pgr_edwardMoore - Experimental

pgr_edwardMoore — Returns the shortest path using Edward-Moore algorithm.

Warning

Possible server crash

  • These functions might create a server crash

Warning

Experimental functions

  • They are not officially of the current release.

  • They likely will not be officially be part of the next release:

    • The functions might not make use of ANY-INTEGER and ANY-NUMERICAL

    • Name might change.

    • Signature might change.

    • Functionality might change.

    • pgTap tests might be missing.

    • Might need c/c++ coding.

    • May lack documentation.

    • Documentation if any might need to be rewritten.

    • Documentation examples might need to be automatically generated.

    • Might need a lot of feedback from the comunity.

    • Might depend on a proposed function of pgRouting

    • Might depend on a deprecated function of pgRouting

Availability

Description

Edward Moore’s Algorithm is an improvement of the Bellman-Ford Algorithm. It can compute the shortest paths from a single source vertex to all other vertices in a weighted directed graph. The main difference between Edward Moore’s Algorithm and Bellman Ford’s Algorithm lies in the run time.

The worst-case running time of the algorithm is \(O(| V | * | E |)\) similar to the time complexity of Bellman-Ford algorithm. However, experiments suggest that this algorithm has an average running time complexity of \(O( | E | )\) for random graphs. This is significantly faster in terms of computation speed.

Thus, the algorithm is at-best, significantly faster than Bellman-Ford algorithm and is at-worst,as good as Bellman-Ford algorithm

The main characteristics are:

  • 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 \(\infty\)

  • 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

  • Running time:

    • Worst case: \(O(| V | * | E |)\)

    • Average case: \(O( | E | )\)

Signatures

Summary

pgr_edwardMoore(Edges SQL, start vid,  end vid  [, directed])
pgr_edwardMoore(Edges SQL, start vid,  end vids [, directed])
pgr_edwardMoore(Edges SQL, start vids, end vid  [, directed])
pgr_edwardMoore(Edges SQL, start vids, end vids [, directed])
pgr_edwardMoore(Edges SQL, Combinations SQL [, directed])
RETURNS (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET

One to One

pgr_edwardMoore(Edges SQL, start vid, end vid [, directed]);
RETURNS (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertex \(6\) to vertex \(10\) on a directed graph

SELECT * FROM pgr_edwardMoore(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, 10, true);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    6 |    4 |    1 |        0
   2 |        2 |    7 |    8 |    1 |        1
   3 |        3 |   11 |    9 |    1 |        2
   4 |        4 |   16 |   16 |    1 |        3
   5 |        5 |   15 |    3 |    1 |        4
   6 |        6 |   10 |   -1 |    0 |        5
(6 rows)

One to Many

pgr_edwardMoore(Edges SQL, start vid, end vids [, directed]);
RETURNS (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertex \(6\) to vertices \(\{ 10, 17\}\) on a directed graph

SELECT * FROM pgr_edwardMoore(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, ARRAY[10, 17]);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |      10 |    6 |    4 |    1 |        0
   2 |        2 |      10 |    7 |    8 |    1 |        1
   3 |        3 |      10 |   11 |    9 |    1 |        2
   4 |        4 |      10 |   16 |   16 |    1 |        3
   5 |        5 |      10 |   15 |    3 |    1 |        4
   6 |        6 |      10 |   10 |   -1 |    0 |        5
   7 |        1 |      17 |    6 |    4 |    1 |        0
   8 |        2 |      17 |    7 |    8 |    1 |        1
   9 |        3 |      17 |   11 |   11 |    1 |        2
  10 |        4 |      17 |   12 |   13 |    1 |        3
  11 |        5 |      17 |   17 |   -1 |    0 |        4
(11 rows)

Many to One

pgr_edwardMoore(Edges SQL, start vids, end vid [, directed]);
RETURNS (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertices \(\{6, 1\}\) to vertex \(17\) on a directed graph

SELECT * FROM pgr_edwardMoore(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[6, 1], 17);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         1 |    1 |    6 |    1 |        0
   2 |        2 |         1 |    3 |    7 |    1 |        1
   3 |        3 |         1 |    7 |    8 |    1 |        2
   4 |        4 |         1 |   11 |   11 |    1 |        3
   5 |        5 |         1 |   12 |   13 |    1 |        4
   6 |        6 |         1 |   17 |   -1 |    0 |        5
   7 |        1 |         6 |    6 |    4 |    1 |        0
   8 |        2 |         6 |    7 |    8 |    1 |        1
   9 |        3 |         6 |   11 |   11 |    1 |        2
  10 |        4 |         6 |   12 |   13 |    1 |        3
  11 |        5 |         6 |   17 |   -1 |    0 |        4
(11 rows)

Many to Many

pgr_edwardMoore(Edges SQL, start vids, end vids [, directed]);
RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertices \(\{6, 1\}\) to vertices \(\{10, 17\}\) on an undirected graph

SELECT * FROM pgr_edwardMoore(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[6, 1], ARRAY[10, 17],
  directed => false);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         1 |      10 |    1 |    6 |    1 |        0
   2 |        2 |         1 |      10 |    3 |    7 |    1 |        1
   3 |        3 |         1 |      10 |    7 |    4 |    1 |        2
   4 |        4 |         1 |      10 |    6 |    2 |    1 |        3
   5 |        5 |         1 |      10 |   10 |   -1 |    0 |        4
   6 |        1 |         1 |      17 |    1 |    6 |    1 |        0
   7 |        2 |         1 |      17 |    3 |    7 |    1 |        1
   8 |        3 |         1 |      17 |    7 |    8 |    1 |        2
   9 |        4 |         1 |      17 |   11 |   11 |    1 |        3
  10 |        5 |         1 |      17 |   12 |   13 |    1 |        4
  11 |        6 |         1 |      17 |   17 |   -1 |    0 |        5
  12 |        1 |         6 |      10 |    6 |    2 |    1 |        0
  13 |        2 |         6 |      10 |   10 |   -1 |    0 |        1
  14 |        1 |         6 |      17 |    6 |    4 |    1 |        0
  15 |        2 |         6 |      17 |    7 |    8 |    1 |        1
  16 |        3 |         6 |      17 |   11 |   11 |    1 |        2
  17 |        4 |         6 |      17 |   12 |   13 |    1 |        3
  18 |        5 |         6 |      17 |   17 |   -1 |    0 |        4
(18 rows)

Combinations

pgr_edwardMoore(Edges SQL, Combinations SQL [, directed]);
RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

Using a combinations table on an undirected graph.

The combinations table:

SELECT source, target FROM combinations;
 source | target
--------+--------
      5 |      6
      5 |     10
      6 |      5
      6 |     15
      6 |     14
(5 rows)

The query:

SELECT * FROM pgr_edwardMoore(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT source, target FROM combinations',
  false);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         5 |       6 |    5 |    1 |    1 |        0
   2 |        2 |         5 |       6 |    6 |   -1 |    0 |        1
   3 |        1 |         5 |      10 |    5 |    1 |    1 |        0
   4 |        2 |         5 |      10 |    6 |    2 |    1 |        1
   5 |        3 |         5 |      10 |   10 |   -1 |    0 |        2
   6 |        1 |         6 |       5 |    6 |    1 |    1 |        0
   7 |        2 |         6 |       5 |    5 |   -1 |    0 |        1
   8 |        1 |         6 |      15 |    6 |    2 |    1 |        0
   9 |        2 |         6 |      15 |   10 |    3 |    1 |        1
  10 |        3 |         6 |      15 |   15 |   -1 |    0 |        2
(10 rows)

Parameters

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

Combinations SQL

TEXT

Combinations SQL as described below

start vid

BIGINT

Identifier of the starting vertex of the path.

start vids

ARRAY[BIGINT]

Array of identifiers of starting vertices.

end vid

BIGINT

Identifier of the ending vertex of the path.

end vids

ARRAY[BIGINT]

Array of identifiers of ending vertices.

Optional parameters

Column

Type

Default

Description

directed

BOOLEAN

true

  • When true the graph is considered Directed

  • When false the graph is considered as Undirected.

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

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

Return columns

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

Column

Type

Description

seq

INTEGER

Sequential value starting from 1.

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. 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_vid to node.

Additional Examples

Example 1:

Demonstration of repeated values are ignored, and result is sorted.

SELECT * FROM pgr_edwardMoore(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         7 |      10 |    7 |    8 |    1 |        0
   2 |        2 |         7 |      10 |   11 |    9 |    1 |        1
   3 |        3 |         7 |      10 |   16 |   16 |    1 |        2
   4 |        4 |         7 |      10 |   15 |    3 |    1 |        3
   5 |        5 |         7 |      10 |   10 |   -1 |    0 |        4
   6 |        1 |         7 |      15 |    7 |    8 |    1 |        0
   7 |        2 |         7 |      15 |   11 |    9 |    1 |        1
   8 |        3 |         7 |      15 |   16 |   16 |    1 |        2
   9 |        4 |         7 |      15 |   15 |   -1 |    0 |        3
  10 |        1 |        10 |       7 |   10 |    5 |    1 |        0
  11 |        2 |        10 |       7 |   11 |    8 |    1 |        1
  12 |        3 |        10 |       7 |    7 |   -1 |    0 |        2
  13 |        1 |        10 |      15 |   10 |    5 |    1 |        0
  14 |        2 |        10 |      15 |   11 |    9 |    1 |        1
  15 |        3 |        10 |      15 |   16 |   16 |    1 |        2
  16 |        4 |        10 |      15 |   15 |   -1 |    0 |        3
  17 |        1 |        15 |       7 |   15 |   16 |    1 |        0
  18 |        2 |        15 |       7 |   16 |    9 |    1 |        1
  19 |        3 |        15 |       7 |   11 |    8 |    1 |        2
  20 |        4 |        15 |       7 |    7 |   -1 |    0 |        3
  21 |        1 |        15 |      10 |   15 |    3 |    1 |        0
  22 |        2 |        15 |      10 |   10 |   -1 |    0 |        1
(22 rows)

Example 2:

Making start vids the same as end vids.

SELECT * FROM pgr_edwardMoore(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         7 |      10 |    7 |    8 |    1 |        0
   2 |        2 |         7 |      10 |   11 |    9 |    1 |        1
   3 |        3 |         7 |      10 |   16 |   16 |    1 |        2
   4 |        4 |         7 |      10 |   15 |    3 |    1 |        3
   5 |        5 |         7 |      10 |   10 |   -1 |    0 |        4
   6 |        1 |         7 |      15 |    7 |    8 |    1 |        0
   7 |        2 |         7 |      15 |   11 |    9 |    1 |        1
   8 |        3 |         7 |      15 |   16 |   16 |    1 |        2
   9 |        4 |         7 |      15 |   15 |   -1 |    0 |        3
  10 |        1 |        10 |       7 |   10 |    5 |    1 |        0
  11 |        2 |        10 |       7 |   11 |    8 |    1 |        1
  12 |        3 |        10 |       7 |    7 |   -1 |    0 |        2
  13 |        1 |        10 |      15 |   10 |    5 |    1 |        0
  14 |        2 |        10 |      15 |   11 |    9 |    1 |        1
  15 |        3 |        10 |      15 |   16 |   16 |    1 |        2
  16 |        4 |        10 |      15 |   15 |   -1 |    0 |        3
  17 |        1 |        15 |       7 |   15 |   16 |    1 |        0
  18 |        2 |        15 |       7 |   16 |    9 |    1 |        1
  19 |        3 |        15 |       7 |   11 |    8 |    1 |        2
  20 |        4 |        15 |       7 |    7 |   -1 |    0 |        3
  21 |        1 |        15 |      10 |   15 |    3 |    1 |        0
  22 |        2 |        15 |      10 |   10 |   -1 |    0 |        1
(22 rows)

Example 3:

Manually assigned vertex combinations.

SELECT * FROM pgr_edwardMoore(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
   3 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   4 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   5 |        3 |         6 |      10 |   11 |    9 |    1 |        2
   6 |        4 |         6 |      10 |   16 |   16 |    1 |        3
   7 |        5 |         6 |      10 |   15 |    3 |    1 |        4
   8 |        6 |         6 |      10 |   10 |   -1 |    0 |        5
   9 |        1 |        12 |      10 |   12 |   13 |    1 |        0
  10 |        2 |        12 |      10 |   17 |   15 |    1 |        1
  11 |        3 |        12 |      10 |   16 |   16 |    1 |        2
  12 |        4 |        12 |      10 |   15 |    3 |    1 |        3
  13 |        5 |        12 |      10 |   10 |   -1 |    0 |        4
(13 rows)

See Also

Indices and tables