ListPlot labeled points is extremely slow

Question

I am using Mathematica 11

Compare below two timings

Table[AbsoluteTiming[ListPlot[RandomReal[1., {n, 2}]]][[1]], {n, 1, 
  200, 20}]
(*{0.0922182, 0.0868473, 0.0458226, 0.0350156, 0.0440754, 0.0346732, \
0.0368516, 0.0397308, 0.0528617, 0.0459663}*)

and

Table[AbsoluteTiming[
   ListPlot[Thread[RandomReal[1., {n, 2}] -> Range[n]]]][[1]], {n, 1, 
  200, 20}]
(*{0.445452, 0.621644, 1.20737, 2.16653, 3.06852, 7.26112, 12.347, \
17.6615, 23.6164, 29.5285}*)

Why plotting labeled points is so slow? Is there workaround?

---

update

Thanks to rcollyer. The slowness is due to auto position algorithm gone crazy when number of points get larger.

A workaround is to specify label position explicitly, for example

Table[AbsoluteTiming[
   ListPlot[
    Labeled[#[[1]], #[[2]], Below] & /@ 
     Thread[RandomReal[1., {n, 2}] -> Range[n]]]][[1]], {n, 1, 200, 
  20}]
(*{0.201465, 0.359929, 0.470717, 0.415873, 0.556001, 0.644012, \
0.707094, 0.945657, 0.874655, 1.12489}*)

Answer 1

As I mentioned above, the problem is in positioning the labels. Without the labels present, ListPlot does not have to do much but parse the data and determine appropriate PlotRange. The addition of labels, though, adds a conundrum: how do we place the labels in a pleasing manner with minimal overlap? This is not straightforward, and as the number of labeled points increases, it becomes even harder to accomplish. As you pointed out, the simplest method is to bypass the automatic placement algorithm, e.g (borrowing your code shamelessly)

Table[First@AbsoluteTiming@
   ListPlot[Labeled[#[[1]], #[[2]], Below] & /@ 
     Thread[RandomReal[1., {n, 2}] -> Range[n]]]
  , {n, 1, 200, 20}
]
(*{0.201465, 0.359929, 0.470717, 0.415873, 0.556001, 0.644012, 
 0.707094, 0.945657, 0.874655, 1.12489}*)

The key thing to note here is that while it scales much better than the automatic algorithm, it does take quite a bit of extra time relative to no labels. So, after a certain point, you should look at only labeling specific points.