pgr_bdDijkstra

pgr_bdDijkstra — Devuelve la(s) rutas más cortas mediante el algoritmo Bidirectional Dijkstra.

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Boost Graph Inside

Disponibilidad:

  • Versión 3.2.0

  • Versión 3.0.0

    • Función oficial

  • Versión 2.5.0

  • Versión 2.4.0

    • Signature change on pgr_bdDijsktra (One to One)

      • Firma antigua ya no soportada

  • Versión 2.0.0

Descripción

Las características principales son:

  • 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.

  • Tiempo de ejecución (peor de los casos): \(O((V \log V + E))\)

  • Para grandes gráficos donde hay un camino entre el vértice inicial y el vértice final:

    • Se espera que termine más rápido que pgr_dijkstra

Firmas

Resumen

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

From vertex \(2\) to vertex \(3\) on a directed graph

SELECT * FROM pgr_bdDijkstra(
  '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_bdDijkstra(Edges SQL, start vid, end vids [, 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 graph

SELECT * FROM pgr_bdDijkstra(
  '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_bdDijkstra(Edges SQL, start vids, end vid  [, 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_bdDijkstra(
  '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 |    8 |    1 |        1
   3 |        3 |         2 |    6 |    9 |    1 |        2
   4 |        4 |         2 |    9 |   15 |    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 |    8 |    1 |        2
   9 |        4 |         7 |    6 |   11 |    1 |        3
  10 |        5 |         7 |   11 |   13 |    1 |        4
  11 |        6 |         7 |   12 |   -1 |    0 |        5
(11 rows)

Muchos a Muchos

pgr_bdDijkstra(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_bdDijkstra(
  '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 |    8 |    1 |        1
   5 |        3 |         2 |      12 |    6 |    9 |    1 |        2
   6 |        4 |         2 |      12 |    9 |   15 |    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_bdDijkstra(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Ejemplo

Using a combinations table on an undirected graph

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_bdDijkstra(
  '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

Return Columns

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.

Additional Examples

Example 1

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

SELECT * FROM pgr_bdDijkstra(
  '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 |   16 |    1 |        0
  11 |        2 |         4 |       5 |    9 |    9 |    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)

Example 2

Making start_vids the same as end_vids.

SELECT * FROM pgr_bdDijkstra(
  '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 |   16 |    1 |        0
  11 |        2 |         4 |       5 |    9 |    9 |    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)

Example 3

Manually assigned vertex combinations.

SELECT * FROM pgr_bdDijkstra(
  '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)

Ver también

Índices y tablas