Grouping connected linestrings in PostGIS?

Question

I have a table of streets I've selected based on a set of attributes (let's say it's speed_limit < 25). There are groups of streets that are locally contiguous; I'd like to group these sets of connected linestrings into GeometryCollections. In the image below, there would be two GeometryCollections: one with the red lines and one with the blue lines.

I tried running a couple of "dissolve, deaggregate" queries along the lines of:

SELECT (ST_Dump(st_union)).geom
FROM 
    (SELECT ST_Union(geom) FROM roads) sq

With everything I've tried, I either end up with a single feature (ST_Union) or my original geometry (ST_Dump of ST_Union).

Maybe it's possible to do this with some kind of WITH RECURSIVE magic?

Answer 1

So, by example. Here's a simple table with two connected groups of edges:

drop table lines;
create table lines ( id integer primary key, geom geometry(linestring) );
insert into lines (id, geom) values ( 1, 'LINESTRING(0 0, 0 1)');
insert into lines (id, geom) values ( 2, 'LINESTRING(0 1, 1 1)');
insert into lines (id, geom) values ( 3, 'LINESTRING(1 1, 1 2)');
insert into lines (id, geom) values ( 4, 'LINESTRING(1 2, 2 2)');
insert into lines (id, geom) values ( 11, 'LINESTRING(10 10, 10 11)');
insert into lines (id, geom) values ( 12, 'LINESTRING(10 11, 11 11)');
insert into lines (id, geom) values ( 13, 'LINESTRING(11 11, 11 12)');
insert into lines (id, geom) values ( 14, 'LINESTRING(11 12, 12 12)');
create index lines_gix on lines using gist(geom);

Now, here's a recursive function that, given the id of an edge, accumulates all the edges that touch:

CREATE OR REPLACE FUNCTION find_connected(integer) returns integer[] AS
$$
WITH RECURSIVE lines_r AS (
  SELECT ARRAY[id] AS idlist, geom, id
  FROM lines 
  WHERE id = $1
  UNION ALL
  SELECT array_append(lines_r.idlist, lines.id) AS idlist, 
         lines.geom AS geom, 
         lines.id AS id
  FROM lines, lines_r
  WHERE ST_Touches(lines.geom, lines_r.geom)
  AND NOT lines_r.idlist @> ARRAY[lines.id]
)
SELECT 
  array_agg(id) AS idlist
  FROM lines_r
$$ 
LANGUAGE 'sql';

That just leaves us needing to find, after each group is accumulated, the id of an edge that is not already part of a group. Which, tragically, requires a second recursive query.

WITH RECURSIVE groups_r AS (
  (SELECT find_connected(id) AS idlist, 
          find_connected(id) AS grouplist, 
          id FROM lines WHERE id = 1)
  UNION ALL
  (SELECT array_cat(groups_r.idlist,find_connected(lines.id)) AS idlist,
         find_connected(lines.id) AS grouplist,
         lines.id
  FROM lines, groups_r
  WHERE NOT idlist @> ARRAY[lines.id]
  LIMIT 1)
)
SELECT id, grouplist
FROM groups_r;   

Which taken together return a nice set with the seed id and each group it accumulated. I leave it as an exercise to the reader to turn the arrays of id back into a query to create geometry for mapping.

 id |   grouplist   
----+---------------
  1 | {1,2,3,4}
 11 | {11,12,13,14}
(2 rows)

Answer 2

Here's an approach that uses a temporary table to incrementally aggregate clusters together. I don't really care for the temporary table approach, but this seems to perform quite well as the number of lines increases (I have 1.2 M lines in my input).

DO
$$
DECLARE
this_id bigint;
this_geom geometry;
cluster_id_match integer;

id_a bigint;
id_b bigint;

BEGIN
DROP TABLE IF EXISTS clusters;
CREATE TABLE clusters (cluster_id serial, ids bigint[], geom geometry);
CREATE INDEX ON clusters USING GIST(geom);

-- Iterate through linestrings, assigning each to a cluster (if there is an intersection)
-- or creating a new cluster (if there is not)
FOR this_id, this_geom IN SELECT id, geom FROM lines LOOP
  -- Look for an intersecting cluster.  (There may be more than one.)
  SELECT cluster_id FROM clusters WHERE ST_Intersects(this_geom, clusters.geom)
     LIMIT 1 INTO cluster_id_match;

  IF cluster_id_match IS NULL THEN
     -- Create a new cluster
     INSERT INTO clusters (ids, geom) VALUES (ARRAY[this_id], this_geom);
  ELSE
     -- Append line to existing cluster
     UPDATE clusters SET geom = ST_Union(this_geom, geom),
                          ids = array_prepend(this_id, ids)
      WHERE clusters.cluster_id = cluster_id_match;
  END IF;
END LOOP;

-- Iterate through the clusters, combining clusters that intersect each other
LOOP
    SELECT a.cluster_id, b.cluster_id FROM clusters a, clusters b 
     WHERE ST_Intersects(a.geom, b.geom)
       AND a.cluster_id < b.cluster_id
      INTO id_a, id_b;

    EXIT WHEN id_a IS NULL;
    -- Merge cluster A into cluster B
    UPDATE clusters a SET geom = ST_Union(a.geom, b.geom), ids = array_cat(a.ids, b.ids)
      FROM clusters b
     WHERE a.cluster_id = id_a AND b.cluster_id = id_b;

    -- Remove cluster B
    DELETE FROM clusters WHERE cluster_id = id_b;
END LOOP;
END;
$$ language plpgsql;