python/doc/source/benchmarks.inc.rst: Add 9d and 10d to ndsort section.

Author: MLopez-Ibanez

python/doc/source/benchmarks.inc.rst

@@ -68,8 +68,9 @@ For dimensions larger than 3, :func:`moocore.is_nondominated` uses the
 best-known :math:`O(n\log^{m-2} n)` algorithm.  `fast-pareto`_ claims to be
 using a :math:`O(n\log^{m-2} n)` algorithm, but the benchmarks suggest that it
 uses a :math:`O(m n^2)` algorithm, although slower than most other packages and
-almost 100 times slower than `moocore`_.  The following plots with ``keep_weakly=True`` show that `moocore`_ is at
-least 10 times faster than the other packages, even for 10D.
+almost 100 times slower than `moocore`_.  The following plots with
+``keep_weakly=True`` show that `moocore`_ is at least 10 times faster than the
+other packages, even for 10D.
 
 |wndom_bench-sphere-4d| |wndom_bench-convex-4d|
 
@@ -117,19 +118,21 @@ Nondominated Sorting (Pareto ranking)
 
 Nondominated sorting (or Pareto ranking) assigns a rank to each point according
 to Pareto-optimality. It can be used to split a set of points into layers of
-nondominated fronts.  For more details, see :func:`moocore.pareto_rank`. This
+nondominated fronts.  For more details, see :func:`moocore.pareto_rank`.  This
 function in `moocore`_ uses a :math:`O(n \log n)` algorithm for 2 dimensions
-and a :math:`O(k\cdot n\log n)` algorithm for 3 dimensions.  As the plots show,
-this makes `moocore`_ significantly faster than `paretoset`_, `pymoo`_ and
-`DESDEO`_.  With higher dimensions, `moocore`_ uses the naive :math:`O(k m
-n^2)` algorithm, similar to `paretoset`_ and `DESDEO`_ (if the latter are
-compiled with `Numba`_). In these benchmarks points are sampled uniformly at
-random within the hyper-cube.
+and a :math:`O(n^2\log n)` algorithm for 3 dimensions.  As the plots show, this
+makes `moocore`_ significantly faster than `paretoset`_, `pymoo`_ and
+`DESDEO`_.  With higher dimensions, `moocore`_ uses a :math:`O(n^2\log^{m-2}n)`
+algorithm instead of the :math:`O(n^3)` algorithm in `paretoset`_ and `DESDEO`_
+(latter is compiled with `Numba`_).  In these benchmarks points are sampled
+uniformly at random within the hyper-cube.
 
 |ndsort_bench-ran-2d| |ndsort_bench-ran-3d|
 
 |ndsort_bench-ran-4d| |ndsort_bench-ran-5d|
 
+|ndsort_bench-ran-9d| |ndsort_bench-ran-10d|
+
 .. |ndsort_bench-ran-2d| image:: _static/bench/ndsort_bench-ran-2d-time.png
    :width: 49%
 
@@ -142,6 +145,12 @@ random within the hyper-cube.
 .. |ndsort_bench-ran-5d| image:: _static/bench/ndsort_bench-ran-5d-time.png
    :width: 49%
 
+.. |ndsort_bench-ran-9d| image:: _static/bench/ndsort_bench-ran-9d-time.png
+   :width: 49%
+
+.. |ndsort_bench-ran-10d| image:: _static/bench/ndsort_bench-ran-10d-time.png
+   :width: 49%
+
 
 .. _bench-hv: