pgr_binaryBreadthFirstSearch
— Returns the shortest path(s) in a binary graph.
Any graph whose edgeweights belongs to the set {0,X}, where ‘X’ is any nonnegative real integer, is termed as a ‘binary graph’.
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Experimental functions
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It is wellknown 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 ‘01 BFS’, is a variation of the standard Breadth First Search problem to solve the SSSP (singlesource shortest path) problem in \(O(E)\), if the weights of each edge belongs to the set {0,X}, where ‘X’ is any nonnegative real integer.
The main Characteristics are:
 Process is done only on ‘binary graphs’. (‘Binary Graph’: Any graph whose edgeweights belongs to the set {0,X}, where ‘X’ is any nonnegative 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: \(O( start\_vids  * E)\)
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
Example:  From vertex \(2\) to vertex \(3\) on an undirected binary graph 

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
Example:  From vertex \(2\) to vertices \(\{3, 5\}\) on an undirected binary graph 

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
Example:  From vertices \(\{2, 11\}\) to vertex \(5\) 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',
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
Example:  From vertices \(\{2, 11\}\) to vertices \(\{3, 5\}\) on an undirected binary graph 

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)
Parameter  Type  Default  Description 

edges_sql  TEXT 
Inner SQL query as described below.  
start_vid  BIGINT 
Identifier of the starting vertex of the path.  
start_vids  ARRAY[BIGINT] 
Array of identifiers of starting vertices.  
end_vid  BIGINT 
Identifier of the ending vertex of the path.  
end_vids  ARRAY[BIGINT] 
Array of identifiers of ending vertices.  
directed  BOOLEAN 
true 

Column  Type  Default  Description 

id  ANYINTEGER 
Identifier of the edge.  
source  ANYINTEGER 
Identifier of the first end point vertex of the edge.  
target  ANYINTEGER 
Identifier of the second end point vertex of the edge.  
cost  ANYNUMERICAL 
Weight of the edge (source, target)


reverse_cost  ANYNUMERICAL 
1  Weight of the edge (target, source),

Where:
ANYINTEGER:  SMALLINT, INTEGER, BIGINT 

ANYNUMERICAL:  SMALLINT, INTEGER, BIGINT, REAL, FLOAT 
Returns set of (seq, path_id, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
Column  Type  Description 

seq  INT 
Sequential value starting from 1. 
path_id  INT 
Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same start_vid to end_vid combination. 
path_seq  INT 
Relative position in the path. Has value 1 for the beginning of a path. 
start_vid  BIGINT 
Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. 
end_vid  BIGINT 
Identifier of the ending vertex. Returned when multiple ending vertices are in the query. 
node  BIGINT 
Identifier of the node in the path from start_vid to 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 
Cost to traverse from node using edge to the next node in the path sequence. 
agg_cost  FLOAT 
Aggregate cost from start_v to node . 
This type of data is used on the examples of this page.
EdwardsMoore 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.
The queries in the previous sections use the table ‘roadworks’. The data of the table:
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