pgr_withPoints¶
Name¶
pgr_withPoints  Returns the shortest path in a graph with additional temporary vertices.
Note
This is a proposed function for version 2.3.
 Is not officially in the version 2.2 release.
Synopsis¶
Modify the graph to include points defined by points_sql. Using Dijkstra algorithm, find the shortest path(s)
Characteristics:¶
The main Characteristics are:
 Process is done only on edges with positive costs.
 Vertices of the graph are:
 positive when it belongs to the edges_sql
 negative when it belongs to the points_sql
 Values are returned when there is a path.
 When the starting vertex and ending vertex are the same, there is no path.
 The agg_cost the non included values (v, v) is 0
 When the starting vertex and ending vertex are the different and there is no path:
 The agg_cost the non included values (u, v) is ∞
 For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.
 The returned values are ordered:
 start_vid ascending
 end_vid ascending
 Runing time: \(O(start\_vids∗(V \log V + E))\)
Signature Summary¶
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid)
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid, directed, driving_side, details)
pgr_withPoints(edges_sql, points_sql, start_vid, end_vids, directed, driving_side, details)
pgr_withPoints(edges_sql, points_sql, start_vids, end_vid, directed, driving_side, details)
pgr_withPoints(edges_sql, points_sql, start_vids, end_vids, directed, driving_side, details)
RETURNS SET OF (seq, path_seq, [start_vid,] [end_vid,] node, edge, cost, agg_cost)
Signatures¶
Minimal signature¶
 The minimal signature:
 Is for a directed graph.
 The driving side is set as b both. So arriving/departing to/from the point(s) can be in any direction.
 No details are given about distance of other points of points_sql query.
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example:  From point 1 to point 3 

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
1, 3);
seq  path_seq  node  edge  cost  agg_cost
+++++
1  1  1  1  0.6  0
2  2  2  4  1  0.6
3  3  5  10  1  1.6
4  4  10  12  0.6  2.6
5  5  3  1  0  3.2
(5 rows)
One to One¶
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid,
directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example:  From point 1 to vertex 3 

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
1, 3,
details := true);
seq  path_seq  node  edge  cost  agg_cost
+++++
1  1  1  1  0.6  0
2  2  2  4  0.7  0.6
3  3  6  4  0.3  1.3
4  4  5  8  1  1.6
5  5  6  9  1  2.6
6  6  9  16  1  3.6
7  7  4  3  1  4.6
8  8  3  1  0  5.6
(8 rows)
One to Many¶
pgr_withPoints(edges_sql, points_sql, start_vid, end_vids,
directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
Example:  From point 1 to point 3 and vertex 5 

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
1, ARRAY[3,5]);
seq  path_seq  end_pid  node  edge  cost  agg_cost
++++++
1  1  3  1  1  0.6  0
2  2  3  2  4  1  0.6
3  3  3  5  10  1  1.6
4  4  3  10  12  0.6  2.6
5  5  3  3  1  0  3.2
6  1  5  1  1  0.6  0
7  2  5  2  4  1  0.6
8  3  5  5  1  0  1.6
(8 rows)
Many to One¶
pgr_withPoints(edges_sql, points_sql, start_vids, end_vid,
directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
Example:  From point 1 and vertex 2 to point 3 

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[1,2], 3);
seq  path_seq  start_pid  node  edge  cost  agg_cost
++++++
1  1  1  1  1  0.6  0
2  2  1  2  4  1  0.6
3  3  1  5  10  1  1.6
4  4  1  10  12  0.6  2.6
5  5  1  3  1  0  3.2
6  1  2  2  4  1  0
7  2  2  5  10  1  1
8  3  2  10  12  0.6  2
9  4  2  3  1  0  2.6
(9 rows)
Many to Many¶
pgr_withPoints(edges_sql, points_sql, start_vids, end_vids,
directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
Example:  From point 1 and vertex 2 to point 3 and vertex 7 

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[1,2], ARRAY[3,7]);
seq  path_seq  start_pid  end_pid  node  edge  cost  agg_cost
+++++++
1  1  1  3  1  1  0.6  0
2  2  1  3  2  4  1  0.6
3  3  1  3  5  10  1  1.6
4  4  1  3  10  12  0.6  2.6
5  5  1  3  3  1  0  3.2
6  1  1  7  1  1  0.6  0
7  2  1  7  2  4  1  0.6
8  3  1  7  5  7  1  1.6
9  4  1  7  8  6  1  2.6
10  5  1  7  7  1  0  3.6
11  1  2  3  2  4  1  0
12  2  2  3  5  10  1  1
13  3  2  3  10  12  0.6  2
14  4  2  3  3  1  0  2.6
15  1  2  7  2  4  1  0
16  2  2  7  5  7  1  1
17  3  2  7  8  6  1  2
18  4  2  7  7  1  0  3
(18 rows)
Description of the Signatures¶
Description of the Edges SQL query¶
edges_sql:  an SQL query, which should return a set of rows with the following columns: 

Column  Type  Description 

id  ANYINTEGER  Identifier of the edge. 
source  ANYINTEGER  Identifier of the first end point vertex of the edge. 
target  ANYINTEGER  Identifier of the second end point vertex of the edge. 
cost  ANYNUMERICAL  Weight of the edge (source, target), If negative: edge (source, target) does not exist, therefore it’s not part of the graph. 
reverse_cost  ANYNUMERICAL  (optional) Weight of the edge (target, source), If negative: edge (target, source) does not exist, therefore it’s not part of the graph. 
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  ANYINTEGER 

edge_id  ANYINTEGER  Identifier of the “closest” edge to the point. 
fraction  ANYNUMERICAL  Value in <0,1> that indicates the relative postition from the first end point of the edge. 
side  CHAR 

Where:
ANYINTEGER:  smallint, int, bigint 

ANYNUMERICAL:  smallint, int, bigint, real, float 
Description of the parameters of the signatures¶
Parameter  Type  Description 

edges_sql  TEXT  Edges SQL query as decribed above. 
points_sql  TEXT  Points SQL query as decribed above. 
start_vid  ANYINTEGER  Starting vertex identifier. When negative: is a point’s pid. 
end_vid  ANYINTEGER  Ending vertex identifier. When negative: is a point’s pid. 
start_vids  ARRAY[ANYINTEGER]  Array of identifiers of starting vertices. When negative: is a point’s pid. 
end_vids  ARRAY[ANYINTEGER]  Array of identifiers of ending vertices. When negative: is a point’s pid. 
directed  BOOLEAN  (optional). When false the graph is considered as Undirected. Default is true which considers the graph as Directed. 
driving_side  CHAR 

details  BOOLEAN  (optional). When true the results will include the points in points_sql that are in the path. Default is false which ignores other points of the points_sql. 
Description of the return values¶
Returns set of (seq, [path_seq,] [start_vid,] [end_vid,] node, edge, cost, agg_cost)
Column  Type  Description 

seq  INTEGER  Row sequence. 
path_seq  INTEGER  Path sequence that indicates the relative position on the path. 
start_vid  BIGINT  Identifier of the starting vertex. When negative: is a point’s pid. 
end_vid  BIGINT  Identifier of the ending vertex. When negative: is a point’s pid. 
node  BIGINT 

edge  BIGINT 

cost  FLOAT 

agg_cost  FLOAT 

Examples¶
Example:  Which path (if any) passes in front of point 6 or vertex 6 with right side driving topology. 

SELECT ('('  start_pid  ' => '  end_pid ') at '  path_seq  'th step:')::TEXT AS path_at,
CASE WHEN edge = 1 THEN ' visits'
ELSE ' passes in front of'
END as status,
CASE WHEN node < 0 THEN 'Point'
ELSE 'Vertex'
END as is_a,
abs(node) as id
FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[1,1], ARRAY[2,3,6,3,6],
driving_side := 'r',
details := true)
WHERE node IN (6,6);
path_at  status  is_a  id
+++
(1 => 6) at 4th step:  visits  Point  6
(1 => 3) at 4th step:  passes in front of  Point  6
(1 => 2) at 4th step:  passes in front of  Point  6
(1 => 2) at 6th step:  passes in front of  Vertex  6
(1 => 3) at 4th step:  passes in front of  Point  6
(1 => 3) at 6th step:  passes in front of  Vertex  6
(1 => 6) at 4th step:  passes in front of  Point  6
(1 => 6) at 6th step:  visits  Vertex  6
(1 => 6) at 3th step:  visits  Point  6
(1 => 3) at 3th step:  passes in front of  Point  6
(1 => 2) at 3th step:  passes in front of  Point  6
(1 => 2) at 5th step:  passes in front of  Vertex  6
(1 => 3) at 3th step:  passes in front of  Point  6
(1 => 3) at 5th step:  passes in front of  Vertex  6
(1 => 6) at 3th step:  passes in front of  Point  6
(1 => 6) at 5th step:  visits  Vertex  6
(16 rows)
Example:  Which path (if any) passes in front of point 6 or vertex 6 with left side driving topology. 

SELECT ('('  start_pid  ' => '  end_pid ') at '  path_seq  'th step:')::TEXT AS path_at,
CASE WHEN edge = 1 THEN ' visits'
ELSE ' passes in front of'
END as status,
CASE WHEN node < 0 THEN 'Point'
ELSE 'Vertex'
END as is_a,
abs(node) as id
FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[1,1], ARRAY[2,3,6,3,6],
driving_side := 'l',
details := true)
WHERE node IN (6,6);
path_at  status  is_a  id
+++
(1 => 6) at 3th step:  visits  Point  6
(1 => 3) at 3th step:  passes in front of  Point  6
(1 => 2) at 3th step:  passes in front of  Point  6
(1 => 2) at 5th step:  passes in front of  Vertex  6
(1 => 3) at 3th step:  passes in front of  Point  6
(1 => 3) at 5th step:  passes in front of  Vertex  6
(1 => 6) at 3th step:  passes in front of  Point  6
(1 => 6) at 5th step:  visits  Vertex  6
(1 => 6) at 4th step:  visits  Point  6
(1 => 3) at 4th step:  passes in front of  Point  6
(1 => 2) at 4th step:  passes in front of  Point  6
(1 => 2) at 6th step:  passes in front of  Vertex  6
(1 => 3) at 4th step:  passes in front of  Point  6
(1 => 3) at 6th step:  passes in front of  Vertex  6
(1 => 6) at 4th step:  passes in front of  Point  6
(1 => 6) at 6th step:  visits  Vertex  6
(16 rows)
Example:  Many to many example with a twist: on undirected graph and showing details. 

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[1,2], ARRAY[3,7],
directed := false,
details := true);
seq  path_seq  start_pid  end_pid  node  edge  cost  agg_cost
+++++++
1  1  1  3  1  1  0.6  0
2  2  1  3  2  4  0.7  0.6
3  3  1  3  6  4  0.3  1.3
4  4  1  3  5  10  1  1.6
5  5  1  3  10  12  0.6  2.6
6  6  1  3  3  1  0  3.2
7  1  1  7  1  1  0.6  0
8  2  1  7  2  4  0.7  0.6
9  3  1  7  6  4  0.3  1.3
10  4  1  7  5  7  1  1.6
11  5  1  7  8  6  0.7  2.6
12  6  1  7  4  6  0.3  3.3
13  7  1  7  7  1  0  3.6
14  1  2  3  2  4  0.7  0
15  2  2  3  6  4  0.3  0.7
16  3  2  3  5  10  1  1
17  4  2  3  10  12  0.6  2
18  5  2  3  3  1  0  2.6
19  1  2  7  2  4  0.7  0
20  2  2  7  6  4  0.3  0.7
21  3  2  7  5  7  1  1
22  4  2  7  8  6  0.7  2
23  5  2  7  4  6  0.3  2.7
24  6  2  7  7  1  0  3
(24 rows)
The queries use the Sample Data network.
History
 Proposed in version 2.2