PostGIS ST_Union Performance

I'm trying to execute a 'dissolve' operation in PostGIS using the ST_Union command. The input layer is admittedly quite large and complex, but the query is extremely slow to the point of being unusable. I read Paul's 2009 post here that lead me to believe that my query should still be fairly fast. I'm using the following command; am I doing something blatantly wrong or inefficient?

SELECT  ST_Union(f.geom) as geom, column1,column2,column3
FROM "inputlayer" As f 
GROUP BY column1,column2,column3