Supported versions: latest (3.8) 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 main dev
Unsupported versions:2.6 2.5 2.4 2.3 2.2

pgr_withPointsKSP

pgr_withPointsKSP — Yen’s algorithm for K shortest paths using Dijkstra.

Availability

Version 4.0.0

• Function promoted to official.

• Breaking change, signatures no longer available:

  • pgr_withpointsksp(text,text,bigint,bigint,integer,boolean,boolean,character,boolean)

Version 3.6.0

• Output columns standardized to (seq, path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)

• Driving side parameter is positional unnamed and compulsory.

  • Valid values depend on kind of graph

• New proposed signatures:

  • pgr_withPointsKSP(One to Many)

  • pgr_withPointsKSP(Many to One)

  • pgr_withPointsKSP(Many to Many)

  • pgr_withPointsKSP(Combinations)

• Deprecated signatures:

  • pgr_withpointsksp(text,text,bigint,bigint,integer,boolean,boolean,character,boolean)

Version 2.2.0

• New proposed function.

Description

Modifies the graph to include the points defined in the Points SQL and using Yen algorithm, finds the $K$ shortest paths.

Boost Graph Inside

Signatures

pgr_withPointsKSP(Edges SQL, Points SQL, start vid, end vid, K, driving_side, [options])

pgr_withPointsKSP(Edges SQL, Points SQL, start vid, end vids, K, driving_side, [options])

pgr_withPointsKSP(Edges SQL, Points SQL, start vids, end vid, K, driving_side, [options])

pgr_withPointsKSP(Edges SQL, Points SQL, start vids, end vids, K, driving_side, [options])

pgr_withPointsKSP(Edges SQL, Points SQL, Combinations SQL, K, driving_side, [options])

options: [directed, heap_paths, details]

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

OR EMPTY SET

One to One

pgr_withPointsKSP(Edges SQL, Points SQL, start vid, end vid, K, driving_side, [options])

options: [directed, heap_paths, details]

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

OR EMPTY SET

Example:

Get 2 paths from Point $1$ to point $2$ on a directed graph with left side driving.

• For a directed graph.

• No details are given about distance of other points of the query.

• No heap paths are returned.

SELECT * FROM pgr_withPointsKSP(
    'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, -2, 2, 'l');
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
   1 |       1 |        1 |        -1 |      -2 |   -1 |    1 |  0.6 |        0
   2 |       1 |        2 |        -1 |      -2 |    6 |    4 |    1 |      0.6
   3 |       1 |        3 |        -1 |      -2 |    7 |    8 |    1 |      1.6
   4 |       1 |        4 |        -1 |      -2 |   11 |   11 |    1 |      2.6
   5 |       1 |        5 |        -1 |      -2 |   12 |   13 |    1 |      3.6
   6 |       1 |        6 |        -1 |      -2 |   17 |   15 |  0.6 |      4.6
   7 |       1 |        7 |        -1 |      -2 |   -2 |   -1 |    0 |      5.2
   8 |       2 |        1 |        -1 |      -2 |   -1 |    1 |  0.6 |        0
   9 |       2 |        2 |        -1 |      -2 |    6 |    4 |    1 |      0.6
  10 |       2 |        3 |        -1 |      -2 |    7 |    8 |    1 |      1.6
  11 |       2 |        4 |        -1 |      -2 |   11 |    9 |    1 |      2.6
  12 |       2 |        5 |        -1 |      -2 |   16 |   15 |  1.6 |      3.6
  13 |       2 |        6 |        -1 |      -2 |   -2 |   -1 |    0 |      5.2
(13 rows)

One to Many

pgr_withPointsKSP(Edges SQL, Points SQL, start vid, end vids, K, driving_side, [options])

options: [directed, heap_paths, details]

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

OR EMPTY SET

Example:

Get 2 paths from point $1$ to point $3$ and vertex $7$ on an undirected graph

SELECT * FROM pgr_withPointsKSP(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  -1, ARRAY[-3, 7], 2, 'B',
  directed => false);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
   1 |       1 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |       1 |        2 |        -1 |      -3 |    6 |    4 |    1 |      0.6
   3 |       1 |        3 |        -1 |      -3 |    7 |   10 |    1 |      1.6
   4 |       1 |        4 |        -1 |      -3 |    8 |   12 |  0.6 |      2.6
   5 |       1 |        5 |        -1 |      -3 |   -3 |   -1 |    0 |      3.2
   6 |       2 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
   7 |       2 |        2 |        -1 |      -3 |    6 |    4 |    1 |      0.6
   8 |       2 |        3 |        -1 |      -3 |    7 |    8 |    1 |      1.6
   9 |       2 |        4 |        -1 |      -3 |   11 |   11 |    1 |      2.6
  10 |       2 |        5 |        -1 |      -3 |   12 |   12 |  0.4 |      3.6
  11 |       2 |        6 |        -1 |      -3 |   -3 |   -1 |    0 |        4
  12 |       3 |        1 |        -1 |       7 |   -1 |    1 |  0.6 |        0
  13 |       3 |        2 |        -1 |       7 |    6 |    4 |    1 |      0.6
  14 |       3 |        3 |        -1 |       7 |    7 |   -1 |    0 |      1.6
  15 |       4 |        1 |        -1 |       7 |   -1 |    1 |  0.6 |        0
  16 |       4 |        2 |        -1 |       7 |    6 |    2 |    1 |      0.6
  17 |       4 |        3 |        -1 |       7 |   10 |    5 |    1 |      1.6
  18 |       4 |        4 |        -1 |       7 |   11 |    8 |    1 |      2.6
  19 |       4 |        5 |        -1 |       7 |    7 |   -1 |    0 |      3.6
(19 rows)

Many to One

pgr_withPointsKSP(Edges SQL, Points SQL, start vids, end vid, K, driving_side, [options])

options: [directed, heap_paths, details]

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

OR EMPTY SET

Example:

Get a path from point $1$ and vertex $6$ to point $3$ on a directed graph with right side driving and details set to True

SELECT * FROM pgr_withPointsKSP(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 6], -3, 1, 'r', details=> true);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
   1 |       1 |        1 |        -1 |      -3 |   -1 |    1 |  0.4 |        0
   2 |       1 |        2 |        -1 |      -3 |    5 |    1 |    1 |      0.4
   3 |       1 |        3 |        -1 |      -3 |    6 |    4 |  0.7 |      1.4
   4 |       1 |        4 |        -1 |      -3 |   -6 |    4 |  0.3 |      2.1
   5 |       1 |        5 |        -1 |      -3 |    7 |   10 |    1 |      2.4
   6 |       1 |        6 |        -1 |      -3 |    8 |   12 |  0.6 |      3.4
   7 |       1 |        7 |        -1 |      -3 |   -3 |   -1 |    0 |        4
   8 |       2 |        1 |         6 |      -3 |    6 |    4 |  0.7 |        0
   9 |       2 |        2 |         6 |      -3 |   -6 |    4 |  0.3 |      0.7
  10 |       2 |        3 |         6 |      -3 |    7 |   10 |    1 |        1
  11 |       2 |        4 |         6 |      -3 |    8 |   12 |  0.6 |        2
  12 |       2 |        5 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
(12 rows)

Many to Many

pgr_withPointsKSP(Edges SQL, Points SQL, start vids, end vids, K, driving_side, [options])

options: [directed, heap_paths, details]

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

OR EMPTY SET

Example:

Get a path from point $1$ and vertex $6$ to point $3$ and vertex $1$ on a directed graph with left side driving and heap_paths set to True

SELECT * FROM pgr_withPointsKSP(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 6], ARRAY[-3, 1], 1, 'l', heap_paths => true);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
   1 |       1 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |       1 |        2 |        -1 |      -3 |    6 |    4 |    1 |      0.6
   3 |       1 |        3 |        -1 |      -3 |    7 |   10 |    1 |      1.6
   4 |       1 |        4 |        -1 |      -3 |    8 |   12 |  0.6 |      2.6
   5 |       1 |        5 |        -1 |      -3 |   -3 |   -1 |    0 |      3.2
   6 |       2 |        1 |        -1 |       1 |   -1 |    1 |  0.6 |        0
   7 |       2 |        2 |        -1 |       1 |    6 |    4 |    1 |      0.6
   8 |       2 |        3 |        -1 |       1 |    7 |    7 |    1 |      1.6
   9 |       2 |        4 |        -1 |       1 |    3 |    6 |    1 |      2.6
  10 |       2 |        5 |        -1 |       1 |    1 |   -1 |    0 |      3.6
  11 |       3 |        1 |         6 |      -3 |    6 |    4 |    1 |        0
  12 |       3 |        2 |         6 |      -3 |    7 |   10 |    1 |        1
  13 |       3 |        3 |         6 |      -3 |    8 |   12 |  0.6 |        2
  14 |       3 |        4 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
  15 |       4 |        1 |         6 |       1 |    6 |    4 |    1 |        0
  16 |       4 |        2 |         6 |       1 |    7 |    7 |    1 |        1
  17 |       4 |        3 |         6 |       1 |    3 |    6 |    1 |        2
  18 |       4 |        4 |         6 |       1 |    1 |   -1 |    0 |        3
(18 rows)

Combinations

pgr_withPointsKSP(Edges SQL, Points SQL, Combinations SQL, K, driving_side, [options])

options: [directed, heap_paths, details]

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

OR EMPTY SET

Example:

Using a combinations table on an directed graph

SELECT * FROM pgr_withPointsKSP(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  'SELECT * FROM (VALUES (-1, 10), (6, -3)) AS combinations(source, target)',
  2, 'r', details => true);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
   1 |       1 |        1 |        -1 |      10 |   -1 |    1 |  0.4 |        0
   2 |       1 |        2 |        -1 |      10 |    5 |    1 |    1 |      0.4
   3 |       1 |        3 |        -1 |      10 |    6 |    4 |  0.7 |      1.4
   4 |       1 |        4 |        -1 |      10 |   -6 |    4 |  0.3 |      2.1
   5 |       1 |        5 |        -1 |      10 |    7 |    8 |    1 |      2.4
   6 |       1 |        6 |        -1 |      10 |   11 |    9 |    1 |      3.4
   7 |       1 |        7 |        -1 |      10 |   16 |   16 |    1 |      4.4
   8 |       1 |        8 |        -1 |      10 |   15 |    3 |    1 |      5.4
   9 |       1 |        9 |        -1 |      10 |   10 |   -1 |    0 |      6.4
  10 |       2 |        1 |        -1 |      10 |   -1 |    1 |  0.4 |        0
  11 |       2 |        2 |        -1 |      10 |    5 |    1 |    1 |      0.4
  12 |       2 |        3 |        -1 |      10 |    6 |    4 |  0.7 |      1.4
  13 |       2 |        4 |        -1 |      10 |   -6 |    4 |  0.3 |      2.1
  14 |       2 |        5 |        -1 |      10 |    7 |    8 |    1 |      2.4
  15 |       2 |        6 |        -1 |      10 |   11 |   11 |    1 |      3.4
  16 |       2 |        7 |        -1 |      10 |   12 |   13 |    1 |      4.4
  17 |       2 |        8 |        -1 |      10 |   17 |   15 |    1 |      5.4
  18 |       2 |        9 |        -1 |      10 |   16 |   16 |    1 |      6.4
  19 |       2 |       10 |        -1 |      10 |   15 |    3 |    1 |      7.4
  20 |       2 |       11 |        -1 |      10 |   10 |   -1 |    0 |      8.4
  21 |       3 |        1 |         6 |      -3 |    6 |    4 |  0.7 |        0
  22 |       3 |        2 |         6 |      -3 |   -6 |    4 |  0.3 |      0.7
  23 |       3 |        3 |         6 |      -3 |    7 |   10 |    1 |        1
  24 |       3 |        4 |         6 |      -3 |    8 |   12 |  0.6 |        2
  25 |       3 |        5 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
(25 rows)

Parameters

Column	Type	Description
Edges SQL	TEXT	Edges SQL as described below
Points SQL	TEXT	Points SQL as described below
Combinations SQL	TEXT	Combinations SQL as described below
start vid	BIGINT	Identifier of the starting vertex of the path. Negative value is for point’s identifier.
start vids	ARRAY[BIGINT]	Array of identifiers of starting vertices. Negative values are for point’s identifiers.
end vid	BIGINT	Identifier of the ending vertex of the path. Negative value is for point’s identifier.
end vids	ARRAY[BIGINT]	Array of identifiers of ending vertices. Negative values are for point’s identifiers.
K	ANY-INTEGER	Number of required paths
driving side	CHAR	Value in [r, R, l, L, b, B] indicating if the driving side is: [r, R] for right driving side (for directed graph only) [l, L] for left driving side (for directed graph only) [b, B] for both (only for undirected graph)

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

Optional parameters

Column	Type	Default	Description
directed	BOOLEAN	true	When true the graph is considered Directed When false the graph is considered as Undirected.

KSP Optional parameters

Column	Type	Default	Description
heap_paths	BOOLEAN	false	When false Returns at most K paths. When true all the calculated paths while processing are returned. Roughly, when the shortest path has N edges, the heap will contain about than N * K paths for small value of K and K > 5.

withPointsKSP optional parameters

Parameter	Type	Default	Description
details	BOOLEAN	false	When true the results will include the points that are in the path. When false the results will not include the points that are in the path.

Inner Queries

Edges SQL

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)
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

Points SQL

Parameter	Type	Default	Description
pid	ANY-INTEGER	value	Identifier of the point. Use with positive value, as internally will be converted to negative value If column is present, it can not be NULL. If column is not present, a sequential negative value 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 position from the first end point of the edge.
side	CHAR	b	Value in [b, r, l, NULL] indicating if the point is: In the right r, In the left l, In both sides b, NULL

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Combinations SQL

Parameter	Type	Description
source	ANY-INTEGER	Identifier of the departure vertex.
target	ANY-INTEGER	Identifier of the arrival vertex.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

Result columns

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

Column	Type	Description
seq	INTEGER	Sequential value starting from 1.
path_id	INTEGER	Path identifier. Has value 1 for the first of a path from start_vid to end_vid.
path_seq	INTEGER	Relative position in the path. Has value 1 for the beginning of a path.
start_vid	BIGINT	Identifier of the starting vertex.
end_vid	BIGINT	Identifier of the ending vertex.
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_vid to node.

Note

When start_vid or end_vid columns have negative values, the identifier is for a Point.

Additional Examples

Use pgr_findCloseEdges in the Points SQL.

Get $2$ paths using left side driving topology, from vertex $1$ to the closest location on the graph of point (2.9, 1.8).

SELECT * FROM pgr_withPointsKSP(
  $e$ SELECT * FROM edges $e$,
  $p$ SELECT edge_id, round(fraction::numeric, 2) AS fraction, side
      FROM pgr_findCloseEdges(
        $$SELECT id, geom FROM edges$$,
        (SELECT ST_POINT(2.9, 1.8)),
        0.5, cap => 2)
  $p$,
  1, -1, 2,'r');
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
   1 |       1 |        1 |         1 |      -1 |    1 |    6 |    1 |        0
   2 |       1 |        2 |         1 |      -1 |    3 |    7 |    1 |        1
   3 |       1 |        3 |         1 |      -1 |    7 |    8 |    1 |        2
   4 |       1 |        4 |         1 |      -1 |   11 |    9 |    1 |        3
   5 |       1 |        5 |         1 |      -1 |   16 |   16 |    1 |        4
   6 |       1 |        6 |         1 |      -1 |   15 |    3 |    1 |        5
   7 |       1 |        7 |         1 |      -1 |   10 |    5 |  0.8 |        6
   8 |       1 |        8 |         1 |      -1 |   -1 |   -1 |    0 |      6.8
   9 |       2 |        1 |         1 |      -1 |    1 |    6 |    1 |        0
  10 |       2 |        2 |         1 |      -1 |    3 |    7 |    1 |        1
  11 |       2 |        3 |         1 |      -1 |    7 |   10 |    1 |        2
  12 |       2 |        4 |         1 |      -1 |    8 |   12 |    1 |        3
  13 |       2 |        5 |         1 |      -1 |   12 |   13 |    1 |        4
  14 |       2 |        6 |         1 |      -1 |   17 |   15 |    1 |        5
  15 |       2 |        7 |         1 |      -1 |   16 |   16 |    1 |        6
  16 |       2 |        8 |         1 |      -1 |   15 |    3 |    1 |        7
  17 |       2 |        9 |         1 |      -1 |   10 |    5 |  0.8 |        8
  18 |       2 |       10 |         1 |      -1 |   -1 |   -1 |    0 |      8.8
(18 rows)

• Point $-1$ corresponds to the closest edge from point (2.9, 1.8).

Left driving side

Get $2$ paths using left side driving topology, from point $1$ to point $3$ with details.

SELECT * FROM pgr_withPointsKSP(
    'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, -3, 2, 'l', details => true);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
   1 |       1 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |       1 |        2 |        -1 |      -3 |    6 |    4 |  0.7 |      0.6
   3 |       1 |        3 |        -1 |      -3 |   -6 |    4 |  0.3 |      1.3
   4 |       1 |        4 |        -1 |      -3 |    7 |   10 |    1 |      1.6
   5 |       1 |        5 |        -1 |      -3 |    8 |   12 |  0.6 |      2.6
   6 |       1 |        6 |        -1 |      -3 |   -3 |   -1 |    0 |      3.2
(6 rows)

Right driving side

Get $2$ paths using right side driving topology from, point $1$ to point $2$ with heap paths and details.

SELECT * FROM pgr_withPointsKSP(
    'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, -2, 2, 'r',
    heap_paths => true, details => true);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
   1 |       1 |        1 |        -1 |      -2 |   -1 |    1 |  0.4 |        0
   2 |       1 |        2 |        -1 |      -2 |    5 |    1 |    1 |      0.4
   3 |       1 |        3 |        -1 |      -2 |    6 |    4 |  0.7 |      1.4
   4 |       1 |        4 |        -1 |      -2 |   -6 |    4 |  0.3 |      2.1
   5 |       1 |        5 |        -1 |      -2 |    7 |    8 |    1 |      2.4
   6 |       1 |        6 |        -1 |      -2 |   11 |    9 |    1 |      3.4
   7 |       1 |        7 |        -1 |      -2 |   16 |   15 |  0.4 |      4.4
   8 |       1 |        8 |        -1 |      -2 |   -2 |   -1 |    0 |      4.8
   9 |       2 |        1 |        -1 |      -2 |   -1 |    1 |  0.4 |        0
  10 |       2 |        2 |        -1 |      -2 |    5 |    1 |    1 |      0.4
  11 |       2 |        3 |        -1 |      -2 |    6 |    4 |  0.7 |      1.4
  12 |       2 |        4 |        -1 |      -2 |   -6 |    4 |  0.3 |      2.1
  13 |       2 |        5 |        -1 |      -2 |    7 |    8 |    1 |      2.4
  14 |       2 |        6 |        -1 |      -2 |   11 |   11 |    1 |      3.4
  15 |       2 |        7 |        -1 |      -2 |   12 |   13 |    1 |      4.4
  16 |       2 |        8 |        -1 |      -2 |   17 |   15 |    1 |      5.4
  17 |       2 |        9 |        -1 |      -2 |   16 |   15 |  0.4 |      6.4
  18 |       2 |       10 |        -1 |      -2 |   -2 |   -1 |    0 |      6.8
  19 |       3 |        1 |        -1 |      -2 |   -1 |    1 |  0.4 |        0
  20 |       3 |        2 |        -1 |      -2 |    5 |    1 |    1 |      0.4
  21 |       3 |        3 |        -1 |      -2 |    6 |    4 |  0.7 |      1.4
  22 |       3 |        4 |        -1 |      -2 |   -6 |    4 |  0.3 |      2.1
  23 |       3 |        5 |        -1 |      -2 |    7 |   10 |    1 |      2.4
  24 |       3 |        6 |        -1 |      -2 |    8 |   12 |  0.6 |      3.4
  25 |       3 |        7 |        -1 |      -2 |   -3 |   12 |  0.4 |        4
  26 |       3 |        8 |        -1 |      -2 |   12 |   13 |    1 |      4.4
  27 |       3 |        9 |        -1 |      -2 |   17 |   15 |    1 |      5.4
  28 |       3 |       10 |        -1 |      -2 |   16 |   15 |  0.4 |      6.4
  29 |       3 |       11 |        -1 |      -2 |   -2 |   -1 |    0 |      6.8
(29 rows)

See Also

• withPoints - Family of functions

• K shortest paths - Category

• Sample Data

Indices and tables

• Index

• Search Page