Bug: Incorrect IntervalIndex.is_overlapping (#49933)

* fix left_sorter to support duplicate left values

* fix style

* add regression test case

* add doc

* change np.argsort to np.lexsort

* remove an unintentionally committed file

Co-authored-by: joelchen <joelchen@umich.edu>

Author: Hikipeko

doc/source/whatsnew/v2.0.0.rst

@@ -701,7 +701,7 @@ Strings
 
 Interval
 ^^^^^^^^
--
+- Bug in :meth:`IntervalIndex.is_overlapping` incorrect output if interval has duplicate left boundaries (:issue:`49581`)
 -
 
 Indexing

pandas/_libs/intervaltree.pxi.in

@@ -81,7 +81,8 @@ cdef class IntervalTree(IntervalMixin):
         """How to sort the left labels; this is used for binary search
         """
         if self._left_sorter is None:
-            self._left_sorter = np.argsort(self.left)
+            values = [self.right, self.left]
+            self._left_sorter = np.lexsort(values)
         return self._left_sorter
 
     @property

pandas/tests/indexes/interval/test_interval.py

@@ -791,6 +791,13 @@ def test_is_overlapping(self, start, shift, na_value, closed):
         result = index.is_overlapping
         assert result is expected
 
+        # intervals with duplicate left values
+        a = [10, 15, 20, 25, 30, 35, 40, 45, 45, 50, 55, 60, 65, 70, 75, 80, 85]
+        b = [15, 20, 25, 30, 35, 40, 45, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90]
+        index = IntervalIndex.from_arrays(a, b, closed="right")
+        result = index.is_overlapping
+        assert result is False
+
     @pytest.mark.parametrize(
         "tuples",
         [