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Notes on pgr_trsp (2.3.2 release)

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Vicky Vergara edited this page Jan 5, 2017 · 19 revisions

Introduction

pgr_trsp code has issues that are not being fixed yet, but as time passes and new functionality is added to pgRouting with wrappers to hide the issues, not to fix them.

For clarity on the queries:

  • _pgr_trsp (with underscore) is the original code
  • pgr_trsp (lower case) represents the wrapper calling the original code
  • pgr_TRSP (upper case) represents the wrapper calling the replacement function, depending on the function, it can be:
    • pgr_dijkstra
    • pgr_dijkstraVia
    • pgr_withPoints
    • _pgr_withPointsVia

This page intentions is to compare the original code with the wrapped version of the trsp group of functions.

The restriction

The restriction used in the examples does not have to do anything with the graph:

  • No vertex has id: 25, 32 or 33
  • No edge has id: 25, 32 or 33
$$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, 32, 33::TEXT AS via_path$$

therefore the shortest path expected are as if there was no restriction involved

The Vertices signature version

No path representation differences

Original code of pgr_trsp throws Error to represent no path found

SELECT * FROM _pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 15, true, true
);
ERROR:  Error computing path: Path Not Found

dijkstra returns EMPTY SET to represent no path found

SELECT * FROM pgr_dijkstra(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 15
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
(0 rows)

pgr_trsp use the pgr_dijkstra when there are no restrictions therefore returns EMPTY SET to represent no path found

SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 15, true, true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
(0 rows)

pgr_trsp use the original code when there are restrictions therefore throws Error to represent no path found

SELECT * FROM pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 15, true, true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
ERROR:  Error computing path: Path Not Found
CONTEXT:  PL/pgSQL function pgr_trsp(text,integer,integer,boolean,boolean,text) line 29 at RETURN QUERY

routing from/to same location there should be no path

using dijkstra to verify (1 to 1)

SELECT * FROM pgr_dijkstra(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 1
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
(0 rows)

This call uses the replacement function because there are no restrictions (1 to 1) therefore is expected to return EMPTY SET to represent no path found

SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    1, 1,  
    true, 
    true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
(0 rows)

call forcing the use of the original code (1 to 1) therefore is expected to return Error to represent no path found but "finds" a path when there should be no path.

SELECT * FROM _pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    1, 1,  
    true, 
    true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |   1 |   1 |    1
   1 |   2 |   4 |    1
   2 |   5 |   8 |    1
   3 |   6 |   9 |    1
   4 |   9 |  16 |    1
   5 |   4 |   3 |    1
   6 |   3 |   2 |    1
   7 |   2 |   1 |    1
   8 |   1 |  -1 |    0
(9 rows)

trsp with restrictions (1 to 1) use the original code is expected to return Error to represent no path found

SELECT * FROM pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    1, 1,  
    true, 
    true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |   1 |   1 |    1
   1 |   2 |   4 |    1
   2 |   5 |   8 |    1
   3 |   6 |   9 |    1
   4 |   9 |  16 |    1
   5 |   4 |   3 |    1
   6 |   3 |   2 |    1
   7 |   2 |   1 |    1
   8 |   1 |  -1 |    0
(9 rows)

trsp calling the original code with restrictions (1 to 1) is expected to return Error to represent no path found but "finds" a path when there should be no path.

SELECT * FROM _pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    1, 1,  
    true, 
    true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |   1 |   1 |    1
   1 |   2 |   4 |    1
   2 |   5 |   8 |    1
   3 |   6 |   9 |    1
   4 |   9 |  16 |    1
   5 |   4 |   3 |    1
   6 |   3 |   2 |    1
   7 |   2 |   1 |    1
   8 |   1 |  -1 |    0
(9 rows)

Undirected graph

using Dijkstra to verify the shortest path from (2 to 3) on undirected graph

SELECT * FROM pgr_dijkstra(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    2, 3, false
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
   1 |        1 |    2 |    2 |    1 |        0
   2 |        2 |    3 |   -1 |    0 |        1
(2 rows)

using the replacement function because there are no restrictions (2 to 3)

SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    2, 3,
    false, 
    true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |   2 |   2 |    1
   1 |   3 |  -1 |    0
(2 rows)

call to the original function (2 to 3) does not find the shortest path

SELECT * FROM _pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    2, 3,
    false, 
    true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |   2 |   4 |    1
   1 |   5 |   8 |    1
   2 |   6 |   9 |    1
   3 |   9 |  16 |    1
   4 |   4 |   3 |    1
   5 |   3 |  -1 |    0
(6 rows)

trsp with restrictions (2 to 3) does not find the shortest path

SELECT * FROM pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    2, 3,
    false, 
    true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |   2 |   4 |    1
   1 |   5 |   8 |    1
   2 |   6 |   9 |    1
   3 |   9 |  16 |    1
   4 |   4 |   3 |    1
   5 |   3 |  -1 |    0
(6 rows)

calling the original code with restrictions (2 to 3) does not find the shortest path

SELECT * FROM _pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    2, 3,
    false, 
    true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |   2 |   4 |    1
   1 |   5 |   8 |    1
   2 |   6 |   9 |    1
   3 |   9 |  16 |    1
   4 |   4 |   3 |    1
   5 |   3 |  -1 |    0
(6 rows)

TRSP edges signature

No path representation differences

Original code of pgr_trsp throws Error to represent no path found

SELECT * FROM _pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 0.5, 17, 0.5, true, true
);
ERROR:  Error computing path: Path Not Found

pgr_withPoints returns EMPTY SET to represent no path found

SELECT * FROM pgr_withPoints(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    $$(SELECT 1 as pid, 1 as edge_id, 0.5::float as fraction)
    UNION
    (SELECT 2, 17, 0.5)$$,
    -1, -2
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
(0 rows)

Definition of a one edge path

Remember that one characteristic of a path is that for a path of N edges it has N+1 vertices.

For this example, suppose points, where the pid are different even if the edge and fraction are different. One point might be on the left side other on the right side, pgr_trsp does not take into account the side of the point Using the original code (with and without restrictions) it returns a path of N edge and N vertex instead of N edge and N+1 vertices

  • with out restrictions
SELECT * FROM _pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 0.5, 1, 0.5, true, true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |    0
(1 row)
  • with restrictions
SELECT * FROM _pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 0.5, 1, 0.5, true, true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |    0
(1 row)

Using the pgr_withPoints it returns a path of N edge and N+1 vertices

SELECT * FROM pgr_withPoints(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    $$(SELECT 1 as pid, 1 as edge_id, 0.5::float as fraction)
    UNION
    (SELECT 2, 1, 0.5)$$,
    -1, -2
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
   1 |        1 |   -1 |    1 |    0 |        0
   2 |        2 |   -2 |   -1 |    0 |        0
(2 rows)

The pgr_withPoints is used when there are no restrictions

SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 0.5, 1, 0.5, true, true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |    0
   1 |  -2 |  -1 |    0
(2 rows)

The original _pgr_trsp code is used when there are restrictions

SELECT * FROM pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 0.5, 1, 0.5, true, true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |    0
(1 row)

note that pgr_withPoints returns an EMPTY SET when the point is the same

SELECT * FROM pgr_withPoints(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    $$(SELECT 1 as pid, 1 as edge_id, 0.5::float as fraction)
    UNION
    (SELECT 2, 1, 0.5)$$,
    -1, -1
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
(0 rows)

Points on the same edge

The pgr_withPoints is used when there are no restrictions

  • it returns a path of N edges and N+1 vertices
SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 0.5, 1, 0.8, true, true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |  0.3
   1 |  -2 |  -1 |    0
(2 rows)

The original _pgr_trsp is used when there are restrictions

  • it returns a path of N edges and N vertex instead of N edge and N+1 vertices
SELECT * FROM pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    1, 0.5, 1, 0.8, true, true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |  0.3
(1 row)

Undirected graph

the shortest path obtained with pgr_withPoints

SELECT * FROM pgr_withPoints(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    $$(SELECT 1 as pid, 4 as edge_id, 0.5::float as fraction)
    UNION
    (SELECT 2, 2, 0.8)$$,
    -1, -2, directed:=false
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
   1 |        1 |   -1 |    4 |  0.5 |        0
   2 |        2 |    2 |    2 |  0.8 |      0.5
   3 |        3 |   -2 |   -1 |    0 |      1.3
(3 rows)

The original _pgr_trsp is used when there are restrictions

SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    4, 0.5, 2, 0.8, false, true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   4 |  0.5
   1 |   2 |   2 |  0.8
   2 |  -2 |  -1 |    0
(3 rows)

when using restrictions the original _pgr_trsp is used internally

  • it returns a path of N edges and N vertex instead of N edge and N+1 vertices
  • it does not return the shortest path.
SELECT * FROM pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    4, 0.5, 2, 0.8, false, true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   4 |  0.5
   1 |   5 |   8 |    1
   2 |   6 |   9 |    1
   3 |   9 |  16 |    1
   4 |   4 |   3 |    1
   5 |   3 |   2 |  0.2
(6 rows)

Using a points of interest table

The points of interest

SELECT * FROM pointsOfInterest;
 pid |  x  |  y  | edge_id | side | fraction |                  the_geom                  |                  newpoint                  
-----+-----+-----+---------+------+----------+--------------------------------------------+--------------------------------------------
   1 | 1.8 | 0.4 |       1 | l    |      0.4 | 0101000000CDCCCCCCCCCCFC3F9A9999999999D93F | 010100000000000000000000409A9999999999D93F
   2 | 4.2 | 2.4 |      15 | r    |      0.4 | 0101000000CDCCCCCCCCCC10403333333333330340 | 010100000000000000000010403333333333330340
   3 | 2.6 | 3.2 |      12 | l    |      0.6 | 0101000000CDCCCCCCCCCC04409A99999999990940 | 0101000000CDCCCCCCCCCC04400000000000000840
   4 | 0.3 | 1.8 |       6 | r    |      0.3 | 0101000000333333333333D33FCDCCCCCCCCCCFC3F | 0101000000333333333333D33F0000000000000040
   5 | 2.9 | 1.8 |       5 | l    |      0.8 | 01010000003333333333330740CDCCCCCCCCCCFC3F | 01010000000000000000000840CDCCCCCCCCCCFC3F
   6 | 2.2 | 1.7 |       4 | b    |      0.7 | 01010000009A99999999990140333333333333FB3F | 01010000000000000000000040333333333333FB3F
(6 rows)

On pgr_trsp, to be able to use the table information:

  • Each parameter has to be extracted explicitly from the table
  • Regardles of the point pid original value
    • will allways be -1 for the first point
    • will allways be -2 for the second point
SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    (SELECT edge_id::INTEGER  FROM pointsOfInterest WHERE pid = 1),
    (SELECT fraction  FROM pointsOfInterest WHERE pid = 1),
    (SELECT edge_id::INTEGER  FROM pointsOfInterest WHERE pid = 6),
    (SELECT fraction  FROM pointsOfInterest WHERE pid = 6),
    true, true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |  0.6
   1 |   2 |   4 |  0.7
   2 |  -2 |  -1 |    0
(3 rows)

On pgr_withPoints, to be able to use the table information:

  • select statement on the pointsOfInterest table
  • Negative the id to represent the id is a pid
  • The points pids in the result are not renumbered
  • The points pids in the result are represented with negative sign
SELECT * FROM pgr_withPoints(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    $$SELECT pid, edge_id, fraction FROM pointsOfInterest$$,
    -1, -6
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
   1 |        1 |   -1 |    1 |  0.6 |        0
   2 |        2 |    2 |    4 |  0.7 |      0.6
   3 |        3 |   -6 |   -1 |    0 |      1.3
(3 rows)

routing from/to the same point there should not be no path (pid -1 to pid -1)

using pgr_withPoints to check results expecting EMPTY SET to represent no path found

SELECT * FROM pgr_withPoints(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    $$SELECT pid, edge_id, fraction FROM pointsOfInterest$$,
    -1, -1
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
(0 rows)

This call uses the replacement function because there are no restrictions

  • Because the pid is not involved the points are considered different
  • it returns a path
SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    (SELECT edge_id::INTEGER  FROM pointsOfInterest WHERE pid = 1),
    (SELECT fraction  FROM pointsOfInterest WHERE pid = 1),
    (SELECT edge_id::INTEGER  FROM pointsOfInterest WHERE pid = 1),
    (SELECT fraction  FROM pointsOfInterest WHERE pid = 1),
    true, true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |    0
   1 |  -2 |  -1 |    0
(2 rows)

pgr_trsp with restrictions use the original code

  • it returns a path of N edges and N vertex instead of N edge and N+1 vertices
SELECT * FROM pgr_trsp(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    (SELECT edge_id::INTEGER  FROM pointsOfInterest WHERE pid = 1),
    (SELECT fraction  FROM pointsOfInterest WHERE pid = 1),
    (SELECT edge_id::INTEGER  FROM pointsOfInterest WHERE pid = 1),
    (SELECT fraction  FROM pointsOfInterest WHERE pid = 1),
    true, true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |    0
(1 row)

passing in front of other points

using pgr_withPoints to verify the shortest path from pids (1 to 3)

SELECT * FROM pgr_withPoints(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    $$SELECT pid, edge_id, fraction FROM pointsOfInterest$$,
    -1, -3
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
   1 |        1 |   -1 |    1 |  0.6 |        0
   2 |        2 |    2 |    4 |    1 |      0.6
   3 |        3 |    5 |   10 |    1 |      1.6
   4 |        4 |   10 |   12 |  0.6 |      2.6
   5 |        5 |   -3 |   -1 |    0 |      3.2
(5 rows)

pgr_withPoints can be used to see when the route passes in front of other points In ths example point pid=6 is passed in front of

SELECT * FROM pgr_withPoints(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost  FROM edge_table$$,
    $$SELECT pid, edge_id, fraction FROM pointsOfInterest$$,
    -1, -3, details:=true
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
   1 |        1 |   -1 |    1 |  0.6 |        0
   2 |        2 |    2 |    4 |  0.7 |      0.6
   3 |        3 |   -6 |    4 |  0.3 |      1.3
   4 |        4 |    5 |   10 |    1 |      1.6
   5 |        5 |   10 |   12 |  0.6 |      2.6
   6 |        6 |   -3 |   -1 |    0 |      3.2
(6 rows)

Can not be used to see if other points are passed in front of. The pointsOfInterest table is not part of the parameter

SELECT * FROM pgr_TRSP(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    (SELECT edge_id::INTEGER  FROM pointsOfInterest WHERE pid = 1),
    (SELECT fraction  FROM pointsOfInterest WHERE pid = 1),
    (SELECT edge_id::INTEGER  FROM pointsOfInterest WHERE pid = 3),
    (SELECT fraction  FROM pointsOfInterest WHERE pid = 3),
    true, true
);
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |  -1 |   1 |  0.6
   1 |   2 |   4 |    1
   2 |   5 |  10 |    1
   3 |  10 |  12 |  0.6
   4 |  -2 |  -1 |    0
(5 rows)

pgr_trspViaVertices

pgr_trspViaVertices No path representation differences

pgr_trspViaVertices throws error when a path on the route was not found this example no path is found (vertex 15 is disconnected) from the big graph

SELECT * FROM _pgr_trspViaVertices(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 15, 2],
    false, 
    true
);
ERROR:  Error computing path: Path Not Found
CONTEXT:  PL/pgSQL function _pgr_trspviavertices(text,integer[],boolean,boolean,text) line 23 at FOR over SELECT rows

In this example there exists a path from 2 to 1 but only complete routes are processed

SELECT * FROM _pgr_trspViaVertices(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 15, 2, 1],
    false, 
    true
);
ERROR:  Error computing path: Path Not Found
CONTEXT:  PL/pgSQL function _pgr_trspviavertices(text,integer[],boolean,boolean,text) line 23 at FOR over SELECT rows

pgr_dijkstraVia returning what paths of the route it finds or EMPTY SET when non is found this case none is found

SELECT * FROM pgr_dijkstraVia(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 15, 2],
    false
);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost 
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
(0 rows)

this case only from 2 to 1 is found

SELECT * FROM pgr_dijkstraVia(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 15, 2, 1],
    false
);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost 
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       3 |        1 |         2 |       1 |    2 |    1 |    1 |        0 |              0
   2 |       3 |        2 |         2 |       1 |    1 |   -2 |    0 |        1 |              1
(2 rows)

the pgr_dijkstraVia used are for complete routes so its marked as strict:=true therefore the expected result is EMPTY SET to represent no route was found

SELECT * FROM pgr_dijkstraVia(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 1, 2],
    false,
    strict := true
);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost 
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
(0 rows)

when a path does not exist on the route

pgr_TRSPViaVertices using the pgr_dijkstraVia when there are no restrictions. Because there is no path from 1 to 1 then there is no complete route 1 to 1 to 2 therefore the expected result is EMPTY SET to represent no route was found

SELECT * FROM pgr_TRSPViaVertices(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 1, 2],
    false, 
    true
);
 seq | id1 | id2 | id3 | cost 
-----+-----+-----+-----+------
(0 rows)

Using the original code Because there is no path from 1 to 1 then there is no complete route 1 to 1 to 2 therefore the expected result is Error to represent no route was found gives a result even that there is no path from 1 to 1

SELECT * FROM _pgr_trspViaVertices(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 1, 2],
    false, 
    true
);
 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 |   2 |    1
   8 |   1 |   2 |   1 |    1
   9 |   2 |   1 |   1 |    1
  10 |   2 |   2 |  -1 |    0
(10 rows)

with restrictions the original code is used

SELECT * FROM pgr_trspViaVertices(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 1, 2],
    false, 
    true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 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 |   2 |    1
   8 |   1 |   2 |   1 |    1
   9 |   2 |   1 |   1 |    1
  10 |   2 |   2 |  -1 |    0
(10 rows)

Using explicitly the original code

SELECT * FROM _pgr_trspViaVertices(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[1, 1, 2],
    false, 
    true,
    $$SELECT 100::float AS to_cost, 25::INTEGER AS target_id, '32, 33'::TEXT AS via_path$$
);
 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 |   2 |    1
   8 |   1 |   2 |   1 |    1
   9 |   2 |   1 |   1 |    1
  10 |   2 |   2 |  -1 |    0
(10 rows)

from 2 to 3 to 2

dijkstra via shows the shortest route on the two paths

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

the replacement function pgr_dijkstraVia is used because there are no restrictions

SELECT * FROM pgr_TRSPViaVertices(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[2, 3, 2],
    false, 
    true
);
 seq | id1 | id2 | id3 | cost 
-----+-----+-----+-----+------
   1 |   1 |   2 |   2 |    1
   2 |   2 |   3 |   2 |    1
   3 |   2 |   2 |  -1 |    0
(3 rows)

forcing to use the original code, it give not give the shortest path from 2 to 3

SELECT * FROM _pgr_trspViaVertices(
    $$SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table$$,
    ARRAY[2, 3, 2],
    false, 
    true
);
 seq | id1 | id2 | id3 | cost 
-----+-----+-----+-----+------
   1 |   1 |   2 |   4 |    1
   2 |   1 |   5 |   8 |    1
   3 |   1 |   6 |   9 |    1
   4 |   1 |   9 |  16 |    1
   5 |   1 |   4 |   3 |    1
   6 |   2 |   3 |   2 |    1
   7 |   2 |   2 |  -1 |    0
(7 rows)

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