pgr_contractionDeadEnd - Proposed

pgr_contractionDeadEnd — Performs graph contraction and returns the contracted vertices and edges.

Proposed

Warning

下一版本的拟议功能。

• 它们并未正式出现在当前版本中。

• 它们可能会正式成为下一个版本的一部分：

  • 这些函数使用 ANY-INTEGER 和 ANY-NUMERICAL

  • 名字可能不会改变。（但仍然有可能改变）

  • 签名可能不会改变。（但仍然有可能改变）

  • 功能可能不会改变。（但仍然有可能改变）

  • pgTap 测试已经完成。 但可能需要更多。

  • 文档可能需要完善。

可用性

• Version 3.8.0

  • 新提议的函数。

描述

收缩通过移除部分顶点和边来减小图的大小，例如，可以添加代表原始边序列的边，从而减少图算法所用的总时间和空间。

主要特点是：

• 仅在具有正成本的边进行处理。

• Does not return the full contracted graph.

  • Only changes on the graph are returned.

• The returned values include:

  • The new edges generated by linear contraction.

  • The modified vertices generated by dead end contraction.

• 返回值的排序如下：

  • column id ascending when its a modified vertex.

  • column id with negative numbers descending when its a new edge.

A node is considered a dead end node when:

• 在无向图上：

  • 相邻顶点的个数为1。

• 在有向图上：

  • When there is only one adjacent vertex or

  • When all edges are incoming regardless of the number of adjacent vertices.

Boost 图内部

签名

pgr_contractionDeadEnd(Edges SQL, [options])

options: [directed, forbidden]

Returns set of (type, id, contracted_vertices, source, target, cost)

示例:

Dead end contraction on an undirected graph.

SELECT * FROM pgr_contractionDeadEnd(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  directed => false);
 type | id | contracted_vertices | source | target | cost
------+----+---------------------+--------+--------+------
 v    |  4 | {2}                 |     -1 |     -1 |   -1
 v    |  6 | {5}                 |     -1 |     -1 |   -1
 v    |  7 | {1,3}               |     -1 |     -1 |   -1
 v    |  8 | {9}                 |     -1 |     -1 |   -1
 v    | 14 | {13}                |     -1 |     -1 |   -1
(5 rows)

• The green nodes are dead end nodes.

  • Node \(3\) is a dead end node after node \(1\) is contracted.

参数

参数	类型	描述
Edges SQL	TEXT	Edges SQL 如下所述。

可选参数

列	类型	默认	描述
directed	BOOLEAN	true	当 true 时，该图被视为有 有向 如果为 false ，则该图被视为 无向。

可选收缩参数

列	类型	默认	描述
forbidden	ARRAY[ ANY-INTEGER ]	Empty	禁止收缩的顶点标识符。

内部查询

Edges SQL

列	类型	默认	描述
id	ANY-INTEGER		边的标识符。
source	ANY-INTEGER		边的第一个端点顶点的标识符。
target	ANY-INTEGER		边的第二个端点顶点的标识符。
cost	ANY-NUMERICAL		边(source, target)的权重
reverse_cost	ANY-NUMERICAL	-1	边(target, source)的权重 当为负时：边（ target, source ）不存在，因此它不是图的一部分。

其中：

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

结果列

Returns set of (type, id, contracted_vertices, source, target, cost)

该函数返回一行数据。该行的列包括：

列	类型	描述
type	TEXT	Value = e indicating the row is an edge.
id	BIGINT	A pseudo id of the edge. 此列中的所有数字都是 DISTINCT 从 -1 开始递减序列。
contracted_vertices	ARRAY[BIGINT]	收缩顶点标识符数组。
source	BIGINT	当前边的源顶点的标识符。
target	BIGINT	当前边的目标顶点的标识符。
cost	FLOAT	Weight of the current edge.

其他示例

无向图上的死端顶点

The green nodes are dead end nodes.

• 它们只有一个相邻节点。

SELECT * FROM pgr_contractionDeadEnd(
$$SELECT * FROM (VALUES
  (1, 1, 2, 1, 1),
  (2, 3, 4, 1, -1),
  (3, 2, 5, 1, 1), (4, 2, 6, 1, 1),
  (5, 3, 5, 1, 1), (5, 3, 6, 1, 1))
  AS edges(id,source,target,cost,reverse_cost)$$,
  directed => true);
 type | id | contracted_vertices | source | target | cost
------+----+---------------------+--------+--------+------
 v    |  2 | {1}                 |     -1 |     -1 |   -1
 v    |  3 | {4}                 |     -1 |     -1 |   -1
(2 rows)

有向图上的死端顶点

• The green nodes are dead end nodes

• 蓝色节点具有无限数量的传入和/或传出边缘。

节点	相邻节点	死端	Reason
\(6\)	\(\{1\}\)	Yes	Has only one adjacent node.
\(7\)	\(\{2\}\)	Yes	Has only one adjacent node.
\(8\)	\(\{2, 3\}\)	Yes	有一个以上的相邻节点，且所有边都是传入的。
\(9\)	\(\{4\}\)	Yes	Has only one adjacent node.
\(10\)	\(\{4, 5\}\)	No	有一个以上的相邻节点，且所有边都是向外的。
\(1,2,3,4,5\)	Many adjacent nodes.	No	Has more than one adjacent node and some edges are incoming and some are outgoing.

From above, nodes \(\{6, 7, 9\}\) are dead ends because the total number of adjacent vertices is one.

When there are more than one adjacent vertex, all edges need to be all incoming edges otherwise it is not a dead end.

SELECT * FROM pgr_contractionDeadEnd(
$$SELECT * FROM (VALUES
  (1, 1, 6, 1, 1),
  (2, 2, 7, 1, -1),
  (3, 2, 8, 1, -1),
  (4, 3, 8, 1, -1),
  (5, 9, 4, 1, -1),
  (6, 10, 4, 1, 1),
  (7, 10, 5, 1, 1),
  /* Rest of the graph */
  (8, 1, 25, 1, 1), (9, 1, 26, 1, 1),
  (10, 2, 25, 1, 1), (11, 2, 26, 1, 1),
  (12, 3, 25, 1, 1), (13, 3, 26, 1, 1),
  (14, 4, 25, 1, 1), (15, 4, 26, 1, 1),
  (16, 5, 25, 1, 1), (17, 5, 26, 1, 1)) AS edges(id,source,target,cost,reverse_cost)$$,
  directed => true);
 type | id | contracted_vertices | source | target | cost
------+----+---------------------+--------+--------+------
 v    |  1 | {6}                 |     -1 |     -1 |   -1
 v    |  2 | {7,8}               |     -1 |     -1 |   -1
 v    |  3 | {8}                 |     -1 |     -1 |   -1
 v    |  4 | {9}                 |     -1 |     -1 |   -1
(4 rows)

Step by step dead end contraction

The dead end contraction will stop until there are no more dead end nodes. For example, from the following graph where \(3\) is the dead end node:

After contracting \(3\), node \(2\) is now a dead end node and is contracted:

After contracting \(2\), stop. Node \(1\) has the information of nodes that were contracted.

SELECT * FROM pgr_contractionDeadEnd(
$$SELECT * FROM (VALUES
  (1, 1, 2, 1, -1),
  (2, 2, 3, 1, -1),
  /* Rest of the graph */
  (3, 1, 25, 1, 1), (4, 1, 26, 1, 1),
  (5, 25, 25, 1, 1), (6, 25, 26, 1, 1)) AS edges(id,source,target,cost,reverse_cost)$$,
  directed => true);
 type | id | contracted_vertices | source | target | cost
------+----+---------------------+--------+--------+------
 v    |  1 | {2,3}               |     -1 |     -1 |   -1
(1 row)

Creating the contracted graph

Steps for the creation of the contracted graph

Add additional columns.

ALTER TABLE vertices ADD is_contracted BOOLEAN DEFAULT false;
ALTER TABLE
ALTER TABLE vertices ADD contracted_vertices BIGINT[];
ALTER TABLE

Save results into a table.

SELECT * INTO contraction_results
FROM pgr_contractionDeadEnd(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  directed => false);
SELECT 5

使用 is_contracted 列来指示收缩的顶点。

UPDATE vertices
SET is_contracted = true
WHERE id IN (SELECT  unnest(contracted_vertices) FROM  contraction_results);
UPDATE 6

Fill contracted_vertices with the information from the results that belong to the vertices.

UPDATE vertices
SET contracted_vertices = contraction_results.contracted_vertices
FROM contraction_results
WHERE type = 'v' AND vertices.id = contraction_results.id;
UPDATE 5

The contracted vertices are not part of the contracted graph.

SELECT id, is_contracted
FROM vertices WHERE is_contracted ORDER BY id;
 id | is_contracted
----+---------------
  1 | t
  2 | t
  3 | t
  5 | t
  9 | t
 13 | t
(6 rows)

收缩图

DROP VIEW IF EXISTS contracted_graph;
NOTICE:  view "contracted_graph" does not exist, skipping
DROP VIEW
CREATE VIEW contracted_graph AS
WITH
vertices_in_graph AS (
  SELECT id FROM vertices WHERE is_contracted = false
)
SELECT id, source, target, cost, reverse_cost
FROM edges
WHERE source IN (SELECT * FROM vertices_in_graph)
AND target IN (SELECT * FROM vertices_in_graph)
ORDER BY id;
CREATE VIEW

Using when departure and destination are in the contracted graph

SELECT *
FROM pgr_dijkstra('SELECT * FROM contracted_graph', 6, 17);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |      17 |    6 |    4 |    1 |        0
   2 |        2 |         6 |      17 |    7 |    8 |    1 |        1
   3 |        3 |         6 |      17 |   11 |   11 |    1 |        2
   4 |        4 |         6 |      17 |   12 |   13 |    1 |        3
   5 |        5 |         6 |      17 |   17 |   -1 |    0 |        4
(5 rows)

Using when departure/destination is not in the contracted graph

SELECT * FROM pgr_dijkstra(
  'WITH cul_de_sac AS (
    SELECT contracted_vertices || id as v
    FROM vertices WHERE 1 = ANY(contracted_vertices))
  SELECT id, source, target, cost, reverse_cost FROM edges, cul_de_sac
  WHERE source = ANY(v) AND target = ANY(v)

  UNION

  SELECT id, source, target, cost, reverse_cost FROM contracted_graph',
  1, 17);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         1 |      17 |    1 |    6 |    1 |        0
   2 |        2 |         1 |      17 |    3 |    7 |    1 |        1
   3 |        3 |         1 |      17 |    7 |    8 |    1 |        2
   4 |        4 |         1 |      17 |   11 |    9 |    1 |        3
   5 |        5 |         1 |      17 |   16 |   15 |    1 |        4
   6 |        6 |         1 |      17 |   17 |   -1 |    0 |        5
(6 rows)

Using when departure and destination are not in the contracted graph

SELECT * FROM pgr_dijkstra(
  'WITH cul_de_sac AS (
    SELECT contracted_vertices || id as v
    FROM vertices WHERE 1 = ANY(contracted_vertices) OR 9 = ANY(contracted_vertices))
  SELECT id, source, target, cost, reverse_cost FROM edges, cul_de_sac WHERE source = ANY(v) AND target = ANY(v)

  UNION

  SELECT id, source, target, cost, reverse_cost FROM contracted_graph',
  1, 9);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         1 |       9 |    1 |    6 |    1 |        0
   2 |        2 |         1 |       9 |    3 |    7 |    1 |        1
   3 |        3 |         1 |       9 |    7 |   10 |    1 |        2
   4 |        4 |         1 |       9 |    8 |   14 |    1 |        3
   5 |        5 |         1 |       9 |    9 |   -1 |    0 |        4
(5 rows)

另请参阅

• 收缩 - 函数族

索引和表格

• Index

• Search Page