pgr_withPointsKSP - Proposed

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

Warning

Proposed functions for next mayor release.

• They are not officially in the current release.

• They will likely officially be part of the next mayor release:

  • The functions make use of ANY-INTEGER and ANY-NUMERICAL

  • Name might not change. (But still can)

  • Signature might not change. (But still can)

  • Functionality might not change. (But still can)

  • pgTap tests have being done. But might need more.

  • Documentation might need refinement.

Boost Graph Inside

Availability

Version 3.6.0

• Standarizing output columns to (seq, path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)

• pgr_withPointsKSP (One to One)

  • Signature change: driving_side parameter changed from named optional to unnamed compulsory driving side.

  • Added start_vid and end_vid result columns.

• New overload functions

  • pgr_withPointsKSP (One to Many)

  • pgr_withPointsKSP (Many to One)

  • pgr_withPointsKSP (Many to Many)

  • pgr_withPointsKSP (Combinations)

• Deprecated signature

  • pgr_withpointsksp(text,text,bigint,bigint,integer,boolean,boolean,char,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.

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, 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 EMTPY 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, node, edge, cost, agg_cost)

OR EMTPY 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, node, edge, cost, agg_cost)

OR EMTPY 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 EMTPY 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, node, edge, cost, agg_cost)

OR EMTPY 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 query as described.
Points SQL	TEXT	Points SQL query as described.
start vid	ANY-INTEGER	Identifier of the departure vertex. Negative values represent a point
end vid	ANY-INTEGER	Identifier of the destination vertex. Negative values represent a point
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 postition 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.
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. \(0\) for the last node of the path.
agg_cost	FLOAT	Aggregate cost from start vid to node.

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)

The queries use the Sample Data network.

See Also

• withPoints - Family of functions

• K shortest paths - Category

• Sample Data

Indices and tables

• Index

• Search Page