# 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" "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 <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