pgr_binaryBreadthFirstSearch - Experimental - pgRouting Manual (3.0)

Description

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 1. If not all edges in graph have the same weight, that we need a more general algorithm, like Dijkstra’s Algorithm which runs in \(O(ElogV)\) 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 ‘0-1 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.

The main Characteristics are:

• Process is done only on ‘binary graphs’. (‘Binary Graph’: Any graph whose edge-weights belongs to the set {0,X}, where ‘X’ is any non-negative real integer.)

• For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.

• The returned values are ordered:

  • start_vid ascending

  • end_vid ascending

• Running time: \(O( start\_vids * E)\)

Signatures

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])
RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET

pgr_binaryBreadthFirstSearch(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET

Example :

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

SELECT * FROM pgr_binaryBreadthFirstSearch(
    'SELECT id, source, target, road_work as cost, reverse_road_work as reverse_cost FROM roadworks',
    2, 3
);
 seq  path_seq  node  edge  cost  agg_cost
-----+----------+------+------+------+----------
   1         1     2     4     0         0
   2         2     5     8     1         0
   3         3     6     9     1         1
   4         4     9    16     0         2
   5         5     4     3     0         2
   6         6     3    -1     0         2
(6 rows)

pgr_binaryBreadthFirstSearch(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

SELECT * FROM pgr_binaryBreadthFirstSearch(
    'SELECT id, source, target, road_work as cost, reverse_road_work as reverse_cost FROM roadworks',
    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)

pgr_binaryBreadthFirstSearch(TEXT edges_sql, BIGINT start_vid, ARRAY[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

SELECT * FROM pgr_binaryBreadthFirstSearch(
    'SELECT id, source, target, road_work as cost FROM roadworks',
    2, ARRAY[3,5],
    FALSE
);
 seq  path_seq  end_vid  node  edge  cost  agg_cost
-----+----------+---------+------+------+------+----------
   1         1        3     2     4     0         0
   2         2        3     5     8     1         0
   3         3        3     6     5     1         1
   4         4        3     3    -1     0         2
   5         1        5     2     4     0         0
   6         2        5     5    -1     0         0
(6 rows)

pgr_binaryBreadthFirstSearch(TEXT edges_sql, ARRAY[ANY_INTEGER] start_vids, BIGINT end_vid,
    BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET

SELECT * FROM pgr_binaryBreadthFirstSearch(
    'SELECT id, source, target, road_work as cost, reverse_road_work as reverse_cost FROM roadworks',
    ARRAY[2,11], 5
);
 seq  path_seq  start_vid  node  edge  cost  agg_cost
-----+----------+-----------+------+------+------+----------
   1         1          2     2     4     0         0
   2         2          2     5    -1     0         0
   3         1         11    11    13     1         0
   4         2         11    12    15     0         1
   5         3         11     9    16     0         1
   6         4         11     4     3     0         1
   7         5         11     3     2     1         1
   8         6         11     2     4     0         2
   9         7         11     5    -1     0         2
(9 rows)

pgr_binaryBreadthFirstSearch(TEXT edges_sql, ARRAY[ANY_INTEGER] start_vids, ARRAY[ANY_INTEGER] end_vids,
    BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

SELECT * FROM pgr_binaryBreadthFirstSearch(
    'SELECT id, source, target, road_work as cost, reverse_road_work as reverse_cost FROM roadworks',
    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     0         0
   4         2          2        5     5    -1     0         0
   5         1         11        3    11    13     1         0
   6         2         11        3    12    15     0         1
   7         3         11        3     9    16     0         1
   8         4         11        3     4     3     0         1
   9         5         11        3     3    -1     0         1
  10         1         11        5    11    12     0         0
  11         2         11        5    10    10     1         0
  12         3         11        5     5    -1     0         1
(12 rows)

Parameters

Inner query

Where:

ANY-INTEGER :

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL :

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Return Columns

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

Example Data

This type of data is used on the examples of this page.

Edwards-Moore Algorithm is best applied when trying to answer queries such as the following: "Find the path with the minimum number from Source to Destination" Here: * Source = Source Vertex, Destination = Any arbitrary destination vertex * X is an event/property * Each edge in the graph is either " X " or " Not X " .

Example: "Find the path with the minimum number of road works from Source to Destination"

Here, a road under work(aka road works ) means that part of the road is occupied for construction work/maintenance.

Here: * Edge ( u , v ) has weight = 0 if no road work is ongoing on the road from u to v . * Edge ( u , v ) has weight = 1 if road work is ongoing on the road from u to v .

Then, upon running the algorithm, we obtain the path with the minimum number of road works from the given source and destination.

Thus, the queries used in the previous section can be interpreted in this manner.

DROP TABLE IF EXISTS roadworks CASCADE;
NOTICE:  table "roadworks" does not exist, skipping
DROP TABLE
CREATE table roadworks (
    id BIGINT not null primary key,
    source BIGINT,
    target BIGINT,
    road_work FLOAT,
    reverse_road_work FLOAT
);
CREATE TABLE
INSERT INTO roadworks(
  id, source, target, road_work, reverse_road_work) VALUES
  (1,  1,  2,  0,  0),
  (2,  2,  3,  -1,  1),
  (3,  3,  4,  -1,  0),
  (4,  2,  5,  0,  0),
  (5,  3,  6,  1,  -1),
  (6,  7,  8,  1,  1),
  (7,  8,  5,  0,  0),
  (8,  5,  6,  1,  1),
  (9,  6,  9,  1,  1),
  (10,  5,  10,  1,  1),
  (11,  6,  11,  1,  -1),
  (12,  10,  11,  0,  -1),
  (13,  11,  12,  1,  -1),
  (14,  10,  13,  1,  1),
  (15,  9,  12,  0,  0),
  (16,  4,  9,  0,  0),
  (17,  14,  15,  0,  0),
  (18,  16,  17,  0,  0);
INSERT 0 18

See Also

• https://cp-algorithms.com/graph/01_bfs.html

• https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#Specialized_variants

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