Datos Muestra

The documentation provides very simple example queries based on a small sample network that resembles a city. To be able to execute the mayority of the examples queries, follow the instructions bellow.

Main graph

A graph consists of a set of edges and a set of vertices.

The following city is to be inserted into the database:

_images/Fig1-originalData.png

Information known at this point is the geometry of the edges, cost values, cpacity values, category values and some locations that are not in the graph.

The process to have working topology starts by inserting the edges. After that everything else is calculated.

Edges

The database design for the documentation of pgRouting, keeps in the same row 2 segments, one in the direction of the geometry and the second in the oposite direction. Therfore some information has the reverse_ prefix which corresponds to the segment on the oposite direction of the geometry.

Columna

Descripción

id

A unique identifier.

source

Identifier of the starting vertex of the geometry geom.

target

Identifier of the ending vertex of the geometry geom

cost

Cost to traverse from source to target.

reverse_cost

Cost to traverse from target to source.

capacity

Flow capacity from source to target.

reverse_capacity

Flow capacity from target to source.

category

Flow capacity from target to source.

reverse_category

Flow capacity from target to source.

x1

\(x\) coordinate of the starting vertex of the geometry.

  • For convinience it is saved on the table but can be calculated as ST_X(ST_StartPoint(geom)).

y2

\(y\) coordinate of the ending vertex of the geometry.

  • For convinience it is saved on the table but can be calculated as ST_Y(ST_EndPoint(geom)).

geom

The geometry of the segments.

CREATE TABLE edges (
    id BIGSERIAL PRIMARY KEY,
    source BIGINT,
    target BIGINT,
    cost FLOAT,
    reverse_cost FLOAT,
    capacity BIGINT,
    reverse_capacity BIGINT,
    x1 FLOAT,
    y1 FLOAT,
    x2 FLOAT,
    y2 FLOAT,
    geom geometry
);
CREATE TABLE

Starting on PostgreSQL 12:

...
x1 FLOAT GENERATED ALWAYS AS (ST_X(ST_StartPoint(geom))) STORED,
y1 FLOAT GENERATED ALWAYS AS (ST_Y(ST_StartPoint(geom))) STORED,
x1 FLOAT GENERATED ALWAYS AS (ST_X(ST_EndPoint(geom))) STORED,
y1 FLOAT GENERATED ALWAYS AS (ST_Y(ST_EndPoint(geom))) STORED,
...

Optionally indexes on different columns can be created. The recomendation is to have

  • id indexed.

  • source and target columns indexed to speed up pgRouting queries.

  • geom indexed to speed up gemetry processes that might be needed in the front end.

For this small example the indexes are skipped, except for id

Edges data

Inserting into the database the information of the edges:

INSERT INTO edges (
    cost, reverse_cost,
    capacity, reverse_capacity, geom) VALUES
( 1,  1,  80, 130,   ST_MakeLine(ST_POINT(2, 0), ST_POINT(2, 1))),
(-1,  1,  -1, 100,   ST_MakeLine(ST_POINT(2, 1), ST_POINT(3, 1))),
(-1,  1,  -1, 130,   ST_MakeLine(ST_POINT(3, 1), ST_POINT(4, 1))),
( 1,  1, 100,  50,   ST_MakeLine(ST_POINT(2, 1), ST_POINT(2, 2))),
( 1, -1, 130,  -1,   ST_MakeLine(ST_POINT(3, 1), ST_POINT(3, 2))),
( 1,  1,  50, 100,   ST_MakeLine(ST_POINT(0, 2), ST_POINT(1, 2))),
( 1,  1,  50, 130,   ST_MakeLine(ST_POINT(1, 2), ST_POINT(2, 2))),
( 1,  1, 100, 130,   ST_MakeLine(ST_POINT(2, 2), ST_POINT(3, 2))),
( 1,  1, 130,  80,   ST_MakeLine(ST_POINT(3, 2), ST_POINT(4, 2))),
( 1,  1, 130,  50,   ST_MakeLine(ST_POINT(2, 2), ST_POINT(2, 3))),
( 1, -1, 130,  -1,   ST_MakeLine(ST_POINT(3, 2), ST_POINT(3, 3))),
( 1, -1, 100,  -1,   ST_MakeLine(ST_POINT(2, 3), ST_POINT(3, 3))),
( 1, -1, 100,  -1,   ST_MakeLine(ST_POINT(3, 3), ST_POINT(4, 3))),
( 1,  1,  80, 130,   ST_MakeLine(ST_POINT(2, 3), ST_POINT(2, 4))),
( 1,  1,  80,  50,   ST_MakeLine(ST_POINT(4, 2), ST_POINT(4, 3))),
( 1,  1,  80,  80,   ST_MakeLine(ST_POINT(4, 1), ST_POINT(4, 2))),
( 1,  1, 130, 100,   ST_MakeLine(ST_POINT(0.5, 3.5), ST_POINT(1.999999999999, 3.5))),
( 1,  1,  50, 130,   ST_MakeLine(ST_POINT(3.5, 2.3), ST_POINT(3.5, 4)));
INSERT 0 18

Negative values on the cost, capacity and category means that the edge do not exist.

Vertices

The vertex information is calculated based on the identifier of the edge and the geometry and saved on a table. Saving all the information provided by pgr_extractVertices – Propuesto:

SELECT * INTO vertices
FROM pgr_extractVertices('SELECT id, geom FROM edges ORDER BY id');
SELECT 17

In this case the because the CREATE statement was not used, the definition of an index on the table is needed.

CREATE SEQUENCE vertices_id_seq;
CREATE SEQUENCE
ALTER TABLE vertices ALTER COLUMN id SET DEFAULT nextval('vertices_id_seq');
ALTER TABLE
ALTER SEQUENCE vertices_id_seq OWNED BY vertices.id;
ALTER SEQUENCE
SELECT setval('vertices_id_seq', (SELECT coalesce(max(id)) FROM vertices));
 setval
--------
     17
(1 row)

The structure of the table is:


                                  Table "public.vertices"
  Column   |       Type       | Collation | Nullable |               Default
-----------+------------------+-----------+----------+--------------------------------------
 id        | bigint           |           |          | nextval('vertices_id_seq'::regclass)
 in_edges  | bigint[]         |           |          |
 out_edges | bigint[]         |           |          |
 x         | double precision |           |          |
 y         | double precision |           |          |
 geom      | geometry         |           |          |

Vertices data

The saved information of the vertices is:

SELECT * FROM vertices;
 id | in_edges | out_edges |       x        |  y  |                    geom
----+----------+-----------+----------------+-----+--------------------------------------------
  1 |          | {6}       |              0 |   2 | 010100000000000000000000000000000000000040
  2 |          | {17}      |            0.5 | 3.5 | 0101000000000000000000E03F0000000000000C40
  3 | {6}      | {7}       |              1 |   2 | 0101000000000000000000F03F0000000000000040
  4 | {17}     |           | 1.999999999999 | 3.5 | 010100000068EEFFFFFFFFFF3F0000000000000C40
  5 |          | {1}       |              2 |   0 | 010100000000000000000000400000000000000000
  6 | {1}      | {2,4}     |              2 |   1 | 01010000000000000000000040000000000000F03F
  7 | {4,7}    | {8,10}    |              2 |   2 | 010100000000000000000000400000000000000040
  8 | {10}     | {12,14}   |              2 |   3 | 010100000000000000000000400000000000000840
  9 | {14}     |           |              2 |   4 | 010100000000000000000000400000000000001040
 10 | {2}      | {3,5}     |              3 |   1 | 01010000000000000000000840000000000000F03F
 11 | {5,8}    | {9,11}    |              3 |   2 | 010100000000000000000008400000000000000040
 12 | {11,12}  | {13}      |              3 |   3 | 010100000000000000000008400000000000000840
 13 |          | {18}      |            3.5 | 2.3 | 01010000000000000000000C406666666666660240
 14 | {18}     |           |            3.5 |   4 | 01010000000000000000000C400000000000001040
 15 | {3}      | {16}      |              4 |   1 | 01010000000000000000001040000000000000F03F
 16 | {9,16}   | {15}      |              4 |   2 | 010100000000000000000010400000000000000040
 17 | {13,15}  |           |              4 |   3 | 010100000000000000000010400000000000000840
(17 rows)

Here is where adding more columns to the vertices table can be done. Additional columns names and types will depend on the application.

The topology

This queries based on the vertices data create a topology by filling the source and target columns in the edges table.

/* -- set the source information */
UPDATE edges AS e
SET source = v.id, x1 = x, y1 = y
FROM vertices AS v
WHERE ST_StartPoint(e.geom) = v.geom;
UPDATE 18
/* -- set the target information */
UPDATE edges AS e
SET target = v.id, x2 = x, y2 = y
FROM vertices AS v
WHERE ST_EndPoint(e.geom) = v.geom;
UPDATE 18

Topology data

SELECT id, source, target
FROM edges ORDER BY id;
 id | source | target
----+--------+--------
  1 |      5 |      6
  2 |      6 |     10
  3 |     10 |     15
  4 |      6 |      7
  5 |     10 |     11
  6 |      1 |      3
  7 |      3 |      7
  8 |      7 |     11
  9 |     11 |     16
 10 |      7 |      8
 11 |     11 |     12
 12 |      8 |     12
 13 |     12 |     17
 14 |      8 |      9
 15 |     16 |     17
 16 |     15 |     16
 17 |      2 |      4
 18 |     13 |     14
(18 rows)

Puntos fuera del grafo

Puntos de interés

Some times the applications work «on the fly» starting from a location that is not a vertex in the graph. Those locations, in pgRrouting are called points of interest.

The information needed in the points of interest is pid, edge_id, side, fraction.

On this documentation there will be some 6 fixed points of interest and they will be stored on a table.

Columna

Descripción

pid

A unique identifier.

edge_id

Identifier of the edge nearest edge that allows an arrival to the point.

side

Is it on the left, right or both sides of the segment edge_id

fraction

Where in the segment is the point located.

geom

The geometry of the points.

newPoint

The geometry of the points moved on top of the segment.

CREATE TABLE pointsOfInterest(
    pid BIGSERIAL PRIMARY KEY,
    edge_id BIGINT,
    side CHAR,
    fraction FLOAT,
    geom geometry,
    newPoint geometry);
CREATE TABLE

Geometría de los puntos de interés

Inserting the data of the points of interest:

INSERT INTO pointsOfInterest (geom) VALUES
(ST_POINT(1.8, 0.4)),
(ST_POINT(4.2, 2.4)),
(ST_POINT(2.6, 3.2)),
(ST_POINT(0.3, 1.8)),
(ST_POINT(2.9, 1.8)),
(ST_POINT(2.2, 1.7));
INSERT 0 6

LLenado de puntos de interés

Using pgr_findCloseEdges Calculating for visual purposes the points over the graph.

UPDATE pointsOfInterest AS p SET
  edge_id = q.edge_id,
  side = q.side,
  fraction = q.fraction,
  newPoint = ST_endPoint(q.edge)
FROM (SELECT * FROM pgr_findCloseEdges(
  $$SELECT id, geom FROM edges$$,
  (SELECT array_agg(geom) FROM pointsOfInterest),
  0.5, partial => false)) AS q
WHERE p.geom = q.geom;
UPDATE 6

A special case to arrive from both sides of the edge.

UPDATE pointsOfInterest SET side = 'b'
WHERE pid = 6;
UPDATE 1

Datos de puntos de interés

SELECT pid, edge_id, side, fraction,
       ST_AsText(geom), ST_AsText(newPoint)
FROM pointsOfInterest
ORDER BY pid;
 pid | edge_id | side |      fraction      |   st_astext    |  st_astext
-----+---------+------+--------------------+----------------+--------------
   1 |       1 | l    |                0.4 | POINT(1.8 0.4) | POINT(2 0.4)
   2 |      15 | r    | 0.3999999999999999 | POINT(4.2 2.4) | POINT(4 2.4)
   3 |      12 | l    | 0.6000000000000001 | POINT(2.6 3.2) | POINT(2.6 3)
   4 |       6 | r    |                0.3 | POINT(0.3 1.8) | POINT(0.3 2)
   5 |       5 | l    |                0.8 | POINT(2.9 1.8) | POINT(3 1.8)
   6 |       4 | b    |                0.7 | POINT(2.2 1.7) | POINT(2 1.7)
(6 rows)

Support tables

Combinaciones

Many functions can be used with a combinations of (source, target) pairs when wanting a route from source to target.

For convinence of this documentations, some combinations will be stored on a table:

CREATE TABLE combinations (
    source BIGINT,
    target BIGINT
);
CREATE TABLE

Insertar los datos:

INSERT INTO combinations (
    source, target) VALUES
(5, 6),
(5, 10),
(6, 5),
(6, 15),
(6, 14);
INSERT 0 5

Combinations data

SELECT * FROM combinations;
 source | target
--------+--------
      5 |      6
      5 |     10
      6 |      5
      6 |     15
      6 |     14
(5 rows)

Restricciones

Some functions accept soft restrictions about the segments.

The creation of the restrictions table

CREATE TABLE restrictions (
    id SERIAL PRIMARY KEY,
    path BIGINT[],
    cost FLOAT
);
CREATE TABLE

Agregando las restricciones

INSERT INTO restrictions (path, cost) VALUES
(ARRAY[4, 7], 100),
(ARRAY[8, 11], 100),
(ARRAY[7, 10], 100),
(ARRAY[3, 5, 9], 4),
(ARRAY[9, 16], 100);
INSERT 0 5

Datos de restricciones

SELECT * FROM restrictions;
 id |  path   | cost
----+---------+------
  1 | {4,7}   |  100
  2 | {8,11}  |  100
  3 | {7,10}  |  100
  4 | {3,5,9} |    4
  5 | {9,16}  |  100
(5 rows)

Imágenes

  • Las flechas rojas corresponden cuando cost > 0 en la tabla de aristas.

  • Las flechas azules corresponden cuando reverse_cost > 0 en la tabla de aristas.

  • Los puntos están fuera del grafo.

  • Haga clic en el grafo para ampliarlo.

Directed graph with cost and reverse_cost

Cuando se trabaja con redes de ciudades, esto se recomienda para el punto de vista de los vehículos.

_images/Fig1-originalData.png

Directed, with cost and reverse_cost

Undirected graph with cost and reverse_cost

Cuando se trabaja con redes de ciudades, esto se recomienda para el punto de vista de los peatones.

_images/Fig6-undirected.png

Undirected, with cost and reverse cost

Directed graph with cost

_images/Fig2-cost.png

Directed, with cost

Undirected graph with cost

_images/Fig4-costUndirected.png

Undirected, with cost

Datos de Recogida y Entrega

This data example lc101 is from data published at https://www.sintef.no/projectweb/top/pdptw/li-lim-benchmark/

Los vehículos

There are 25 vehciles in the problem all with the same characteristics.

CREATE TABLE v_lc101(
  id BIGINT NOT NULL primary key,
  capacity BIGINT DEFAULT 200,
  start_x FLOAT DEFAULT 30,
  start_y FLOAT DEFAULT 50,
  start_open INTEGER DEFAULT 0,
  start_close INTEGER DEFAULT 1236);
CREATE TABLE
/* create 25 vehciles */
INSERT INTO v_lc101 (id)
(SELECT * FROM generate_series(1, 25));
INSERT 0 25

The original orders

The data comes in different rows for the pickup and the delivery of the same order.

CREATE table lc101_c(
  id BIGINT not null primary key,
  x DOUBLE PRECISION,
  y DOUBLE PRECISION,
  demand INTEGER,
  open INTEGER,
  close INTEGER,
  service INTEGER,
  pindex BIGINT,
  dindex BIGINT
);
CREATE TABLE
/* the original data */
INSERT INTO lc101_c(
  id,     x,    y, demand, open, close, service, pindex, dindex) VALUES
(  1,    45,   68,   -10,   912,   967,   90,   11,    0),
(  2,    45,   70,   -20,   825,   870,   90,    6,    0),
(  3,    42,   66,    10,    65,   146,   90,    0,   75),
(  4,    42,   68,   -10,   727,   782,   90,    9,    0),
(  5,    42,   65,    10,    15,    67,   90,    0,    7),
(  6,    40,   69,    20,   621,   702,   90,    0,    2),
(  7,    40,   66,   -10,   170,   225,   90,    5,    0),
(  8,    38,   68,    20,   255,   324,   90,    0,   10),
(  9,    38,   70,    10,   534,   605,   90,    0,    4),
( 10,    35,   66,   -20,   357,   410,   90,    8,    0),
( 11,    35,   69,    10,   448,   505,   90,    0,    1),
( 12,    25,   85,   -20,   652,   721,   90,   18,    0),
( 13,    22,   75,    30,    30,    92,   90,    0,   17),
( 14,    22,   85,   -40,   567,   620,   90,   16,    0),
( 15,    20,   80,   -10,   384,   429,   90,   19,    0),
( 16,    20,   85,    40,   475,   528,   90,    0,   14),
( 17,    18,   75,   -30,    99,   148,   90,   13,    0),
( 18,    15,   75,    20,   179,   254,   90,    0,   12),
( 19,    15,   80,    10,   278,   345,   90,    0,   15),
( 20,    30,   50,    10,    10,    73,   90,    0,   24),
( 21,    30,   52,   -10,   914,   965,   90,   30,    0),
( 22,    28,   52,   -20,   812,   883,   90,   28,    0),
( 23,    28,   55,    10,   732,   777,    0,    0,  103),
( 24,    25,   50,   -10,    65,   144,   90,   20,    0),
( 25,    25,   52,    40,   169,   224,   90,    0,   27),
( 26,    25,   55,   -10,   622,   701,   90,   29,    0),
( 27,    23,   52,   -40,   261,   316,   90,   25,    0),
( 28,    23,   55,    20,   546,   593,   90,    0,   22),
( 29,    20,   50,    10,   358,   405,   90,    0,   26),
( 30,    20,   55,    10,   449,   504,   90,    0,   21),
( 31,    10,   35,   -30,   200,   237,   90,   32,    0),
( 32,    10,   40,    30,    31,   100,   90,    0,   31),
( 33,     8,   40,    40,    87,   158,   90,    0,   37),
( 34,     8,   45,   -30,   751,   816,   90,   38,    0),
( 35,     5,   35,    10,   283,   344,   90,    0,   39),
( 36,     5,   45,    10,   665,   716,    0,    0,  105),
( 37,     2,   40,   -40,   383,   434,   90,   33,    0),
( 38,     0,   40,    30,   479,   522,   90,    0,   34),
( 39,     0,   45,   -10,   567,   624,   90,   35,    0),
( 40,    35,   30,   -20,   264,   321,   90,   42,    0),
( 41,    35,   32,   -10,   166,   235,   90,   43,    0),
( 42,    33,   32,    20,    68,   149,   90,    0,   40),
( 43,    33,   35,    10,    16,    80,   90,    0,   41),
( 44,    32,   30,    10,   359,   412,   90,    0,   46),
( 45,    30,   30,    10,   541,   600,   90,    0,   48),
( 46,    30,   32,   -10,   448,   509,   90,   44,    0),
( 47,    30,   35,   -10,  1054,  1127,   90,   49,    0),
( 48,    28,   30,   -10,   632,   693,   90,   45,    0),
( 49,    28,   35,    10,  1001,  1066,   90,    0,   47),
( 50,    26,   32,    10,   815,   880,   90,    0,   52),
( 51,    25,   30,    10,   725,   786,    0,    0,  101),
( 52,    25,   35,   -10,   912,   969,   90,   50,    0),
( 53,    44,    5,    20,   286,   347,   90,    0,   58),
( 54,    42,   10,    40,   186,   257,   90,    0,   60),
( 55,    42,   15,   -40,    95,   158,   90,   57,    0),
( 56,    40,    5,    30,   385,   436,   90,    0,   59),
( 57,    40,   15,    40,    35,    87,   90,    0,   55),
( 58,    38,    5,   -20,   471,   534,   90,   53,    0),
( 59,    38,   15,   -30,   651,   740,   90,   56,    0),
( 60,    35,    5,   -40,   562,   629,   90,   54,    0),
( 61,    50,   30,   -10,   531,   610,   90,   67,    0),
( 62,    50,   35,    20,   262,   317,   90,    0,   68),
( 63,    50,   40,    50,   171,   218,   90,    0,   74),
( 64,    48,   30,    10,   632,   693,    0,    0,  102),
( 65,    48,   40,    10,    76,   129,   90,    0,   72),
( 66,    47,   35,    10,   826,   875,   90,    0,   69),
( 67,    47,   40,    10,    12,    77,   90,    0,   61),
( 68,    45,   30,   -20,   734,   777,   90,   62,    0),
( 69,    45,   35,   -10,   916,   969,   90,   66,    0),
( 70,    95,   30,   -30,   387,   456,   90,   81,    0),
( 71,    95,   35,    20,   293,   360,   90,    0,   77),
( 72,    53,   30,   -10,   450,   505,   90,   65,    0),
( 73,    92,   30,   -10,   478,   551,   90,   76,    0),
( 74,    53,   35,   -50,   353,   412,   90,   63,    0),
( 75,    45,   65,   -10,   997,  1068,   90,    3,    0),
( 76,    90,   35,    10,   203,   260,   90,    0,   73),
( 77,    88,   30,   -20,   574,   643,   90,   71,    0),
( 78,    88,   35,    20,   109,   170,    0,    0,  104),
( 79,    87,   30,    10,   668,   731,   90,    0,   80),
( 80,    85,   25,   -10,   769,   820,   90,   79,    0),
( 81,    85,   35,    30,    47,   124,   90,    0,   70),
( 82,    75,   55,    20,   369,   420,   90,    0,   85),
( 83,    72,   55,   -20,   265,   338,   90,   87,    0),
( 84,    70,   58,    20,   458,   523,   90,    0,   89),
( 85,    68,   60,   -20,   555,   612,   90,   82,    0),
( 86,    66,   55,    10,   173,   238,   90,    0,   91),
( 87,    65,   55,    20,    85,   144,   90,    0,   83),
( 88,    65,   60,   -10,   645,   708,   90,   90,    0),
( 89,    63,   58,   -20,   737,   802,   90,   84,    0),
( 90,    60,   55,    10,    20,    84,   90,    0,   88),
( 91,    60,   60,   -10,   836,   889,   90,   86,    0),
( 92,    67,   85,    20,   368,   441,   90,    0,   93),
( 93,    65,   85,   -20,   475,   518,   90,   92,    0),
( 94,    65,   82,   -10,   285,   336,   90,   96,    0),
( 95,    62,   80,   -20,   196,   239,   90,   98,    0),
( 96,    60,   80,    10,    95,   156,   90,    0,   94),
( 97,    60,   85,    30,   561,   622,    0,    0,  106),
( 98,    58,   75,    20,    30,    84,   90,    0,   95),
( 99,    55,   80,   -20,   743,   820,   90,  100,    0),
( 100,   55,   85,    20,   647,   726,   90,    0,   99),
( 101,   25,   30,   -10,   725,   786,   90,   51,    0),
( 102,   48,   30,   -10,   632,   693,   90,   64,    0),
( 103,   28,   55,   -10,   732,   777,   90,   23,    0),
( 104,   88,   35,   -20,   109,   170,   90,   78,    0),
( 105,    5,   45,   -10,   665,   716,   90,   36,    0),
( 106,   60,   85,   -30,   561,   622,   90,   97,    0);
INSERT 0 106

Las órdenes

The original data needs to be converted to an appropiate table:

WITH deliveries AS (SELECT * FROM lc101_c WHERE dindex = 0)
SELECT
  row_number() over() AS id, p.demand,
  p.id as p_node_id, p.x AS p_x, p.y AS p_y, p.open AS p_open, p.close as p_close, p.service as p_service,
  d.id as d_node_id, d.x AS d_x, d.y AS d_y, d.open AS d_open, d.close as d_close, d.service as d_service
INTO c_lc101
FROM deliveries as d JOIN lc101_c as p ON (d.pindex = p.id);
SELECT 53
SELECT * FROM c_lc101 LIMIT 1;
 id | demand | p_node_id | p_x | p_y | p_open | p_close | p_service | d_node_id | d_x | d_y | d_open | d_close | d_service
----+--------+-----------+-----+-----+--------+---------+-----------+-----------+-----+-----+--------+---------+-----------
  1 |     10 |         3 |  42 |  66 |     65 |     146 |        90 |        75 |  45 |  65 |    997 |    1068 |        90
(1 row)