pgr_edwardMoore  Experimental
¶
pgr_edwardMoore
— Returns the shortest path using EdwardMoore algorithm.
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_edwardMoore
(Combinations)
Version 3.0.0
New experimental signatures:
pgr_edwardMoore
(One to One)pgr_edwardMoore
(One to Many)pgr_edwardMoore
(Many to One)pgr_edwardMoore
(Many to Many)
Description¶
Edward Moore’s Algorithm is an improvement of the BellmanFord Algorithm. It can compute the shortest paths from a single source vertex to all other vertices in a weighted directed graph. The main difference between Edward Moore’s Algorithm and Bellman Ford’s Algorithm lies in the run time.
The worstcase running time of the algorithm is \(O( V  *  E )\) similar to the time complexity of BellmanFord algorithm. However, experiments suggest that this algorithm has an average running time complexity of \(O(  E  )\) for random graphs. This is significantly faster in terms of computation speed.
Thus, the algorithm is atbest, significantly faster than BellmanFord algorithm and is atworst,as good as BellmanFord algorithm
The main characteristics are:
Values are returned when there is a path.
When the starting vertex and ending vertex are the same, there is no path.
The agg_cost the non included values (v, v) is \(0\)
When the starting vertex and ending vertex are the different and there is no path:
The agg_cost the non included values (u, v) is \(\infty\)
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:
Worst case: \(O( V  *  E )\)
Average case: \(O(  E  )\)
Signatures¶
Summary
directed
])directed
])directed
])directed
])(seq, path_seq, [start_vid], [end_vid], node, edge, cost, agg_cost)
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_edwardMoore(
'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_edwardMoore(
'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_edwardMoore(
'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_edwardMoore(
'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_edwardMoore(
'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
Return columns¶
Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost,
agg_cost)
Column 
Type 
Description 



Sequential value starting from 1. 


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 1:
Demonstration of repeated values are ignored, and result is sorted.
SELECT * FROM pgr_edwardMoore(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
+++++++
1  1  7  10  7  8  1  0
2  2  7  10  11  9  1  1
3  3  7  10  16  16  1  2
4  4  7  10  15  3  1  3
5  5  7  10  10  1  0  4
6  1  7  15  7  8  1  0
7  2  7  15  11  9  1  1
8  3  7  15  16  16  1  2
9  4  7  15  15  1  0  3
10  1  10  7  10  5  1  0
11  2  10  7  11  8  1  1
12  3  10  7  7  1  0  2
13  1  10  15  10  5  1  0
14  2  10  15  11  9  1  1
15  3  10  15  16  16  1  2
16  4  10  15  15  1  0  3
17  1  15  7  15  16  1  0
18  2  15  7  16  9  1  1
19  3  15  7  11  8  1  2
20  4  15  7  7  1  0  3
21  1  15  10  15  3  1  0
22  2  15  10  10  1  0  1
(22 rows)
 Example 2:
Making start vids the same as end vids.
SELECT * FROM pgr_edwardMoore(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
+++++++
1  1  7  10  7  8  1  0
2  2  7  10  11  9  1  1
3  3  7  10  16  16  1  2
4  4  7  10  15  3  1  3
5  5  7  10  10  1  0  4
6  1  7  15  7  8  1  0
7  2  7  15  11  9  1  1
8  3  7  15  16  16  1  2
9  4  7  15  15  1  0  3
10  1  10  7  10  5  1  0
11  2  10  7  11  8  1  1
12  3  10  7  7  1  0  2
13  1  10  15  10  5  1  0
14  2  10  15  11  9  1  1
15  3  10  15  16  16  1  2
16  4  10  15  15  1  0  3
17  1  15  7  15  16  1  0
18  2  15  7  16  9  1  1
19  3  15  7  11  8  1  2
20  4  15  7  7  1  0  3
21  1  15  10  15  3  1  0
22  2  15  10  10  1  0  1
(22 rows)
 Example 3:
Manually assigned vertex combinations.
SELECT * FROM pgr_edwardMoore(
'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