# pgRouting Manual (2.5)

## pgRouting Concepts

Contents

- pgRouting Concepts
  - Getting Started
    - Create a routing Database
    - Load Data
    - Build a Routing Topology
    - Check the Routing Topology
    - Compute a Path
  - Inner Queries
    - Description of the edges_sql query for dijkstra like functions
    - Description of the edges_sql query (id is not necessary)
    - Description of the parameters of the signatures
    - Description of the edges_sql query for astar like functions
    - Description of the edges_sql query for Max-flow like functions
    - Description of the Points SQL query
  - Return columns & values
    - Description of the return values for a path
    - Description of the return values for a Cost function
    - Description of the Return Values
  - Advanced Topics
    - Routing Topology
    - Graph Analytics
    - Analyze a Graph
    - Analyze One Way Streets
      - Example
  - Performance Tips
    - For the Routing functions
    - For the topology functions:
  - How to contribute

## 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
- Load Data
- Build a Routing Topology
- Check the Routing Topology
- Compute a Path

### 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"

### Load Data

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

shp2pgsql:

- this is the postgresql shapefile loader

ogr2ogr:

- this is a vector data conversion utility

osm2pgsql:

- 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);

- pgr_createTopology

### 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);
    select pgr_analyzeoneway('myroads',  s_in_rules, s_out_rules,
                                         t_in_rules, t_out_rules
                                         direction)
    select pgr_nodeNetwork('myroads', 0.001);

- pgr_analyzeGraph
- pgr_analyzeOneway
- pgr_nodeNetwork

### 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.

- pgr_dijkstra

## Inner Queries

- Description of the edges_sql query for dijkstra like functions
- Description of the edges_sql query (id is not necessary)
- Description of the parameters of the signatures
- Description of the edges_sql query for astar like functions
- Description of the edges_sql query for Max-flow like functions
- Description of the Points SQL query

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

### Description of the edges_sql query for dijkstra like 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.

Where:

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

### Description of the parameters of the signatures

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.

### Description of the edges_sql query for astar like 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
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Description of the edges_sql query for Max-flow like 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.

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

### 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
ANY-NUMERICAL: | smallint, int, bigint, real, float

## Return columns & values

- Description of the return values for a path
- Description of the return values for a Cost function
- Description of the Return Values

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

### Description of the 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_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. 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.
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 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_id | `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).

## Advanced Topics

- Routing Topology
- Graph Analytics
- Analyze a Graph
- Analyze One Way Streets
  - Example

### 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
        ADD COLUMN source integer,
        ADD COLUMN target integer,
        ADD COLUMN cost_len double precision,
        ADD COLUMN cost_time double precision,
        ADD COLUMN rcost_len double precision,
        ADD COLUMN rcost_time double precision,
        ADD COLUMN x1 double precision,
        ADD COLUMN y1 double precision,
        ADD COLUMN x2 double precision,
        ADD COLUMN y2 double precision,
        ADD COLUMN to_cost double precision,
        ADD COLUMN rule text,
        ADD COLUMN isolated integer;

    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 dead ends. Please 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:                            Dead ends: 20028
    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;
    deadends
    ----------
        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
- For the topology functions:

### 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');

## How to contribute

Wiki

- Edit an existing pgRouting Wiki page.
- Or create a new Wiki page
  - Create a page on the pgRouting Wiki
  - Give the title an appropriate name
- Example

Adding Functionaity to pgRouting

Consult the developer’s documentation

Indices and tables

- Index
- Search Page