# pgRouting Manual (2.5)

## All Pairs - Family of Functions

The following functions work on all vertices pair combinations

## 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" "http://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 <SIZE> 30 tests were executed to get the average The tested query is:

    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 <SIZE> 30 tests were executed to get the average The tested edge query is:

    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

- pgr_johnson
- pgr_floydWarshall
- Boost floyd-Warshall algorithm

Indices and tables

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