All Pairs - Family of Functions - pgRouting Manual (3.4)
All Pairs - Family of Functions
The following functions work on all vertices pair combinations
-
pgr_floydWarshall - Floyd-Warshall’s algorithm.
-
pgr_johnson - Johnson’s algorithm
Introduction
The main characteristics are:
-
It does not return a path.
-
Returns the sum of the costs of the shortest path for each pair of nodes in the graph.
-
Process is done only on edges with positive costs.
-
Boost returns a \(V \times V\) matrix, where the infinity values. Represent the distance between vertices for which there is no path.
-
We return only the non infinity values in form of a set of (start_vid, end_vid, agg_cost) .
-
-
Let be the case the values returned are stored in a table, so the unique index would be the pair: (start_vid, end_vid) .
-
For the undirected graph, the results are symmetric.
-
The agg_cost of (u, v) is the same as for (v, u) .
-
-
When start_vid = end_vid , the agg_cost = 0.
-
Recommended, use a bounding box of no more than 3500 edges.
Parameters
Parameter |
Type |
Default |
Description |
---|---|---|---|
|
Edges SQL as described below. |
Optional parameters
Column |
Type |
Default |
Description |
---|---|---|---|
|
|
|
|
Inner Queries
Edges SQL
Column |
Type |
Default |
Description |
---|---|---|---|
|
ANY-INTEGER |
Identifier of the first end point vertex of the edge. |
|
|
ANY-INTEGER |
Identifier of the second end point vertex of the edge. |
|
|
ANY-NUMERICAL |
Weight of the edge (
|
|
|
ANY-NUMERICAL |
-1 |
Weight of the edge (
|
Where:
- ANY-INTEGER :
-
SMALLINT
,INTEGER
,BIGINT
- ANY-NUMERICAL :
-
SMALLINT
,INTEGER
,BIGINT
,REAL
,FLOAT
Result Columns
Set of
(start_vid,
end_vid,
agg_cost)
Column |
Type |
Description |
---|---|---|
|
|
Identifier of the starting vertex. |
|
|
Identifier of the ending vertex. |
|
|
Aggregate cost from
|
Performance
- The following tests:
-
-
non server computer
-
with AMD 64 CPU
-
4G memory
-
trusty
-
posgreSQL version 9.3
-
Data
The following data was used
BBOX="-122.8,45.4,-122.5,45.6" wget --progress=dot:mega -O "sampledata.osm" "https://www.overpass-api.de/api/xapi?*[bbox=][@meta]"
Data processing was done with osm2pgrouting-alpha
createdb portland
psql -c "create extension postgis" portland
psql -c "create extension pgrouting" portland
osm2pgrouting -f sampledata.osm -d portland -s 0
Results
- Test :
-
One
This test is not with a bounding box
The density of the passed graph is extremely low.
For each
SELECT count(*) FROM pgr_floydWarshall(
'SELECT gid as id, source, target, cost, reverse_cost
FROM ways where id <= <SIZE>');
SELECT count(*) FROM pgr_johnson(
'SELECT gid as id, source, target, cost, reverse_cost
FROM ways where id <= <SIZE>');
The results of this tests are presented as:
- SIZE :
-
is the number of edges given as input.
- EDGES :
-
is the total number of records in the query.
- DENSITY :
-
is the density of the data \(\dfrac{E}{V \times (V-1)}\) .
- OUT ROWS :
-
is the number of records returned by the queries.
- Floyd-Warshall :
-
is the average execution time in seconds of pgr_floydWarshall.
- Johnson :
-
is the average execution time in seconds of pgr_johnson.
SIZE |
EDGES |
DENSITY |
OUT ROWS |
Floyd-Warshall |
Johnson |
---|---|---|---|---|---|
500 |
500 |
0.18E-7 |
1346 |
0.14 |
0.13 |
1000 |
1000 |
0.36E-7 |
2655 |
0.23 |
0.18 |
1500 |
1500 |
0.55E-7 |
4110 |
0.37 |
0.34 |
2000 |
2000 |
0.73E-7 |
5676 |
0.56 |
0.37 |
2500 |
2500 |
0.89E-7 |
7177 |
0.84 |
0.51 |
3000 |
3000 |
1.07E-7 |
8778 |
1.28 |
0.68 |
3500 |
3500 |
1.24E-7 |
10526 |
2.08 |
0.95 |
4000 |
4000 |
1.41E-7 |
12484 |
3.16 |
1.24 |
4500 |
4500 |
1.58E-7 |
14354 |
4.49 |
1.47 |
5000 |
5000 |
1.76E-7 |
16503 |
6.05 |
1.78 |
5500 |
5500 |
1.93E-7 |
18623 |
7.53 |
2.03 |
6000 |
6000 |
2.11E-7 |
20710 |
8.47 |
2.37 |
6500 |
6500 |
2.28E-7 |
22752 |
9.99 |
2.68 |
7000 |
7000 |
2.46E-7 |
24687 |
11.82 |
3.12 |
7500 |
7500 |
2.64E-7 |
26861 |
13.94 |
3.60 |
8000 |
8000 |
2.83E-7 |
29050 |
15.61 |
4.09 |
8500 |
8500 |
3.01E-7 |
31693 |
17.43 |
4.63 |
9000 |
9000 |
3.17E-7 |
33879 |
19.19 |
5.34 |
9500 |
9500 |
3.35E-7 |
36287 |
20.77 |
6.24 |
10000 |
10000 |
3.52E-7 |
38491 |
23.26 |
6.51 |
- Test :
-
Two
This test is with a bounding box
The density of the passed graph higher than of the Test One.
For each
WITH
buffer AS (
SELECT ST_Buffer(ST_Centroid(ST_Extent(the_geom)), SIZE) AS geom
FROM ways),
bbox AS (
SELECT ST_Envelope(ST_Extent(geom)) as box FROM buffer)
SELECT gid as id, source, target, cost, reverse_cost
FROM ways where the_geom && (SELECT box from bbox);
The tested queries
SELECT count(*) FROM pgr_floydWarshall(<edge query>)
SELECT count(*) FROM pgr_johnson(<edge query>)
The results of this tests are presented as:
- SIZE :
-
is the size of the bounding box.
- EDGES :
-
is the total number of records in the query.
- DENSITY :
-
is the density of the data \(\dfrac{E}{V \times (V-1)}\) .
- OUT ROWS :
-
is the number of records returned by the queries.
- Floyd-Warshall :
-
is the average execution time in seconds of pgr_floydWarshall.
- Johnson :
-
is the average execution time in seconds of pgr_johnson.
SIZE |
EDGES |
DENSITY |
OUT ROWS |
Floyd-Warshall |
Johnson |
---|---|---|---|---|---|
0.001 |
44 |
0.0608 |
1197 |
0.10 |
0.10 |
0.002 |
99 |
0.0251 |
4330 |
0.10 |
0.10 |
0.003 |
223 |
0.0122 |
18849 |
0.12 |
0.12 |
0.004 |
358 |
0.0085 |
71834 |
0.16 |
0.16 |
0.005 |
470 |
0.0070 |
116290 |
0.22 |
0.19 |
0.006 |
639 |
0.0055 |
207030 |
0.37 |
0.27 |
0.007 |
843 |
0.0043 |
346930 |
0.64 |
0.38 |
0.008 |
996 |
0.0037 |
469936 |
0.90 |
0.49 |
0.009 |
1146 |
0.0032 |
613135 |
1.26 |
0.62 |
0.010 |
1360 |
0.0027 |
849304 |
1.87 |
0.82 |
0.011 |
1573 |
0.0024 |
1147101 |
2.65 |
1.04 |
0.012 |
1789 |
0.0021 |
1483629 |
3.72 |
1.35 |
0.013 |
1975 |
0.0019 |
1846897 |
4.86 |
1.68 |
0.014 |
2281 |
0.0017 |
2438298 |
7.08 |
2.28 |
0.015 |
2588 |
0.0015 |
3156007 |
10.28 |
2.80 |
0.016 |
2958 |
0.0013 |
4090618 |
14.67 |
3.76 |
0.017 |
3247 |
0.0012 |
4868919 |
18.12 |
4.48 |
See Also
Indices and tables