pgr_dijkstra¶
pgr_dijkstra — Shortest path(s) using Dijkstra algorithm.
Boost Graph Inside¶
Disponibilidad
Versión 3.1.0
Nuevas funciones Propuestas:
pgr_dijkstra(Combinations)
Versión 3.0.0
Funciones oficiales
Version 2.2.0
Nuevas funciones propuestas:
pgr_dijkstra(One to Many)pgr_dijkstra(Many to One)pgr_dijkstra(Many to Many)
Versión 2.1.0
Signature change on
pgr_dijkstra(One to One)
Versión 2.0.0
Official
pgr_dijkstra(One to One)
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 as described below |
|
|
Combinations SQL as described below |
|
start vid |
|
Identificador del vértice inicial de la ruta. |
start vids |
|
Arreglo de identificadores de vértices iniciales. |
end vid |
|
Identificador del vértice final de la ruta. |
end vids |
|
Arreglo de identificadores de vértices finales. |
Optional parameters¶
Columna |
Tipo |
default |
Descripción |
|---|---|---|---|
|
|
|
|
Consultas internas¶
Edges SQL¶
Columna |
Tipo |
x Defecto |
Descripción |
|---|---|---|---|
|
ANY-INTEGER |
Identificador de la arista. |
|
|
ANY-INTEGER |
Identificador del primer vértice extremo de la arista. |
|
|
ANY-INTEGER |
Identificador del segundo vértice extremo de la arista. |
|
|
ANY-NUMERICAL |
Weight of the edge ( |
|
|
ANY-NUMERICAL |
-1 |
Weight of the edge (
|
Donde:
- ANY-INTEGER
SMALLINT,INTEGER,BIGINT- ANY-NUMERICAL
SMALLINT,INTEGER,BIGINT,REAL,FLOAT
Combinations SQL¶
Parámetro |
Tipo |
Descripción |
|---|---|---|
|
ANY-INTEGER |
Identifier of the departure vertex. |
|
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 |
|---|---|---|
|
|
Valor secuencial a partir de 1. |
|
|
Posición relativa en la ruta. Tiene el valor 1 para el principio de una ruta. |
|
|
Identificador del vértice inicial. Se devuelve cuando hay varias vetrices iniciales en la consulta. |
|
|
Identificador del vértice final. Se devuelve cuando hay varios vértices finales en la consulta. |
|
|
Identificador del nodo en la ruta de |
|
|
Identifier of the edge used to go from |
|
|
Costo del desplazamiento desde |
|
|
Aggregate cost from |
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_vidsthe same asend_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¶
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¶
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¶
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¶
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¶
Las consultas utilizan la red Datos Muestra .
Índices y tablas