Description

Edges SQL

TEXT

SQL query as described.

Restrictions SQL

TEXT

SQL query as described.

Combinations SQL

TEXT

Combinations SQL as described below

start vid

ANY-INTEGER

Identifier of the departure vertex.

start vids

ARRAY [ANY-INTEGER]

Array of identifiers of destination vertices.

end vid

ANY-INTEGER

Identifier of the departure vertex.

end vids

ARRAY [ANY-INTEGER]

Array of identifiers of destination vertices.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

### 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

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

### Restrictions SQL¶

Column

Type

Description

path

ARRAY [ANY-INTEGER]

Sequence of edge identifiers that form a path that is not allowed to be taken. - Empty arrays or NULL arrays are ignored. - Arrays that have a NULL element will raise an exception.

Cost

ANY-NUMERICAL

Cost of taking the forbidden path.

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

## Result Columns¶

Returns set of (seq, path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)

Column

Type

Description

seq

INTEGER

Sequential value starting from 1.

path_id

INTEGER

Path identifier.

• Has value 1 for the first of a path from start_vid to end_vid.

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.

end_vid

BIGINT

Identifier of the ending vertex.

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.