diff --git a/nova/compute/provider_tree.py b/nova/compute/provider_tree.py
index 7be5d8b91a1d..06bb0521e13a 100644
--- a/nova/compute/provider_tree.py
+++ b/nova/compute/provider_tree.py
@@ -25,6 +25,7 @@ import os_traits
 from oslo_concurrency import lockutils
 from oslo_log import log as logging
 from oslo_utils import uuidutils
+import six
 
 from nova.i18n import _
 
@@ -232,7 +233,12 @@ class ProviderTree(object):
     def __init__(self):
         """Create an empty provider tree."""
         self.lock = lockutils.internal_lock(_LOCK_NAME)
-        self.roots = []
+        self.roots_by_uuid = {}
+        self.roots_by_name = {}
+
+    @property
+    def roots(self):
+        return six.itervalues(self.roots_by_uuid)
 
     def get_provider_uuids(self, name_or_uuid=None):
         """Return a list, in top-down traversable order, of the UUIDs of all
@@ -343,7 +349,8 @@ class ProviderTree(object):
 
                 provider = _Provider.from_dict(pd)
                 if parent_uuid is None:
-                    self.roots.append(provider)
+                    self.roots_by_uuid[provider.uuid] = provider
+                    self.roots_by_name[provider.name] = provider
                 else:
                     parent = self._find_with_lock(parent_uuid)
                     parent.add_child(provider)
@@ -357,7 +364,8 @@ class ProviderTree(object):
             parent = self._find_with_lock(found.parent_uuid)
             parent.remove_child(found)
         else:
-            self.roots.remove(found)
+            del self.roots_by_uuid[found.uuid]
+            del self.roots_by_name[found.name]
 
     def remove(self, name_or_uuid):
         """Safely removes the provider identified by the supplied name_or_uuid
@@ -393,10 +401,21 @@ class ProviderTree(object):
                 raise ValueError(err % uuid)
 
             p = _Provider(name, uuid=uuid, generation=generation)
-            self.roots.append(p)
+            self.roots_by_uuid[uuid] = p
+            self.roots_by_name[name] = p
             return p.uuid
 
     def _find_with_lock(self, name_or_uuid, return_root=False):
+        # Optimization for large number of roots (e.g. ironic): if name_or_uuid
+        # represents a root, this is O(1).
+        found = self.roots_by_uuid.get(name_or_uuid)
+        if found:
+            return found
+        found = self.roots_by_name.get(name_or_uuid)
+        if found:
+            return found
+
+        # Okay, it's a child; do it the hard way.
         for root in self.roots:
             found = root.find(name_or_uuid)
             if found:
diff --git a/nova/tests/unit/virt/libvirt/test_driver.py b/nova/tests/unit/virt/libvirt/test_driver.py
index 1b1a6b381191..60476a6fef32 100644
--- a/nova/tests/unit/virt/libvirt/test_driver.py
+++ b/nova/tests/unit/virt/libvirt/test_driver.py
@@ -21490,7 +21490,8 @@ class LibvirtDriverTestCase(test.NoDBTestCase, TraitsComparisonMixin):
         self.assertRaises(exception.ComputeResourcesUnavailable,
                           drvr._allocate_mdevs, allocations=allocations)
 
-    def test_allocate_mdevs_with_no_idea_of_the_provider(self):
+    @mock.patch.object(libvirt_driver.LOG, 'warning')
+    def test_allocate_mdevs_with_no_idea_of_the_provider(self, mock_warning):
         drvr = libvirt_driver.LibvirtDriver(fake.FakeVirtAPI(), True)
         # Mock the fact update_provider_tree() should have run
         drvr.provider_tree = self._get_fake_provider_tree_with_vgpu()
@@ -21517,6 +21518,9 @@ class LibvirtDriverTestCase(test.NoDBTestCase, TraitsComparisonMixin):
         # Remember, rp2 has a wrong naming convention
         self.assertRaises(exception.ComputeResourcesUnavailable,
                           drvr._allocate_mdevs, allocations=allocations)
+        mock_warning.assert_called_once_with(
+            "pGPU device name %(name)s can't be guessed from the ProviderTree "
+            "roots %(roots)s", {'name': 'oops_I_did_it_again', 'roots': 'cn'})
 
     @mock.patch.object(libvirt_driver.LibvirtDriver, '_get_mediated_devices')
     @mock.patch.object(libvirt_driver.LibvirtDriver,
diff --git a/nova/virt/libvirt/driver.py b/nova/virt/libvirt/driver.py
index ad1aa6293934..a982960f7e4d 100644
--- a/nova/virt/libvirt/driver.py
+++ b/nova/virt/libvirt/driver.py
@@ -6366,7 +6366,7 @@ class LibvirtDriver(driver.ComputeDriver):
             rp_name = allocated_rp.name
             # There can be multiple roots, we need to find the root name
             # to guess the physical device name
-            roots = self.provider_tree.roots
+            roots = list(self.provider_tree.roots)
             for root in roots:
                 if rp_name.startswith(root.name + '_'):
                     # The RP name convention is :
@@ -6374,10 +6374,11 @@ class LibvirtDriver(driver.ComputeDriver):
                     parent_device = rp_name[len(root.name) + 1:]
                     break
             else:
-                LOG.warning("pGPU device name %(name)s can't be guessed from "
-                            "the ProviderTree "
-                            "roots %(roots)s", {'name': rp_name,
-                                                 'roots': roots})
+                LOG.warning(
+                    "pGPU device name %(name)s can't be guessed from the "
+                    "ProviderTree roots %(roots)s",
+                    {'name': rp_name,
+                     'roots': ', '.join([root.name for root in roots])})
                 # We f... have no idea what was the parent device
                 # If we can't find devices having available VGPUs, just raise
                 raise exception.ComputeResourcesUnavailable(