How to check overlap between two sets of linestrings using PostGIS

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I have two sets of LINESTRINGS, each set containing around 50 LINESTRINGS (which form a road), using PostGIS how do I check whether these two sets overlap or not?

As simplexio pointed out, the ST_Overlaps function is an excellent start; however, you should check out this post that explains some of the nuances and varying behaviours between ST_Overlaps and ST_Intersects - specifically when two geometries are identical.

Here is a query that I use to detect overlaps in a road network - two line geometries that share a line segment. You can remove the t1.id <> t2.id test if you are testing overlaps between two different tables.

SELECT t1.id FROM t1, t2 WHERE t1.id <> t2.id AND ST_Intersects(t1.geom, t2.geom) AND Upper(ST_GeometryType(ST_Intersection(t1.geom, t2.geom))) LIKE '%LINE%