pgr_dijkstra

pgr_dijkstra — Shortest path(s) using Dijkstra algorithm.

_images/boost-inside.jpeg

Boost Graph Inside

Disponibilidad

  • Versión 3.1.0

  • Versión 3.0.0

    • Funciones oficiales

  • Version 2.2.0

  • Versión 2.1.0

  • Versión 2.0.0

Descripción

Dijkstra’s algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956. It is a graph search algorithm that solves the shortest path problem for a graph with non-negative edge path costs, producing a shortest path from a starting vertex to an ending vertex. This implementation can be used with a directed graph and an undirected graph.

  • El proceso se realiza sólo en las aristas con costos positivos.

    • A negative value on a cost column is interpreted as the edge does not exist.

  • Valores son regresados cuando hay una ruta.

  • When there is no path:

    • When the starting vertex and ending vertex are the same.

      • The aggregate cost of the non included values \((v, v)\) is \(0\)

    • Cuando el vértice inicial y el vértice final son diferentes y no hay camino:

      • The aggregate cost the non included values \((u, v)\) is \(\infty\)

  • For optimization purposes, any duplicated value in the starting vertices or on the ending vertices are ignored.

  • Running time: \(O(| start\ vids | * (V \log V + E))\)

  • Tiempo de ejecución: \(O(| start\_vids | * (V \log V + E))\)

Firmas

Resumen

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

Uno a Uno

pgr_dijkstra(Edges SQL, start vid,  end vid  [, directed])
pgr_dijkstra(Edges SQL, start vid, end vid  [, directed])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Ejemplo

Del vértice \(2\) al vértice \(3\) en un grafo dirigido

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edge_table',
  2, 3, true);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |    8 |    1 |        1
   3 |        3 |    6 |    9 |    1 |        2
   4 |        4 |    9 |   16 |    1 |        3
   5 |        5 |    4 |    3 |    1 |        4
   6 |        6 |    3 |   -1 |    0 |        5
(6 rows)

One to Many

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

From vertex \(2\) to vertices \(\{3, 12\}\) on a directed

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edge_table',
  2, ARRAY[3, 12]);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |       3 |    2 |    4 |    1 |        0
   2 |        2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |       3 |    6 |    9 |    1 |        2
   4 |        4 |       3 |    9 |   16 |    1 |        3
   5 |        5 |       3 |    4 |    3 |    1 |        4
   6 |        6 |       3 |    3 |   -1 |    0 |        5
   7 |        1 |      12 |    2 |    4 |    1 |        0
   8 |        2 |      12 |    5 |    8 |    1 |        1
   9 |        3 |      12 |    6 |    9 |    1 |        2
  10 |        4 |      12 |    9 |   15 |    1 |        3
  11 |        5 |      12 |   12 |   -1 |    0 |        4
(11 rows)

Muchos a Uno

pgr_dijkstra(Edges SQL, start vids, end vids [, directed])
RETURNS SET OF (seq, path_seq, start vid, node, edge, cost, agg_cost)
OR EMPTY SET
Ejemplo

From vertices \(\{2, 7\}\) to vertex \(12\) on a directed graph

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edge_table',
  ARRAY[2, 7], 12);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         2 |    2 |    4 |    1 |        0
   2 |        2 |         2 |    5 |   10 |    1 |        1
   3 |        3 |         2 |   10 |   12 |    1 |        2
   4 |        4 |         2 |   11 |   13 |    1 |        3
   5 |        5 |         2 |   12 |   -1 |    0 |        4
   6 |        1 |         7 |    7 |    6 |    1 |        0
   7 |        2 |         7 |    8 |    7 |    1 |        1
   8 |        3 |         7 |    5 |   10 |    1 |        2
   9 |        4 |         7 |   10 |   12 |    1 |        3
  10 |        5 |         7 |   11 |   13 |    1 |        4
  11 |        6 |         7 |   12 |   -1 |    0 |        5
(11 rows)

Muchos a Muchos

pgr_dijkstra(Edges SQL, start vids, end vids [, directed])
RETURNS SET OF (seq, path_seq, start vid, end vid, node, edge, cost, agg_cost)
OR EMPTY SET
Ejemplo

From vertices \(\{2, 7\}\) to vertices \(\{3, 12\}\) on an undirected graph

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edge_table',
  ARRAY[2, 7], ARRAY[3, 12],
  directed => false);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       3 |    2 |    2 |    1 |        0
   2 |        2 |         2 |       3 |    3 |   -1 |    0 |        1
   3 |        1 |         2 |      12 |    2 |    4 |    1 |        0
   4 |        2 |         2 |      12 |    5 |   10 |    1 |        1
   5 |        3 |         2 |      12 |   10 |   12 |    1 |        2
   6 |        4 |         2 |      12 |   11 |   13 |    1 |        3
   7 |        5 |         2 |      12 |   12 |   -1 |    0 |        4
   8 |        1 |         7 |       3 |    7 |    6 |    1 |        0
   9 |        2 |         7 |       3 |    8 |    7 |    1 |        1
  10 |        3 |         7 |       3 |    5 |    4 |    1 |        2
  11 |        4 |         7 |       3 |    2 |    2 |    1 |        3
  12 |        5 |         7 |       3 |    3 |   -1 |    0 |        4
  13 |        1 |         7 |      12 |    7 |    6 |    1 |        0
  14 |        2 |         7 |      12 |    8 |    7 |    1 |        1
  15 |        3 |         7 |      12 |    5 |    8 |    1 |        2
  16 |        4 |         7 |      12 |    6 |    9 |    1 |        3
  17 |        5 |         7 |      12 |    9 |   15 |    1 |        4
  18 |        6 |         7 |      12 |   12 |   -1 |    0 |        5
(18 rows)

Combinaciones

pgr_dijkstra(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (seq, path_seq, start vid, end vid, node, edge, cost, agg_cost)
OR EMPTY SET
Ejemplo

Uso de una tabla de combinaciones en un grafo no direccionado

The combinations table:

SELECT source, target FROM combinations_table;
 source | target
--------+--------
      1 |      2
      1 |      3
      2 |      1
      2 |      4
      2 |     17
(5 rows)

The query:

SELECT * FROM pgr_Dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  'SELECT source, target FROM combinations_table',
  false);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         1 |       2 |    1 |    1 |    1 |        0
   2 |        2 |         1 |       2 |    2 |   -1 |    0 |        1
   3 |        1 |         1 |       3 |    1 |    1 |    1 |        0
   4 |        2 |         1 |       3 |    2 |    2 |    1 |        1
   5 |        3 |         1 |       3 |    3 |   -1 |    0 |        2
   6 |        1 |         2 |       1 |    2 |    1 |    1 |        0
   7 |        2 |         2 |       1 |    1 |   -1 |    0 |        1
   8 |        1 |         2 |       4 |    2 |    2 |    1 |        0
   9 |        2 |         2 |       4 |    3 |    3 |    1 |        1
  10 |        3 |         2 |       4 |    4 |   -1 |    0 |        2
(10 rows)

Parámetros

Columna

Tipo

Descripción

Edges SQL

TEXT

Edges SQL as described below

Combinations SQL

TEXT

Combinations SQL as described below

start vid

BIGINT

Identificador del vértice inicial de la ruta.

start vids

ARRAY[BIGINT]

Arreglo de identificadores de vértices iniciales.

end vid

BIGINT

Identificador del vértice final de la ruta.

end vids

ARRAY[BIGINT]

Arreglo de identificadores de vértices finales.

Optional parameters

Columna

Tipo

default

Descripción

directed

BOOLEAN

true

  • When true the graph is considered Directed

  • Cuando false el gráfo se considera No Dirigido.

Consultas internas

Edges SQL

Columna

Tipo

x Defecto

Descripción

id

ANY-INTEGER

Identificador de la arista.

source

ANY-INTEGER

Identificador del primer vértice extremo de la arista.

target

ANY-INTEGER

Identificador del segundo vértice extremo de la arista.

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.

Donde:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Combinations SQL

Parámetro

Tipo

Descripción

source

ANY-INTEGER

Identifier of the departure vertex.

target

ANY-INTEGER

Identifier of the arrival vertex.

Donde:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

Columnas de Devoluciones

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

Columna

Tipo

Descripción

seq

INTEGER

Valor secuencial a partir de 1.

path_seq

INTEGER

Posición relativa en la ruta. Tiene el valor 1 para el principio de una ruta.

start_vid

BIGINT

Identificador del vértice inicial. Se devuelve cuando hay varias vetrices iniciales en la consulta.

end_vid

BIGINT

Identificador del vértice final. Se devuelve cuando hay varios vértices finales en la consulta.

node

BIGINT

Identificador del nodo en la ruta de start_vid a 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

Costo del desplazamiento desde node usando `` edge`` hasta el siguiente nodo en la secuencia de ruta.

agg_cost

FLOAT

Aggregate cost from start_vid to node.

Ejemplos Adicionales

Ejemplo

Demonstration of repeated values are ignored, and result is sorted.

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edge_table',
  ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         3 |       4 |    3 |    5 |    1 |        0
   2 |        2 |         3 |       4 |    6 |    9 |    1 |        1
   3 |        3 |         3 |       4 |    9 |   16 |    1 |        2
   4 |        4 |         3 |       4 |    4 |   -1 |    0 |        3
   5 |        1 |         3 |       5 |    3 |    2 |    1 |        0
   6 |        2 |         3 |       5 |    2 |    4 |    1 |        1
   7 |        3 |         3 |       5 |    5 |   -1 |    0 |        2
   8 |        1 |         4 |       3 |    4 |    3 |    1 |        0
   9 |        2 |         4 |       3 |    3 |   -1 |    0 |        1
  10 |        1 |         4 |       5 |    4 |    3 |    1 |        0
  11 |        2 |         4 |       5 |    3 |    5 |    1 |        1
  12 |        3 |         4 |       5 |    6 |    8 |    1 |        2
  13 |        4 |         4 |       5 |    5 |   -1 |    0 |        3
  14 |        1 |         5 |       3 |    5 |    8 |    1 |        0
  15 |        2 |         5 |       3 |    6 |    9 |    1 |        1
  16 |        3 |         5 |       3 |    9 |   16 |    1 |        2
  17 |        4 |         5 |       3 |    4 |    3 |    1 |        3
  18 |        5 |         5 |       3 |    3 |   -1 |    0 |        4
  19 |        1 |         5 |       4 |    5 |    8 |    1 |        0
  20 |        2 |         5 |       4 |    6 |    9 |    1 |        1
  21 |        3 |         5 |       4 |    9 |   16 |    1 |        2
  22 |        4 |         5 |       4 |    4 |   -1 |    0 |        3
(22 rows)

Ejemplo

Making start_vids the same as end_vids.

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edge_table',
  ARRAY[5, 3, 4], ARRAY[5, 3, 4]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         3 |       4 |    3 |    5 |    1 |        0
   2 |        2 |         3 |       4 |    6 |    9 |    1 |        1
   3 |        3 |         3 |       4 |    9 |   16 |    1 |        2
   4 |        4 |         3 |       4 |    4 |   -1 |    0 |        3
   5 |        1 |         3 |       5 |    3 |    2 |    1 |        0
   6 |        2 |         3 |       5 |    2 |    4 |    1 |        1
   7 |        3 |         3 |       5 |    5 |   -1 |    0 |        2
   8 |        1 |         4 |       3 |    4 |    3 |    1 |        0
   9 |        2 |         4 |       3 |    3 |   -1 |    0 |        1
  10 |        1 |         4 |       5 |    4 |    3 |    1 |        0
  11 |        2 |         4 |       5 |    3 |    5 |    1 |        1
  12 |        3 |         4 |       5 |    6 |    8 |    1 |        2
  13 |        4 |         4 |       5 |    5 |   -1 |    0 |        3
  14 |        1 |         5 |       3 |    5 |    8 |    1 |        0
  15 |        2 |         5 |       3 |    6 |    9 |    1 |        1
  16 |        3 |         5 |       3 |    9 |   16 |    1 |        2
  17 |        4 |         5 |       3 |    4 |    3 |    1 |        3
  18 |        5 |         5 |       3 |    3 |   -1 |    0 |        4
  19 |        1 |         5 |       4 |    5 |    8 |    1 |        0
  20 |        2 |         5 |       4 |    6 |    9 |    1 |        1
  21 |        3 |         5 |       4 |    9 |   16 |    1 |        2
  22 |        4 |         5 |       4 |    4 |   -1 |    0 |        3
(22 rows)

Ejemplo

Manually assigned vertex combinations.

SELECT * FROM pgr_Dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3)) AS combinations (source, target)');
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
   2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
   4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
   5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
   6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
   7 |        1 |         2 |       5 |    2 |    4 |    1 |        0
   8 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
   9 |        1 |        11 |       3 |   11 |   13 |    1 |        0
  10 |        2 |        11 |       3 |   12 |   15 |    1 |        1
  11 |        3 |        11 |       3 |    9 |   16 |    1 |        2
  12 |        4 |        11 |       3 |    4 |    3 |    1 |        3
  13 |        5 |        11 |       3 |    3 |   -1 |    0 |        4
(13 rows)

Los ejemplos de esta sección se basan en la red Datos Muestra.

For directed graphs with cost and reverse_cost columns

_images/Fig1-originalData.png

Directed graph with cost and reverse cost columns

Example 1

Path from \(2\) to \(3\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  2, 3
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |    8 |    1 |        1
   3 |        3 |    6 |    9 |    1 |        2
   4 |        4 |    9 |   16 |    1 |        3
   5 |        5 |    4 |    3 |    1 |        4
   6 |        6 |    3 |   -1 |    0 |        5
(6 rows)

Example 2

Path from \(2\) to \(5\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  2, 5
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |   -1 |    0 |        1
(2 rows)

Example 3

Path from \(11\) to \(3\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  11, 3
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   11 |   13 |    1 |        0
   2 |        2 |   12 |   15 |    1 |        1
   3 |        3 |    9 |   16 |    1 |        2
   4 |        4 |    4 |    3 |    1 |        3
   5 |        5 |    3 |   -1 |    0 |        4
(5 rows)

Example 4

Path from \(11\) to \(5\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  11, 5
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   11 |   13 |    1 |        0
   2 |        2 |   12 |   15 |    1 |        1
   3 |        3 |    9 |    9 |    1 |        2
   4 |        4 |    6 |    8 |    1 |        3
   5 |        5 |    5 |   -1 |    0 |        4
(5 rows)

Example 5

Using One to Many to get the solution of examples 1 and 2

Paths \(\{2\}\rightarrow\{3, 5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  2, ARRAY[3, 5]
);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |       3 |    2 |    4 |    1 |        0
   2 |        2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |       3 |    6 |    9 |    1 |        2
   4 |        4 |       3 |    9 |   16 |    1 |        3
   5 |        5 |       3 |    4 |    3 |    1 |        4
   6 |        6 |       3 |    3 |   -1 |    0 |        5
   7 |        1 |       5 |    2 |    4 |    1 |        0
   8 |        2 |       5 |    5 |   -1 |    0 |        1
(8 rows)

Example 6

Using Many to One to get the solution of examples 2 and 4

Paths \(\{2, 11\}\rightarrow\{5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  ARRAY[2, 11], 5
);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         2 |    2 |    4 |    1 |        0
   2 |        2 |         2 |    5 |   -1 |    0 |        1
   3 |        1 |        11 |   11 |   13 |    1 |        0
   4 |        2 |        11 |   12 |   15 |    1 |        1
   5 |        3 |        11 |    9 |    9 |    1 |        2
   6 |        4 |        11 |    6 |    8 |    1 |        3
   7 |        5 |        11 |    5 |   -1 |    0 |        4
(7 rows)

Example 7

Using Many to Many to get the solution of examples 1 to 4

Paths \(\{2, 11\}\rightarrow\{3, 5\}\)

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

Example 8

Using Combinations to get the solution of examples 1 to 3

Paths \(\{2\}\rightarrow\{3, 5\}\cup\{11\}\rightarrow\{3\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3)) AS combinations (source, target)'
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
   2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
   4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
   5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
   6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
   7 |        1 |         2 |       5 |    2 |    4 |    1 |        0
   8 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
   9 |        1 |        11 |       3 |   11 |   13 |    1 |        0
  10 |        2 |        11 |       3 |   12 |   15 |    1 |        1
  11 |        3 |        11 |       3 |    9 |   16 |    1 |        2
  12 |        4 |        11 |       3 |    4 |    3 |    1 |        3
  13 |        5 |        11 |       3 |    3 |   -1 |    0 |        4
(13 rows)

For undirected graphs with cost and reverse_cost columns

_images/Fig6-undirected.png

Undirected graph with cost and reverse cost columns

Example 9

Path from \(2\) to \(3\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, 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)

Example 10

Path from \(2\) to \(5\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  2, 5,
  false
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |   -1 |    0 |        1
(2 rows)

Example 11

Path from \(11\) to \(3\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  11, 3,
  false
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   11 |   11 |    1 |        0
   2 |        2 |    6 |    5 |    1 |        1
   3 |        3 |    3 |   -1 |    0 |        2
(3 rows)

Example 12

Path from \(11\) to \(5\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  11, 5,
  false
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   11 |   11 |    1 |        0
   2 |        2 |    6 |    8 |    1 |        1
   3 |        3 |    5 |   -1 |    0 |        2
(3 rows)

Example 13

Using One to Many to get the solution of examples 9 and 10

Paths \(\{2\}\rightarrow\{3, 5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  2, ARRAY[3,5],
  false
);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |       3 |    2 |    2 |    1 |        0
   2 |        2 |       3 |    3 |   -1 |    0 |        1
   3 |        1 |       5 |    2 |    4 |    1 |        0
   4 |        2 |       5 |    5 |   -1 |    0 |        1
(4 rows)

Example 14

Using Many to One to get the solution of examples 10 and 12

Paths \(\{2, 11\}\rightarrow\{5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  ARRAY[2,11], 5,
  false
);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         2 |    2 |    4 |    1 |        0
   2 |        2 |         2 |    5 |   -1 |    0 |        1
   3 |        1 |        11 |   11 |   12 |    1 |        0
   4 |        2 |        11 |   10 |   10 |    1 |        1
   5 |        3 |        11 |    5 |   -1 |    0 |        2
(5 rows)

Example 15

Using Many to Many to get the solution of examples 9 to 12

Paths \(\{2, 11\}\rightarrow\{3, 5\}\)

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

Example 16

Using Combinations to get the solution of examples 9 to 11

Paths \(\{2\}\rightarrow\{3, 5\}\cup\{11\}\rightarrow\{3\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3)) AS combinations (source, target)',
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       3 |    2 |    2 |    1 |        0
   2 |        2 |         2 |       3 |    3 |   -1 |    0 |        1
   3 |        1 |         2 |       5 |    2 |    4 |    1 |        0
   4 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
   5 |        1 |        11 |       3 |   11 |   11 |    1 |        0
   6 |        2 |        11 |       3 |    6 |    5 |    1 |        1
   7 |        3 |        11 |       3 |    3 |   -1 |    0 |        2
(7 rows)

For directed graphs only with cost column

_images/Fig2-cost.png

Directed graph only with cost column

Example 17

Path from \(2\) to \(3\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  2, 3
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)

Example 18

Path from \(2\) to \(5\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  2, 5
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |   -1 |    0 |        1
(2 rows)

Example 19

Path from \(11\) to \(3\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  11, 3
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)

Example 20

Path from \(11\) to \(5\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  11, 5
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)

Example 21

Using One to Many to get the solution of examples 17 and 18

Paths \(\{2\}\rightarrow\{3, 5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  2, ARRAY[3,5]
);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |       5 |    2 |    4 |    1 |        0
   2 |        2 |       5 |    5 |   -1 |    0 |        1
(2 rows)

Example 22

Using Many to One to get the solution of examples 18 and 20

Paths \(\{2, 11\}\rightarrow\{5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  ARRAY[2,11], 5
);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         2 |    2 |    4 |    1 |        0
   2 |        2 |         2 |    5 |   -1 |    0 |        1
(2 rows)

Example 23

Using Many to Many to get the solution of examples 17 to 20

Paths \(\{2, 11\}\rightarrow\{3, 5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  ARRAY[2, 11], ARRAY[3,5]
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       5 |    2 |    4 |    1 |        0
   2 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
(2 rows)

Example 24

Using Combinations to get the solution of examples 17 to 19

Paths \(\{2\}\rightarrow\{3, 5\}\cup\{11\}\rightarrow\{3\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3)) AS combinations (source, target)'
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       5 |    2 |    4 |    1 |        0
   2 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
(2 rows)

For undirected graphs only with cost column

_images/Fig4-costUndirected.png

Undirected graph only with cost column

Example 25

Path from \(2\) to \(3\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  2, 3,
  false
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |    8 |    1 |        1
   3 |        3 |    6 |    5 |    1 |        2
   4 |        4 |    3 |   -1 |    0 |        3
(4 rows)

Example 26

Path from \(2\) to \(5\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  2, 5,
  false
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |   -1 |    0 |        1
(2 rows)

Example 27

Path from \(11\) to \(3\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  11, 3,
  false
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   11 |   11 |    1 |        0
   2 |        2 |    6 |    5 |    1 |        1
   3 |        3 |    3 |   -1 |    0 |        2
(3 rows)

Example 28

Path from \(11\) to \(5\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  11, 5,
  false
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   11 |   11 |    1 |        0
   2 |        2 |    6 |    8 |    1 |        1
   3 |        3 |    5 |   -1 |    0 |        2
(3 rows)

Example 29

Using One to Many to get the solution of examples 17 and 18

Paths \(\{2\}\rightarrow\{3, 5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  2, ARRAY[3,5],
  false
);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |       3 |    2 |    4 |    1 |        0
   2 |        2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |       3 |    6 |    5 |    1 |        2
   4 |        4 |       3 |    3 |   -1 |    0 |        3
   5 |        1 |       5 |    2 |    4 |    1 |        0
   6 |        2 |       5 |    5 |   -1 |    0 |        1
(6 rows)

Example 30

Using Many to One to get the solution of examples 18 and 20

Paths \(\{2, 11\}\rightarrow\{5\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  ARRAY[2,11], 5,
  false
);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         2 |    2 |    4 |    1 |        0
   2 |        2 |         2 |    5 |   -1 |    0 |        1
   3 |        1 |        11 |   11 |   12 |    1 |        0
   4 |        2 |        11 |   10 |   10 |    1 |        1
   5 |        3 |        11 |    5 |   -1 |    0 |        2
(5 rows)

Example 31

Using Many to Many to get the solution of examples 17 to 20

Paths \(\{2, 11\}\rightarrow\{3, 5\}\)

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

Example 32

Using Combinations to get the solution of examples 17 to 19

Paths \(\{2\}\rightarrow\{3, 5\}\cup\{11\}\rightarrow\{3\}\)

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edge_table',
  'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3)) AS combinations (source, target)',
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
   2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |         2 |       3 |    6 |    5 |    1 |        2
   4 |        4 |         2 |       3 |    3 |   -1 |    0 |        3
   5 |        1 |         2 |       5 |    2 |    4 |    1 |        0
   6 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
   7 |        1 |        11 |       3 |   11 |   11 |    1 |        0
   8 |        2 |        11 |       3 |    6 |    5 |    1 |        1
   9 |        3 |        11 |       3 |    3 |   -1 |    0 |        2
(9 rows)

Equivalencias entre firmas

The following examples find the path for \(\{2\}\rightarrow\{3\}\)

Example 33

Using One to One

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  2, 3
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |    8 |    1 |        1
   3 |        3 |    6 |    9 |    1 |        2
   4 |        4 |    9 |   16 |    1 |        3
   5 |        5 |    4 |    3 |    1 |        4
   6 |        6 |    3 |   -1 |    0 |        5
(6 rows)

Example 34

Using One to Many

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  2, ARRAY[3]
);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |       3 |    2 |    4 |    1 |        0
   2 |        2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |       3 |    6 |    9 |    1 |        2
   4 |        4 |       3 |    9 |   16 |    1 |        3
   5 |        5 |       3 |    4 |    3 |    1 |        4
   6 |        6 |       3 |    3 |   -1 |    0 |        5
(6 rows)

Example 35

Using Many to One

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  ARRAY[2], 3
);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         2 |    2 |    4 |    1 |        0
   2 |        2 |         2 |    5 |    8 |    1 |        1
   3 |        3 |         2 |    6 |    9 |    1 |        2
   4 |        4 |         2 |    9 |   16 |    1 |        3
   5 |        5 |         2 |    4 |    3 |    1 |        4
   6 |        6 |         2 |    3 |   -1 |    0 |        5
(6 rows)

Example 36

Using Many to Many

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  ARRAY[2], ARRAY[3]
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
   2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
   4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
   5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
   6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
(6 rows)

Example 37

Using Combinations

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  'SELECT * FROM (VALUES(2, 3)) AS combinations (source, target)'
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
   2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
   4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
   5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
   6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
(6 rows)

Ver también

Índices y tablas