BUG: IntervalIndex.overlapping with duplicate left boundaries

doc/source/whatsnew/v2.0.0.rst

@@ -672,7 +672,7 @@ 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 +81,9 @@ 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)
+            left_right = np.asarray([(self.left[i], self.right[i]) for i in range(0,
+                len(self.left))], dtype=[('l', self.dtype), ('r', self.dtype)])
+            self._left_sorter = np.argsort(left_right, order=('l', 'r'))
         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
 
+        # intervales 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",
         [