# pgRouting Concepts¶

## Getting Started¶

This is a simple guide to walk you through the steps of getting started with pgRouting. In this guide we will cover:

### Create a routing Database¶

The first thing we need to do is create a database and load pgrouting in the database. Typically you will create a database for each project. Once you have a database to work in, your can load your data and build your application in that database. This makes it easy to move your project later if you want to to say a production server.

For Postgresql 9.2 and later versions

createdb mydatabase
psql mydatabase -c "create extension postgis"
psql mydatabase -c "create extension pgrouting"


How you load your data will depend in what form it comes it. There are various OpenSource tools that can help you, like:

osm2pgrouting: this is a tool for loading OSM data into postgresql with pgRouting requirements this is the postgresql shapefile loader this is a vector data conversion utility this is a tool for loading OSM data into postgresql

So these tools and probably others will allow you to read vector data so that you may then load that data into your database as a table of some kind. At this point you need to know a little about your data structure and content. One easy way to browse your new data table is with pgAdmin3 or phpPgAdmin.

### Build a Routing Topology¶

Next we need to build a topology for our street data. What this means is that for any given edge in your street data the ends of that edge will be connected to a unique node and to other edges that are also connected to that same unique node. Once all the edges are connected to nodes we have a graph that can be used for routing with pgrouting. We provide a tool that will help with this:

Note

this step is not needed if data is loaded with osm2pgrouting

select pgr_createTopology('myroads', 0.000001);


### Check the Routing Topology¶

There are lots of possible sources for errors in a graph. The data that you started with may not have been designed with routing in mind. A graph has some very specific requirements. One is that it is NODED, this means that except for some very specific use cases, each road segment starts and ends at a node and that in general is does not cross another road segment that it should be connected to.

There can be other errors like the direction of a one-way street being entered in the wrong direction. We do not have tools to search for all possible errors but we have some basic tools that might help.

select pgr_analyzegraph('myroads', 0.000001);
t_in_rules, t_out_rules
direction)


### Compute a Path¶

Once you have all the preparation work done above, computing a route is fairly easy. We have a lot of different algorithms that can work with your prepared road network. The general form of a route query is:

select pgr_dijkstra(SELECT * FROM myroads', 1, 2)


As you can see this is fairly straight forward and you can look and the specific algorithms for the details of the signatures and how to use them. These results have information like edge id and/or the node id along with the cost or geometry for the step in the path from start to end. Using the ids you can join these result back to your edge table to get more information about each step in the path.

## Group of Functions¶

A function might have different overloads. Across this documentation, to indicate which overload we use the following terms:

Depending on the overload are the parameters used, keeping consistency across all functions.

### One to One¶

When routing from:

• From one starting vertex
• to one ending vertex

### One to Many¶

When routing from:

• From one starting vertex
• to many ending vertices

### Many to One¶

When routing from:

• From many starting vertices
• to one ending vertex

### Many to Many¶

When routing from:

• From many starting vertices
• to many ending vertices

### Combinations¶

When routing from:

• From many different starting vertices
• to many different ending vertices
• Every tuple specifies a pair of a start vertex and an end vertex
• Users can define the combinations as desired.

## Inner Queries¶

There are several kinds of valid inner queries and also the columns returned are depending of the function. Which kind of inner query will depend on the function(s) requirements. To simplify variety of types, ANY-INTEGER and ANY-NUMERICAL is used.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Description of the edges_sql query for dijkstra like functions¶

Column Type Default Description
id ANY-INTEGER   Identifier of the edge.
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
cost ANY-NUMERICAL

Weight of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_cost ANY-NUMERICAL -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Description of the edges_sql query (id is not necessary)

edges_sql: an SQL query, which should return a set of rows with the following columns:
Column Type Default Description
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
cost ANY-NUMERICAL

Weight of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_cost ANY-NUMERICAL -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT SMALLINT, INTEGER, BIGINT, REAL, FLOAT

## Parameters¶

Parameter Type Default Description
edges_sql TEXT   SQL query as described above.
via_vertices ARRAY[ANY-INTEGER]   Array of ordered vertices identifiers that are going to be visited.
directed BOOLEAN true
• When true Graph is considered Directed
• When false the graph is considered as Undirected.
strict BOOLEAN false
• When false ignores missing paths returning all paths found
• When true if a path is missing stops and returns EMPTY SET
U_turn_on_edge BOOLEAN true
• When true departing from a visited vertex will not try to avoid using the edge used to reach it. In other words, U turn using the edge with same id is allowed.
• When false when a departing from a visited vertex tries to avoid using the edge used to reach it. In other words, U turn using the edge with same id is used when no other path is found.

### edges_sql query for aStar - Family of functions and aStar - Family of functions functions¶

edges_sql: an SQL query, which should return a set of rows with the following columns:
Column Type Default Description
id ANY-INTEGER   Identifier of the edge.
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
cost ANY-NUMERICAL

Weight of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_cost ANY-NUMERICAL -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.
x1 ANY-NUMERICAL   X coordinate of source vertex.
y1 ANY-NUMERICAL   Y coordinate of source vertex.
x2 ANY-NUMERICAL   X coordinate of target vertex.
y2 ANY-NUMERICAL   Y coordinate of target vertex.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Edges SQL: an SQL query of a directed graph of capacities, which should return a set of rows with the following columns:
Column Type Default Description
id ANY-INTEGER   Identifier of the edge.
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
capacity ANY-INTEGER

Weight of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_capacity ANY-INTEGER -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT
Edges SQL: an SQL query of a directed graph of capacities, which should return a set of rows with the following columns:
Column Type Default Description
id ANY-INTEGER   Identifier of the edge.
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
capacity ANY-INTEGER

Capacity of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_capacity ANY-INTEGER -1

Capacity of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.
cost ANY-NUMERICAL   Weight of the edge (source, target) if it exists.
reverse_cost ANY-NUMERICAL 0 Weight of the edge (target, source) if it exists.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT smallint, int, bigint, real, float

Description of the Points SQL query

points_sql: an SQL query, which should return a set of rows with the following columns:
Column Type Description
pid ANY-INTEGER

(optional) Identifier of the point.

• If column present, it can not be NULL.
• If column not present, a sequential identifier will be given automatically.
edge_id ANY-INTEGER Identifier of the “closest” edge to the point.
fraction ANY-NUMERICAL Value in <0,1> that indicates the relative postition from the first end point of the edge.
side CHAR

(optional) Value in [‘b’, ‘r’, ‘l’, NULL] indicating if the point is:

• In the right, left of the edge or
• If it doesn’t matter with ‘b’ or NULL.
• If column not present ‘b’ is considered.

Where:

ANY-INTEGER: smallint, int, bigint smallint, int, bigint, real, float

### Description of the combinations_sql query for dijkstra like functions¶

Column Type Default Description
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT

## Return columns & values¶

There are several kinds of columns returned are depending of the function.

### Return values for a path¶

Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)

Column Type Description
seq INT Sequential value starting from 1.
path_seq INT Relative position in the path. Has value 1 for the beginning of a path.
start_vid BIGINT

Identifier of the starting vertex. Returned when multiple starting vetrices are in the query.

end_vid BIGINT

Identifier of the ending vertex. Returned when multiple ending vertices are in the query.

node BIGINT Identifier of the node in the path from start_vid to end_vid.
edge BIGINT Identifier of the edge used to go from node to the next node in the path sequence. -1 for the last node of the path.
cost FLOAT Cost to traverse from node using edge to the next node in the path sequence.
agg_cost FLOAT Aggregate cost from start_v to node.

### Return values for multiple paths from the same source and destination¶

Returns set of (seq, path_id, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)

Column Type Description
seq INT Sequential value starting from 1.
path_id INT Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same start_vid to end_vid combination.
path_seq INT Relative position in the path. Has value 1 for the beginning of a path.
start_vid BIGINT

Identifier of the starting vertex. Returned when multiple starting vetrices are in the query.

end_vid BIGINT

Identifier of the ending vertex. Returned when multiple ending vertices are in the query.

node BIGINT Identifier of the node in the path from start_vid to end_vid.
edge BIGINT Identifier of the edge used to go from node to the next node in the path sequence. -1 for the last node of the path.
cost FLOAT Cost to traverse from node using edge to the next node in the path sequence.
agg_cost FLOAT Aggregate cost from start_v to node.

### Description of the return values for a Cost Matrix - Category function¶

Returns SET OF (start_vid, end_vid, agg_cost)

Column Type Description
start_vid BIGINT Identifier of the starting vertex. Used when multiple starting vetrices are in the query.
end_vid BIGINT Identifier of the ending vertex. Used when multiple ending vertices are in the query.
agg_cost FLOAT Aggregate cost from start_vid to end_vid.

### Description of the Return Values¶

Column Type Description
seq INT Sequential value starting from 1.
edge BIGINT Identifier of the edge in the original query(edges_sql).
start_vid BIGINT Identifier of the first end point vertex of the edge.
end_vid BIGINT Identifier of the second end point vertex of the edge.
flow BIGINT Flow through the edge in the direction (start_vid, end_vid).
residual_capacity BIGINT Residual capacity of the edge in the direction (start_vid, end_vid).
Column Type Description
seq INT Sequential value starting from 1.
edge BIGINT Identifier of the edge in the original query(edges_sql).
source BIGINT Identifier of the first end point vertex of the edge.
target BIGINT Identifier of the second end point vertex of the edge.
flow BIGINT Flow through the edge in the direction (source, target).
residual_capacity BIGINT Residual capacity of the edge in the direction (source, target).
cost FLOAT The cost of sending this flow through the edge in the direction (source, target).
agg_cost FLOAT The aggregate cost.

### Routing Topology¶

Overview

Typically when GIS files are loaded into the data database for use with pgRouting they do not have topology information associated with them. To create a useful topology the data needs to be “noded”. This means that where two or more roads form an intersection there it needs to be a node at the intersection and all the road segments need to be broken at the intersection, assuming that you can navigate from any of these segments to any other segment via that intersection.

You can use the graph analysis functions to help you see where you might have topology problems in your data. If you need to node your data, we also have a function pgr_nodeNetwork() that might work for you. This function splits ALL crossing segments and nodes them. There are some cases where this might NOT be the right thing to do.

For example, when you have an overpass and underpass intersection, you do not want these noded, but pgr_nodeNetwork does not know that is the case and will node them which is not good because then the router will be able to turn off the overpass onto the underpass like it was a flat 2D intersection. To deal with this problem some data sets use z-levels at these types of intersections and other data might not node these intersection which would be ok.

For those cases where topology needs to be added the following functions may be useful. One way to prep the data for pgRouting is to add the following columns to your table and then populate them as appropriate. This example makes a lot of assumption like that you original data tables already has certain columns in it like one_way, fcc, and possibly others and that they contain specific data values. This is only to give you an idea of what you can do with your data.

ALTER TABLE edge_table

SELECT pgr_createTopology('edge_table', 0.000001, 'the_geom', 'id');


The function pgr_createTopology will create the vertices_tmp table and populate the source and target columns. The following example populated the remaining columns. In this example, the fcc column contains feature class code and the CASE statements converts it to an average speed.

UPDATE edge_table SET x1 = st_x(st_startpoint(the_geom)),
y1 = st_y(st_startpoint(the_geom)),
x2 = st_x(st_endpoint(the_geom)),
y2 = st_y(st_endpoint(the_geom)),
cost_len  = st_length_spheroid(the_geom, 'SPHEROID["WGS84",6378137,298.25728]'),
rcost_len = st_length_spheroid(the_geom, 'SPHEROID["WGS84",6378137,298.25728]'),
len_km = st_length_spheroid(the_geom, 'SPHEROID["WGS84",6378137,298.25728]')/1000.0,
len_miles = st_length_spheroid(the_geom, 'SPHEROID["WGS84",6378137,298.25728]')
/ 1000.0 * 0.6213712,
speed_mph = CASE WHEN fcc='A10' THEN 65
WHEN fcc='A15' THEN 65
WHEN fcc='A20' THEN 55
WHEN fcc='A25' THEN 55
WHEN fcc='A30' THEN 45
WHEN fcc='A35' THEN 45
WHEN fcc='A40' THEN 35
WHEN fcc='A45' THEN 35
WHEN fcc='A50' THEN 25
WHEN fcc='A60' THEN 25
WHEN fcc='A61' THEN 25
WHEN fcc='A62' THEN 25
WHEN fcc='A64' THEN 25
WHEN fcc='A70' THEN 15
WHEN fcc='A69' THEN 10
ELSE null END,
speed_kmh = CASE WHEN fcc='A10' THEN 104
WHEN fcc='A15' THEN 104
WHEN fcc='A20' THEN 88
WHEN fcc='A25' THEN 88
WHEN fcc='A30' THEN 72
WHEN fcc='A35' THEN 72
WHEN fcc='A40' THEN 56
WHEN fcc='A45' THEN 56
WHEN fcc='A50' THEN 40
WHEN fcc='A60' THEN 50
WHEN fcc='A61' THEN 40
WHEN fcc='A62' THEN 40
WHEN fcc='A64' THEN 40
WHEN fcc='A70' THEN 25
WHEN fcc='A69' THEN 15
ELSE null END;

-- UPDATE the cost information based on oneway streets

UPDATE edge_table SET
cost_time = CASE
WHEN one_way='TF' THEN 10000.0
ELSE cost_len/1000.0/speed_kmh::numeric*3600.0
END,
rcost_time = CASE
WHEN one_way='FT' THEN 10000.0
ELSE cost_len/1000.0/speed_kmh::numeric*3600.0
END;

-- clean up the database because we have updated a lot of records

VACUUM ANALYZE VERBOSE edge_table;


Now your database should be ready to use any (most?) of the pgRouting algorithms.

### Graph Analytics¶

Overview

It is common to find problems with graphs that have not been constructed fully noded or in graphs with z-levels at intersection that have been entered incorrectly. An other problem is one way streets that have been entered in the wrong direction. We can not detect errors with respect to “ground” truth, but we can look for inconsistencies and some anomalies in a graph and report them for additional inspections.

We do not current have any visualization tools for these problems, but I have used mapserver to render the graph and highlight potential problem areas. Someone familiar with graphviz might contribute tools for generating images with that.

### Analyze a Graph¶

With pgr_analyzeGraph the graph can be checked for errors. For example for table “mytab” that has “mytab_vertices_pgr” as the vertices table:

SELECT pgr_analyzeGraph('mytab', 0.000002);
NOTICE:  Performing checks, pelase wait...
NOTICE:  Analyzing for gaps. Please wait...
NOTICE:  Analyzing for isolated edges. Please wait...
NOTICE:  Analyzing for ring geometries. Please wait...
NOTICE:  Analyzing for intersections. Please wait...
NOTICE:              ANALYSIS RESULTS FOR SELECTED EDGES:
NOTICE:                    Isolated segments: 158
NOTICE:  Potential gaps found near dead ends: 527
NOTICE:               Intersections detected: 2560
NOTICE:                      Ring geometries: 0
pgr_analyzeGraph
----------
OK
(1 row)


In the vertices table “mytab_vertices_pgr”:

• Deadends are identified by cnt=1
• Potencial gap problems are identified with chk=1.
SELECT count(*) as deadends  FROM mytab_vertices_pgr WHERE cnt = 1;
----------
20028
(1 row)

SELECT count(*) as gaps  FROM mytab_vertices_pgr WHERE chk = 1;
gaps
-----
527
(1 row)


For isolated road segments, for example, a segment where both ends are deadends. you can find these with the following query:

SELECT *
FROM mytab a, mytab_vertices_pgr b, mytab_vertices_pgr c
WHERE a.source=b.id AND b.cnt=1 AND a.target=c.id AND c.cnt=1;


If you want to visualize these on a graphic image, then you can use something like mapserver to render the edges and the vertices and style based on cnt or if they are isolated, etc. You can also do this with a tool like graphviz, or geoserver or other similar tools.

### Analyze One Way Streets¶

pgr_analyzeOneWay analyzes one way streets in a graph and identifies any flipped segments. Basically if you count the edges coming into a node and the edges exiting a node the number has to be greater than one.

This query will add two columns to the vertices_tmp table ein int and eout int and populate it with the appropriate counts. After running this on a graph you can identify nodes with potential problems with the following query.

The rules are defined as an array of text strings that if match the col value would be counted as true for the source or target in or out condition.

#### Example¶

Lets assume we have a table “st” of edges and a column “one_way” that might have values like:

• ‘FT’ - oneway from the source to the target node.
• ‘TF’ - oneway from the target to the source node.
• ‘B’ - two way street.
• ‘’ - empty field, assume twoway.
• <NULL> - NULL field, use two_way_if_null flag.

Then we could form the following query to analyze the oneway streets for errors.

SELECT pgr_analyzeOneway('mytab',
ARRAY['', 'B', 'TF'],
ARRAY['', 'B', 'FT'],
ARRAY['', 'B', 'FT'],
ARRAY['', 'B', 'TF'],
);

-- now we can see the problem nodes
SELECT * FROM mytab_vertices_pgr WHERE ein=0 OR eout=0;

-- and the problem edges connected to those nodes
SELECT gid FROM mytab a, mytab_vertices_pgr b WHERE a.source=b.id AND ein=0 OR eout=0
UNION
SELECT gid FROM mytab a, mytab_vertices_pgr b WHERE a.target=b.id AND ein=0 OR eout=0;


Typically these problems are generated by a break in the network, the one way direction set wrong, maybe an error related to z-levels or a network that is not properly noded.

The above tools do not detect all network issues, but they will identify some common problems. There are other problems that are hard to detect because they are more global in nature like multiple disconnected networks. Think of an island with a road network that is not connected to the mainland network because the bridge or ferry routes are missing.

## Performance Tips¶

### For the Routing functions¶

To get faster results bound your queries to the area of interest of routing to have, for example, no more than one million rows.

Use an inner query SQL that does not include some edges in the routing function

SELECT id, source, target from edge_table WHERE
id < 17 and
the_geom  && (select st_buffer(the_geom,1) as myarea FROM  edge_table where id = 5)


Integrating the inner query to the pgRouting function:

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target from edge_table WHERE
id < 17 and
the_geom  && (select st_buffer(the_geom,1) as myarea FROM  edge_table where id = 5)',
1, 2)


### For the topology functions:¶

When “you know” that you are going to remove a set of edges from the edges table, and without those edges you are going to use a routing function you can do the following:

Analize the new topology based on the actual topology:

pgr_analyzegraph('edge_table',rows_where:='id < 17');


Or create a new topology if the change is permanent:

pgr_createTopology('edge_table',rows_where:='id < 17');
pgr_analyzegraph('edge_table',rows_where:='id < 17');
`

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