pgr_binaryBreadthFirstSearch  Experimental¶
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’.
Warning
Possible server crash
These functions might create a server crash
Warning
Experimental functions
They are not officially of the current release.
They likely will not be officially be part of the next release:
The functions might not make use of ANYINTEGER and ANYNUMERICAL
Name might change.
Signature might change.
Functionality might change.
pgTap tests might be missing.
Might need c/c++ coding.
May lack documentation.
Documentation if any might need to be rewritten.
Documentation examples might need to be automatically generated.
Might need a lot of feedback from the comunity.
Might depend on a proposed function of pgRouting
Might depend on a deprecated function of pgRouting
Availability
Version 3.2.0
New experimental function:
pgr_binaryBreadthFirstSearch(Combinations)
Version 3.0.0
New experimental function
Description¶
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: \(O( start\_vids  * E)\)
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])
pgr_binaryBreadthFirstSearch(Edges SQL, Combinations SQL [, directed])  Proposed on v3.2
RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET
pgr_binaryBreadthFirstSearch(Edges SQL, start_vid, 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)
One to One¶
pgr_binaryBreadthFirstSearch(Edges SQL, start_vid, end_vid [, directed]);
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)
One to many¶
pgr_binaryBreadthFirstSearch(Edges SQL, start_vid, end_vids [, directed]);
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)
Many to One¶
pgr_binaryBreadthFirstSearch(Edges SQL, start_vids, end_vid [, directed]);
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)
Many to Many¶
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
 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)
Combinations¶
pgr_binaryBreadthFirstSearch(Edges SQL, Combinations SQL [, directed]);
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
 Example
Using a combinations table 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',
'SELECT * FROM ( VALUES (2, 3), (11, 5) ) AS t(source, target)',
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  11  5  11  12  0  0
4  2  11  5  10  10  1  0
5  3  11  5  5  1  0  1
(5 rows)
Parameters¶
Parameter 
Type 
Default 
Description 

Edges SQL 

Edges query as described below. 

Combinations SQL 

Combinations query as described below. 

start_vid 

Identifier of the starting vertex of the path. 

start_vids 

Array of identifiers of starting vertices. 

end_vid 

Identifier of the ending vertex of the path. 

end_vids 

Array of identifiers of ending vertices. 

directed 



Inner queries¶
Edges query¶
Column 
Type 
Default 
Description 

id 

Identifier of the edge. 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 

cost 

Weight of the edge (source, target)


reverse_cost 

1 
Weight of the edge (target, source),

Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
 ANYNUMERICAL
SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Combinations query¶
Column 
Type 
Default 
Description 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 
Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
Return Columns¶
Returns set of (seq, path_id, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
Column 
Type 
Description 

seq 

Sequential value starting from 1. 
path_id 

Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same 
path_seq 

Relative position in the path. Has value 1 for the beginning of a path. 
start_vid 

Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. 
end_vid 

Identifier of the ending vertex. Returned when multiple ending vertices are in the query. 
node 

Identifier of the node in the path from 
edge 

Identifier of the edge used to go from 
cost 

Cost to traverse from 
agg_cost 

Aggregate cost from 
Example Data¶
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.
Table Data¶
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
See Also¶
Indices and tables