• Versiones soportadas: Última (3.3) 3.2 3.1 3.0

• Versiones no soportadas: 2.6 2.5

pgr_bdDijkstraCost

pgr_bdDijkstraCost — Devuelve la ruta(s) más corta utilizando el algoritmo de Dijkstra Bidireccional.

Boost Graph Inside

Availability

• Versión 3.2.0

  • New proposed signature:

    • pgr_bdDijkstraCost (Combinations)

• Versión 3.0.0

  • Función oficial

• Versión 2.5.0

  • Nueva función propuesta

Descripción

The pgr_bdDijkstraCost function sumarizes of the cost of the shortest path(s) using the bidirectional Dijkstra Algorithm.

• 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

• It does not return a path.

• Returns the sum of the costs of the shortest path of each pair combination of nodes requested.

• Let be the case the values returned are stored in a table, so the unique index would be the pair: (start_vid, end_vid).

• Depending on the function and its parameters, the results can be symmetric.

  • The aggregate cost of \((u, v)\) is the same as for \((v, u)\).

• Any duplicated value in the start or end vertex identifiers are ignored.

• The returned values are ordered:

  • start_vid ascending

  • end_vid ascending

Firmas

Resumen

pgr_bdDijkstraCost(Edges SQL, start vid, end vid  [, directed])
pgr_bdDijkstraCost(Edges SQL, start vid, end vids [, directed])
pgr_bdDijkstraCost(Edges SQL, start vids, end vid  [, directed])
pgr_bdDijkstraCost(Edges SQL, start vids, end vids [, directed])
pgr_bdDijkstraCost(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Uno a Uno

pgr_bdDijkstraCost(Edges SQL, start vid, end vid  [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Ejemplo

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

SELECT * FROM pgr_bdDijkstraCost(
  'select id, source, target, cost, reverse_cost from edge_table',
  2, 3, true);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        5
(1 row)

Uno a Muchos

pgr_bdDijkstraCost(Edges SQL, start vid, end vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Ejemplo

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

SELECT * FROM pgr_bdDijkstraCost(
  'select id, source, target, cost, reverse_cost from edge_table',
  2, ARRAY[3, 12]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        5
         2 |      12 |        4
(2 rows)

Muchos a Uno

pgr_bdDijkstraCost(Edges SQL, start vids, end vid  [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Ejemplo

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

SELECT * FROM pgr_bdDijkstraCost(
  'select id, source, target, cost, reverse_cost from edge_table',
  ARRAY[2, 7], 12);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |      12 |        4
         7 |      12 |        5
(2 rows)

Muchos a Muchos

pgr_bdDijkstraCost(Edges SQL, start vids, end vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Ejemplo

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

SELECT * FROM pgr_bdDijkstraCost(
  'select id, source, target, cost, reverse_cost from edge_table',
  ARRAY[2, 7], ARRAY[3, 12],
  directed => false);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        1
         2 |      12 |        4
         7 |       3 |        4
         7 |      12 |        5
(4 rows)

Combinaciones

pgr_bdDijkstraCost(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (start_vid, end_vid, 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_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  'SELECT source, target FROM combinations_table',
  false);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         1 |       2 |        1
         1 |       3 |        2
         2 |       1 |        1
         2 |       4 |        2
(4 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

Set of (start_vid, end_vid, agg_cost)

Columna	Tipo	Descripción
start_vid	BIGINT	Identificador del vértice inicial.
end_vid	BIGINT	Identificador del vértice final.
agg_cost	FLOAT	Coste agregado de start_vid a end_vid.

Additional Examples

Example 1

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

SELECT * FROM pgr_bdDijkstraCost(
  'select id, source, target, cost, reverse_cost from edge_table',
  ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         3 |       4 |        3
         3 |       5 |        2
         4 |       3 |        1
         4 |       5 |        3
         5 |       3 |        4
         5 |       4 |        3
(6 rows)

Example 2

Making start_vids the same as end_vids.

SELECT * FROM pgr_bdDijkstraCost(
  'select id, source, target, cost, reverse_cost from edge_table',
  ARRAY[5, 3, 4], ARRAY[5, 3, 4]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         3 |       4 |        3
         3 |       5 |        2
         4 |       3 |        1
         4 |       5 |        3
         5 |       3 |        4
         5 |       4 |        3
(6 rows)

Example 3

Manually assigned vertex combinations.

SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edge_table',
  'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3)) AS combinations (source, target)');
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        5
         2 |       5 |        1
        11 |       3 |        4
(3 rows)

Ver también

• Bidirectional Dijkstra - Familia de funciones

• Datos Muestra

• https://www.cs.princeton.edu/courses/archive/spr06/cos423/Handouts/EPP%20shortest%20path%20algorithms.pdf

• https://en.wikipedia.org/wiki/Bidirectional_search

Índices y tablas

• Índice

• Página de Búsqueda