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 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 signature:
pgr_binaryBreadthFirstSearch(Combinations)
Version 3.0.0
New experimental signatures:
pgr_binaryBreadthFirstSearch(One to One)
pgr_binaryBreadthFirstSearch(One to Many)
pgr_binaryBreadthFirstSearch(Many to One)
pgr_binaryBreadthFirstSearch(Many to Many)
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 alledges 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¶
Summary
directed
])directed
])directed
])directed
])(seq, path_seq, [start_vid], [end_vid], node, edge, cost, agg_cost)
Note: Using the Sample Data Network as all weights are same (i.e \(1`\))
One to One¶
directed
])(seq, path_seq, node, edge, cost, agg_cost)
 Example:
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¶
directed
])(seq, path_seq, end_vid, node, edge, cost, agg_cost)
 Example:
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)
Many to One¶
directed
])(seq, path_seq, start_vid, node, edge, cost, agg_cost)
 Example:
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)
Many to Many¶
directed
])(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
 Example:
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)
Combinations¶
(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
 Example:
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)
Parameters¶
Column 
Type 
Description 


Edges SQL as described below 


Combinations SQL 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. 
Optional parameters¶
Column 
Type 
Default 
Description 





Inner Queries¶
Edges SQL¶
Column 
Type 
Default 
Description 


ANYINTEGER 
Identifier of the edge. 


ANYINTEGER 
Identifier of the first end point vertex of the edge. 


ANYINTEGER 
Identifier of the second end point vertex of the edge. 


ANYNUMERICAL 
Weight of the edge ( 


ANYNUMERICAL 
1 
Weight of the edge (

Where:
 ANYINTEGER:
SMALLINT
,INTEGER
,BIGINT
 ANYNUMERICAL:
SMALLINT
,INTEGER
,BIGINT
,REAL
,FLOAT
Combinations SQL¶
Parameter 
Type 
Description 


ANYINTEGER 
Identifier of the departure vertex. 

ANYINTEGER 
Identifier of the arrival vertex. 
Where:
 ANYINTEGER:
SMALLINT
,INTEGER
,BIGINT
Result columns¶
Set of (seq, path_id, path_seq [, start_vid] [, end_vid], node, edge, cost,
agg_cost)
Column 
Type 
Description 



Sequential value starting from 1. 


Path identifier.



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


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


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


Identifier of the node in the path from 


Identifier of the edge used to go from 


Cost to traverse from 


Aggregate cost from 
Additional Examples¶
 Example:
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)
See Also¶
Indices and tables