# pgr_trspVia - Proposed¶

pgr_trspVia Route that goes through a list of 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 function:

• pgr_trspVia (One Via)

## Description¶

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 $$i < size\_of(via\;vertices)$$ trying not to use restricted paths.

The paths represents the sections of the route.

The general algorithm is as follows:

• Execute a pgr_dijkstraVia - Proposed.

• For the set of sub paths of the solution that pass through a restriction then

• Execute the TRSP algorithm with restrictions for the paths.

• NOTE when this is done, U_turn_on_edge flag is ignored.

## Signatures¶

### One Via¶

pgr_trspVia(Edges SQL, Restrictions SQL, via vertices, [options])
options: [directed, strict, U_turn_on_edge]
RETURNS SET OF (seq, path_id, 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 $$\{ 5, 1, 8\}$$ in that order on an directed graph.

SELECT * FROM pgr_trspVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[5, 1, 8]);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
1 |       1 |        1 |         5 |       1 |    5 |    1 |    1 |        0 |              0
2 |       1 |        2 |         5 |       1 |    6 |    4 |    1 |        1 |              1
3 |       1 |        3 |         5 |       1 |    7 |   10 |    1 |        2 |              2
4 |       1 |        4 |         5 |       1 |    8 |   12 |    1 |        3 |              3
5 |       1 |        5 |         5 |       1 |   12 |   13 |    1 |        4 |              4
6 |       1 |        6 |         5 |       1 |   17 |   15 |    1 |        5 |              5
7 |       1 |        7 |         5 |       1 |   16 |    9 |    1 |        6 |              6
8 |       1 |        8 |         5 |       1 |   11 |    8 |    1 |        7 |              7
9 |       1 |        9 |         5 |       1 |    7 |    7 |    1 |        8 |              8
10 |       1 |       10 |         5 |       1 |    3 |    6 |    1 |        9 |              9
11 |       1 |       11 |         5 |       1 |    1 |   -1 |    0 |       10 |             10
12 |       2 |        1 |         1 |       8 |    1 |    6 |    1 |        0 |             10
13 |       2 |        2 |         1 |       8 |    3 |    7 |    1 |        1 |             11
14 |       2 |        3 |         1 |       8 |    7 |   10 |  101 |        2 |             12
15 |       2 |        4 |         1 |       8 |    8 |   -2 |    0 |      103 |            113
(15 rows)



## Parameters¶

Parameter

Type

Description

Edges SQL

TEXT

Edges SQL query as described.

Restrictions SQL

TEXT

Restrictions SQL query as described.

via vertices

ARRAY[ ANY-INTEGER ]

Array of ordered vertices identifiers that are going to be visited.

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.

### Via optional parameters¶

Parameter

Type

Default

Description

strict

BOOLEAN

false

• When true if a path is missing stops and returns EMPTY SET

• When false ignores missing paths returning all paths found

U_turn_on_edge

BOOLEAN

true

• When true departing from a visited vertex will not try to avoid

## 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

## Result Columns¶

Column

Type

Description

seq

INTEGER

Sequential value starting from 1.

path_id

INTEGER

Identifier of a path. Has value 1 for the first path.

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 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 path sequence.

agg_cost

FLOAT

Aggregate cost from start_vid to node.

route_agg_cost

FLOAT

Total cost from start_vid of seq = 1 to end_vid of the current seq.

All this examples are about the route that visits the vertices $$\{5, 7, 1, 8, 15\}$$ in that order on a directed graph.

### The main query¶

SELECT * FROM pgr_trspVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[5, 7, 1, 8, 15]);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
1 |       1 |        1 |         5 |       7 |    5 |    1 |    1 |        0 |              0
2 |       1 |        2 |         5 |       7 |    6 |    4 |    1 |        1 |              1
3 |       1 |        3 |         5 |       7 |    7 |   -1 |    0 |        2 |              2
4 |       2 |        1 |         7 |       1 |    7 |    7 |    1 |        0 |              2
5 |       2 |        2 |         7 |       1 |    3 |    6 |    1 |        1 |              3
6 |       2 |        3 |         7 |       1 |    1 |   -1 |    0 |        2 |              4
7 |       3 |        1 |         1 |       8 |    1 |    6 |    1 |        0 |              4
8 |       3 |        2 |         1 |       8 |    3 |    7 |    1 |        1 |              5
9 |       3 |        3 |         1 |       8 |    7 |   10 |  101 |        2 |              6
10 |       3 |        4 |         1 |       8 |    8 |   -1 |    0 |      103 |            107
11 |       4 |        1 |         8 |      15 |    8 |   12 |    1 |        0 |            107
12 |       4 |        2 |         8 |      15 |   12 |   13 |    1 |        1 |            108
13 |       4 |        3 |         8 |      15 |   17 |   15 |    1 |        2 |            109
14 |       4 |        4 |         8 |      15 |   16 |   16 |    1 |        3 |            110
15 |       4 |        5 |         8 |      15 |   15 |   -2 |    0 |        4 |            111
(15 rows)



#### Aggregate cost of the third path.¶

SELECT agg_cost FROM pgr_trspVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[5, 7, 1, 8, 15])
WHERE path_id = 3 AND edge < 0;
agg_cost
----------
103
(1 row)



#### Route’s aggregate cost of the route at the end of the third path.¶

SELECT route_agg_cost FROM pgr_trspVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[5, 7, 1, 8, 15])
WHERE path_id = 3 AND edge < 0;
route_agg_cost
----------------
107
(1 row)



#### Nodes visited in the route.¶

SELECT row_number() over () as node_seq, node
FROM pgr_trspVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[5, 7, 1, 8, 15])
WHERE edge <> -1 ORDER BY seq;
node_seq | node
----------+------
1 |    5
2 |    6
3 |    7
4 |    3
5 |    1
6 |    3
7 |    7
8 |    8
9 |   12
10 |   17
11 |   16
12 |   15
(12 rows)



#### The aggregate costs of the route when the visited vertices are reached.¶

SELECT path_id, route_agg_cost FROM pgr_trspVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[5, 7, 1, 8, 15])
WHERE edge < 0;
path_id | route_agg_cost
---------+----------------
1 |              2
2 |              4
3 |            107
4 |            111
(4 rows)



#### Status of “passes in front” or “visits” of the nodes.¶

SELECT seq, route_agg_cost, node, agg_cost ,
CASE WHEN edge = -1 THEN $$visits$$
ELSE $$passes in front$$
END as status
FROM pgr_trspVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[5, 7, 1, 8, 15])
WHERE agg_cost <> 0 or seq = 1;
seq | route_agg_cost | node | agg_cost |     status
-----+----------------+------+----------+-----------------
1 |              0 |    5 |        0 | passes in front
2 |              1 |    6 |        1 | passes in front
3 |              2 |    7 |        2 | visits
5 |              3 |    3 |        1 | passes in front
6 |              4 |    1 |        2 | visits
8 |              5 |    3 |        1 | passes in front
9 |              6 |    7 |        2 | passes in front
10 |            107 |    8 |      103 | visits
12 |            108 |   12 |        1 | passes in front
13 |            109 |   17 |        2 | passes in front
14 |            110 |   16 |        3 | passes in front
15 |            111 |   15 |        4 | passes in front
(12 rows)



### Simulation of how algorithm works.¶

The algorithm performs a pgr_dijkstraVia - Proposed

SELECT * FROM pgr_dijkstraVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
ARRAY[6, 3, 6]);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
1 |       1 |        1 |         6 |       3 |    6 |    4 |    1 |        0 |              0
2 |       1 |        2 |         6 |       3 |    7 |    7 |    1 |        1 |              1
3 |       1 |        3 |         6 |       3 |    3 |   -1 |    0 |        2 |              2
4 |       2 |        1 |         3 |       6 |    3 |    7 |    1 |        0 |              2
5 |       2 |        2 |         3 |       6 |    7 |    4 |    1 |        1 |              3
6 |       2 |        3 |         3 |       6 |    6 |   -2 |    0 |        2 |              4
(6 rows)



Detects which of the sub paths pass through a restriction in this case is for the path_id = 5 from 6 to 3 because the path $$15 \rightarrow 1$$ is restricted.

Executes the pgr_trsp - Proposed algorithm for the conflicting paths.

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



From the pgr_dijkstraVia - Proposed result it removes the conflicting paths and builds the solution with the results of the pgr_trsp - Proposed algorithm:

WITH
solutions AS (
SELECT path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost FROM pgr_dijkstraVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
ARRAY[6, 3, 6]) WHERE path_id != 1
UNION
SELECT 1 AS path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost FROM pgr_trsp(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
6, 3)),
with_seq AS (
SELECT row_number() over(ORDER BY path_id, path_seq) AS seq, *
FROM solutions),
aggregation AS (SELECT seq, SUM(cost) OVER(ORDER BY seq) AS route_agg_cost FROM with_seq)
SELECT with_seq.*, COALESCE(route_agg_cost, 0) AS route_agg_cost
FROM with_seq LEFT JOIN aggregation ON (with_seq.seq = aggregation.seq + 1);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
1 |       1 |        1 |         6 |       3 |    6 |    4 |    1 |        0 |              0
2 |       1 |        2 |         6 |       3 |    7 |   10 |    1 |        1 |              1
3 |       1 |        3 |         6 |       3 |    8 |   12 |    1 |        2 |              2
4 |       1 |        4 |         6 |       3 |   12 |   13 |    1 |        3 |              3
5 |       1 |        5 |         6 |       3 |   17 |   15 |    1 |        4 |              4
6 |       1 |        6 |         6 |       3 |   16 |    9 |    1 |        5 |              5
7 |       1 |        7 |         6 |       3 |   11 |    8 |    1 |        6 |              6
8 |       1 |        8 |         6 |       3 |    7 |    7 |    1 |        7 |              7
9 |       1 |        9 |         6 |       3 |    3 |   -1 |    0 |        8 |              8
10 |       2 |        1 |         3 |       6 |    3 |    7 |    1 |        0 |              8
11 |       2 |        2 |         3 |       6 |    7 |    4 |    1 |        1 |              9
12 |       2 |        3 |         3 |       6 |    6 |   -2 |    0 |        2 |             10
(12 rows)



Getting the same result as pgr_trspVia:

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


Example 8:

Sometimes U_turn_on_edge flag is ignored when is set to false.

The first step, doing a pgr_dijkstraVia - Proposed does consider not making a U turn on the same edge. But the path $$16 \rightarrow 13$$ (Rows 4 and 5) is restricted and the result is using it.

SELECT * FROM pgr_dijkstraVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
ARRAY[6, 7, 6], 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 |         6 |       7 |    6 |    4 |    1 |        0 |              0
2 |       1 |        2 |         6 |       7 |    7 |   -1 |    0 |        1 |              1
3 |       2 |        1 |         7 |       6 |    7 |    8 |    1 |        0 |              1
4 |       2 |        2 |         7 |       6 |   11 |    9 |    1 |        1 |              2
5 |       2 |        3 |         7 |       6 |   16 |   16 |    1 |        2 |              3
6 |       2 |        4 |         7 |       6 |   15 |    3 |    1 |        3 |              4
7 |       2 |        5 |         7 |       6 |   10 |    2 |    1 |        4 |              5
8 |       2 |        6 |         7 |       6 |    6 |   -2 |    0 |        5 |              6
(8 rows)



When executing the pgr_trsp - Proposed algorithm for the conflicting path, there is no U_turn_on_edge flag.

SELECT 1 AS path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost FROM pgr_trsp(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
7, 6);
path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
---------+----------+-----------+---------+------+------+------+----------
1 |        1 |         7 |       6 |    7 |    4 |    1 |        0
1 |        2 |         7 |       6 |    6 |   -1 |    0 |        1
(2 rows)



Therefore the result ignores the U_turn_on_edge flag when set to false.

SELECT * FROM pgr_trspVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
ARRAY[6, 7, 6], 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 |         6 |       7 |    6 |    4 |    1 |        0 |              0
2 |       1 |        2 |         6 |       7 |    7 |   -1 |    0 |        1 |              1
3 |       2 |        1 |         7 |       6 |    7 |    4 |    1 |        0 |              1
4 |       2 |        2 |         7 |       6 |    6 |   -2 |    0 |        1 |              2
(4 rows)