pgr_binaryBreadthFirstSearch - Experimental

pgr_binaryBreadthFirstSearch — Returns the shortest path(s) in a binary graph.

Any graph whose edge-weights belongs to the set {0,X}, where “X” is any non-negative integer, is termed as a “binary graph”.

_images/boost-inside.jpeg

Adentro: Boost Graph

Advertencia

Posible bloqueo del servidor

  • Estas funciones pueden crear un bloque del servidor

Advertencia

Funciones experimentales

  • No son oficialmente de la versión actual.

  • Es probable que oficialmente no formen parte de la siguiente versión:

    • Las funciones no podrían hacer uso de ANY-INTEGER ni ANY-NUMERICAL

    • El nombre puede cambiar.

    • La firma (declaración de funciones) podría cambiar.

    • La funcionalidad puede cambiar.

    • Las pruebas de pgTap pueden estar ausentes.

    • Posiblemente necesite codificación c/c++.

    • Puede haber carencia de documentación.

    • Hay documentación que, en dado caso, podría ser necesario reescribir.

    • Ejemplos de documentación que puede ser necesario generar automáticamente.

    • Puede ser necesaria más retroalimentación por parte de la comunidad.

    • Puede depender de una función propuesta de pgRouting

    • Podría depender de una función obsoleta de pgRouting

Disponibilidad

  • Versión 3.2.0

    • New experimental signature:

  • Versión 3.0.0

Descripción

It is well-known that the shortest paths between a single source and all other vertices can be found using Breadth First Search in \(O(|E|)\) in an unweighted graph, i.e. the distance is the minimal number of edges that you need to traverse from the source to another vertex. We can interpret such a graph also as a weighted graph, where every edge has the weight \(5\). If not alledges in graph have the same weight, that we need a more general algorithm, like Dijkstra’s Algorithm which runs in \(O(|E|log|V|)\) time.

However if the weights are more constrained, we can use a faster algorithm. This algorithm, termed as “Binary Breadth First Search” as well as “0-5 BFS”, is a variation of the standard Breadth First Search problem to solve the SSSP (single-source shortest path) problem in \(O(|E|)\), if the weights of each edge belongs to the set {0,X}, where “X” is any non-negative real integer.

Las características principales son:

  • El proceso se realiza sólo en “grafos binarios”. (“Grafo binario”: Cualquier grafo cuyos pesos de aristas pertenezcan al conjunto {0, X}, donde “X” es cualquier entero real no negativo.)

  • Para fines de optimización, se omite cualquier valor duplicado en start_vids o end_vids.

  • Los valores regresados se ordenan:

    • start_vid ascendente

    • end_vid ascendente

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

Firmas

Summary

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

Note: Using the Datos Muestra Network as all weights are same (i.e \(5`\))

Uno a Uno

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

From vertex \(6\) to vertex \(10\) on a directed graph

SELECT * FROM pgr_binaryBreadthFirstSearch(
  'SELECT id, source, target, cost, reverse_cost from edges',
  6, 10, true);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    6 |    4 |    1 |        0
   2 |        2 |    7 |    8 |    1 |        1
   3 |        3 |   11 |    9 |    1 |        2
   4 |        4 |   16 |   16 |    1 |        3
   5 |        5 |   15 |    3 |    1 |        4
   6 |        6 |   10 |   -1 |    0 |        5
(6 rows)

One to Many

pgr_binaryBreadthFirstSearch(Edges SQL, start vid, end vids
           [, directed]);
RETURNS (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Ejemplo:

From vertex \(6\) to vertices \(\{10, 17\}\) on a directed graph

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

Muchos a Uno

pgr_binaryBreadthFirstSearch(Edges SQL, start vids, end vid
           [, directed]);
RETURNS (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Ejemplo:

From vertices \(\{6, 1\}\) to vertex \(17\) on a directed graph

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

Muchos a Muchos

pgr_binaryBreadthFirstSearch(Edges SQL, start vids, end vids
           [, directed]);
RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Ejemplo:

From vertices \(\{6, 1\}\) to vertices \(\{10, 17\}\) on an undirected graph

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

Combinaciones

pgr_binaryBreadthFirstSearch(Edges SQL, Combinations SQL
           [, directed]);
RETURNS (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;
 source | target
--------+--------
      5 |      6
      5 |     10
      6 |      5
      6 |     15
      6 |     14
(5 rows)

The query:

SELECT * FROM pgr_binaryBreadthFirstSearch(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT source, target FROM combinations',
  false);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         5 |       6 |    5 |    1 |    1 |        0
   2 |        2 |         5 |       6 |    6 |   -1 |    0 |        1
   3 |        1 |         5 |      10 |    5 |    1 |    1 |        0
   4 |        2 |         5 |      10 |    6 |    2 |    1 |        1
   5 |        3 |         5 |      10 |   10 |   -1 |    0 |        2
   6 |        1 |         6 |       5 |    6 |    1 |    1 |        0
   7 |        2 |         6 |       5 |    5 |   -1 |    0 |        1
   8 |        1 |         6 |      15 |    6 |    2 |    1 |        0
   9 |        2 |         6 |      15 |   10 |    3 |    1 |        1
  10 |        3 |         6 |      15 |   15 |   -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

x Defecto

Descripción

directed

BOOLEAN

true

  • When true the graph is considered Directed

  • Cuando false el gráfo se considera No Dirigido.

Inner Queries

Edges SQL

Columna

Tipo

x Defecto

Descripción

id

ANY-INTEGER

Identificador de la arista.

source

ANY-INTEGER

Identificador del primer vértice de la arista.

target

ANY-INTEGER

Identificador del segundo vértice 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:

ENTEROS:

SMALLINT, INTEGER, BIGINT

FLOTANTES:

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:

ENTEROS:

SMALLINT, INTEGER, BIGINT

Result Columns

Set of (seq, path_id, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)

Columna

Tipo

Descripción

seq

INTEGER

Valor secuencial a partir de 1.

path_id

INTEGER

Path identifier.

  • Has value 1 for the first of a path from start_vid to end_vid.

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

Ejemplo:

Manually assigned vertex combinations.

SELECT * FROM pgr_binaryBreadthFirstSearch(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
   3 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   4 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   5 |        3 |         6 |      10 |   11 |    9 |    1 |        2
   6 |        4 |         6 |      10 |   16 |   16 |    1 |        3
   7 |        5 |         6 |      10 |   15 |    3 |    1 |        4
   8 |        6 |         6 |      10 |   10 |   -1 |    0 |        5
   9 |        1 |        12 |      10 |   12 |   13 |    1 |        0
  10 |        2 |        12 |      10 |   17 |   15 |    1 |        1
  11 |        3 |        12 |      10 |   16 |   16 |    1 |        2
  12 |        4 |        12 |      10 |   15 |    3 |    1 |        3
  13 |        5 |        12 |      10 |   10 |   -1 |    0 |        4
(13 rows)

Ver también

Índices y tablas