sorting - Gather list elements by labels

The following list has some elements that are labeled. For example {1, 2} -> 1, {-1, 3} -> 3, etc:

list = {{1, 2}, {-1, 3}, {5, 6}, {-3, 4}, {7, 8}, {-9, 1}, {0, 1}};
labels = {1, 3, 2, 1, 2, 1, 3};

What is a good way to gather list's elements clustered according to their labels?

clusters = {{{1 ,2}, {-3, 4}, {-9, 1}}, {{5, 6}, {7, 8}}, {{-1, 3}, {0, 1}}}

Answer

I believe the best way is to use an Ordering function with recognition of duplicates.
Please see that (self) Q&A for an explanation.

myOrdering[a_List] := GatherBy[Ordering@a, a[[#]] &]

list[[#]] & /@ myOrdering[labels]

{{{1, 2}, {-3, 4}, {-9, 1}}, {{5, 6}, {7, 8}}, {{-1, 3}, {0, 1}}}

---

Benchmarking

And updated benchmark for recent versions, performed in 10.1.0.

Note: in version 7 Pick was orders of magnitude slower in this test. Now it is competitive but it still falls behind as the number of unique labels increases.

myOrdering[a_List] := GatherBy[Ordering@a, a[[#]] &]

f1[{list_, labels_}] :=
  Extract[list, Position[labels, #]] & /@ Union@labels

f2[{list_, labels_}] :=
  Pick[list, labels, #] & /@ Union@labels


f3[{list_, labels_}] :=
  GatherBy[Sort[Transpose@{labels, list}, OrderedQ[{#1[[1]], #2[[1]]}] &], 
   First][[All, All, 2]]

f4[{list_, labels_}] :=
  Reap[MapThread[Sow, {list, labels}], Union@labels][[2, All, 1]]

f5[{list_, labels_}] :=
  list[[#]] & /@ myOrdering[labels]


g[n_] := RandomInteger[⌈n/4⌉, #] & /@ {{n, 2}, n}


Needs["GeneralUtilities`"]

BenchmarkPlot[{f1, f2, f3, f4, f5}, g, 10]