Centrality week-2

configuration.conf

@@ -46,6 +46,7 @@ planar              | Y | Y | Y
 dominator           | Y | Y | Y
 ordering            | Y | Y | Y
 circuits            | Y | Y | Y
+metrics             | N | N | N
 #----------------------
 # SQL only directories
 #----------------------

doc/metrics/CMakeLists.txt

@@ -0,0 +1,14 @@
+
+SET(LOCAL_FILES
+    allpairs-family.rst
+    pgr_floydWarshall.rst
+    pgr_johnson.rst
+    )
+
+foreach (f ${LOCAL_FILES})
+    configure_file(${f} "${PGR_DOCUMENTATION_SOURCE_DIR}/${f}")
+    list(APPEND LOCAL_DOC_FILES  ${PGR_DOCUMENTATION_SOURCE_DIR}/${f})
+endforeach()
+
+set(PROJECT_DOC_FILES ${PROJECT_DOC_FILES} ${LOCAL_DOC_FILES} PARENT_SCOPE)
+

doc/metrics/metrics-family.rst

@@ -0,0 +1,268 @@
+..
+   ****************************************************************************
+    pgRouting Manual
+    Copyright(c) pgRouting Contributors
+
+    This documentation is licensed under a Creative Commons Attribution-Share
+    Alike 3.0 License: https://creativecommons.org/licenses/by-sa/3.0/
+   ****************************************************************************
+
+|
+
+
+
+All Pairs - Family of Functions
+===============================================================================
+
+The following functions work on all vertices pair combinations
+
+.. index from here
+
+* :doc:`pgr_floydWarshall` - Floyd-Warshall's algorithm.
+* :doc:`pgr_johnson` - Johnson's algorithm
+
+.. index to here
+
+.. toctree::
+    :hidden:
+
+    pgr_floydWarshall
+    pgr_johnson
+
+Introduction
+-------------------------------------------------------------------------------
+
+.. characteristics_start
+
+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 :math:`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.**
+
+.. characteristics_end
+
+Parameters
+-------------------------------------------------------------------------------
+
+.. edges_start
+
+.. list-table::
+   :width: 81
+   :widths: auto
+   :header-rows: 1
+
+   * - Parameter
+     - Type
+     - Default
+     - Description
+   * - `Edges SQL`_
+     - ``TEXT``
+     -
+     - `Edges SQL`_ as described below.
+
+.. edges_end
+
+Optional parameters
+...............................................................................
+
+.. include:: dijkstra-family.rst
+    :start-after: dijkstra_optionals_start
+    :end-before: dijkstra_optionals_end
+
+Inner Queries
+-------------------------------------------------------------------------------
+
+Edges SQL
+...............................................................................
+
+.. include:: pgRouting-concepts.rst
+    :start-after: no_id_edges_sql_start
+    :end-before: no_id_edges_sql_end
+
+Result columns
+-------------------------------------------------------------------------------
+
+.. include:: pgRouting-concepts.rst
+    :start-after: return_cost_start
+    :end-before: return_cost_end
+
+
+Performance
+------------------------------------------------------------------------------
+
+The following tests:
+ - non server computer
+ - with AMD 64 CPU
+ - 4G memory
+ - trusty
+ - posgreSQL version 9.3
+
+Data
+.........................................
+
+The following data was used
+
+.. parsed-literal::
+
+    BBOX="-122.8,45.4,-122.5,45.6"
+    wget --progress=dot:mega -O "sampledata.osm" \
+         "https://www.overpass-api.de/api/xapi?*[bbox=${BBOX}][@meta]"
+
+
+Data processing was done with osm2pgrouting-alpha
+
+.. parsed-literal::
+
+    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:
+
+.. parsed-literal::
+
+     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 :math:`\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:
+
+.. parsed-literal::
+
+    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
+
+.. parsed-literal::
+
+    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 :math:`\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
+.........................................
+
+* :doc:`pgr_johnson`
+* :doc:`pgr_floydWarshall`
+* Boost `floyd-Warshall
+  <https://www.boost.org/libs/graph/doc/floyd_warshall_shortest.html>`__
+
+.. rubric:: Indices and tables
+
+* :ref:`genindex`
+* :ref:`search`
+