diff --git a/sql/filesort.cc b/sql/filesort.cc
index 4fbc2a64b5b..b4f5b03692b 100644
--- a/sql/filesort.cc
+++ b/sql/filesort.cc
@@ -52,7 +52,7 @@ private:
   uchar                     **m_sort_keys;
   size_t                      m_compare_length;
   Sort_param                 *m_sort_param;
-  Queue<uchar*,uchar*,size_t> m_queue;
+  Queue<uchar*, size_t> m_queue;
 };
 
 
@@ -68,7 +68,7 @@ int Bounded_queue::init(ha_rows max_elements, size_t cmplen,
   if (max_elements >= UINT_MAX - 1)
     return 1;
   // We allocate space for one extra element, for replace when queue is full.
-  return m_queue.init((uint)max_elements + 1, 0, true,
+  return m_queue.init((uint)max_elements + 1, true,
                       (decltype(m_queue)::Queue_compare)get_ptr_compare(cmplen),
                       &m_compare_length);
 }
diff --git a/sql/item_subselect.cc b/sql/item_subselect.cc
index 501ff7892fa..f8bea817b46 100644
--- a/sql/item_subselect.cc
+++ b/sql/item_subselect.cc
@@ -6654,7 +6654,7 @@ subselect_rowid_merge_engine::init(MY_BITMAP *non_null_key_parts,
     if (merge_keys[i]->sort_keys())
       return TRUE;
 
-  if (pq.init(merge_keys_count, 0, false,
+  if (pq.init(merge_keys_count, false,
               subselect_rowid_merge_engine::cmp_keys_by_cur_rownum))
     return TRUE;
 
@@ -6713,8 +6713,9 @@ subselect_rowid_merge_engine::cmp_keys_by_null_selectivity(Ordered_key **k1,
 */
 
 int
-subselect_rowid_merge_engine::cmp_keys_by_cur_rownum(void *, Ordered_key *k1,
-                                                     Ordered_key *k2)
+subselect_rowid_merge_engine::cmp_keys_by_cur_rownum(void *,
+                                                     const Ordered_key *k1,
+                                                     const Ordered_key *k2)
 {
   rownum_t r1= k1->current();
   rownum_t r2= k2->current();
diff --git a/sql/item_subselect.h b/sql/item_subselect.h
index b8fd530c73c..0c1a509a30f 100644
--- a/sql/item_subselect.h
+++ b/sql/item_subselect.h
@@ -1368,7 +1368,7 @@ public:
     return FALSE;
   };
   /* Return the current index element. */
-  rownum_t current()
+  rownum_t current() const
   {
     DBUG_ASSERT(key_buff_elements && cur_key_idx < key_buff_elements);
     return key_buff[cur_key_idx];
@@ -1507,7 +1507,7 @@ protected:
     Priority queue of Ordered_key indexes, one per NULLable column.
     This queue is used by the partial match algorithm in method exec().
   */
-  Queue<Ordered_key, Ordered_key> pq;
+  Queue<Ordered_key> pq;
 protected:
   /*
     Comparison function to compare keys in order of decreasing bitmap
@@ -1518,7 +1518,9 @@ protected:
     Comparison function used by the priority queue pq, the 'smaller' key
     is the one with the smaller current row number.
   */
-  static int cmp_keys_by_cur_rownum(void *arg, Ordered_key *k1, Ordered_key *k2);
+  static int cmp_keys_by_cur_rownum(void *arg,
+                                    const Ordered_key *k1,
+                                    const Ordered_key *k2);
 
   bool test_null_row(rownum_t row_num);
   bool exists_complementing_null_row(MY_BITMAP *keys_to_complement);
diff --git a/sql/sql_hset.h b/sql/sql_hset.h
index 80e45b160a9..9893726a7a3 100644
--- a/sql/sql_hset.h
+++ b/sql/sql_hset.h
@@ -62,18 +62,28 @@ public:
     @retval FALSE OK. The value either was inserted or existed
                   in the hash.
   */
-  bool insert(T *value)
+  bool insert(const T *value)
   {
     return my_hash_insert(&m_hash, reinterpret_cast<const uchar*>(value));
   }
-  bool remove(T *value)
+  bool remove(const T *value)
   {
-    return my_hash_delete(&m_hash, reinterpret_cast<uchar*>(value));
+    return my_hash_delete(&m_hash,
+                          reinterpret_cast<uchar*>(const_cast<T*>(value)));
   }
   T *find(const void *key, size_t klen) const
   {
     return (T*)my_hash_search(&m_hash, reinterpret_cast<const uchar *>(key), klen);
   }
+
+  T *find(const T *other) const
+  {
+    DBUG_ASSERT(m_hash.get_key);
+    size_t klen;
+    uchar *key= m_hash.get_key(reinterpret_cast<const uchar *>(other),
+                               &klen, false);
+    return find(key, klen);
+  }
   /** Is this hash set empty? */
   bool is_empty() const { return m_hash.records == 0; }
   /** Returns the number of unique elements. */
diff --git a/sql/sql_list.h b/sql/sql_list.h
index 048624e6a22..bcffdfeabff 100644
--- a/sql/sql_list.h
+++ b/sql/sql_list.h
@@ -496,8 +496,8 @@ public:
   inline List() :base_list() {}
   inline List(const List<T> &tmp, MEM_ROOT *mem_root) :
     base_list(tmp, mem_root) {}
-  inline bool push_back(T *a) { return base_list::push_back(a); }
-  inline bool push_back(T *a, MEM_ROOT *mem_root)
+  inline bool push_back(const T *a) { return base_list::push_back((void *)a); }
+  inline bool push_back(const T *a, MEM_ROOT *mem_root)
   { return base_list::push_back((void*) a, mem_root); }
   inline bool push_front(const T *a) { return base_list::push_front(a); }
   inline bool push_front(const T *a, MEM_ROOT *mem_root)
diff --git a/sql/sql_queue.h b/sql/sql_queue.h
index 9bba089bac4..d7d16ea26fe 100644
--- a/sql/sql_queue.h
+++ b/sql/sql_queue.h
@@ -16,24 +16,25 @@
 #ifndef QUEUE_INCLUDED
 #define QUEUE_INCLUDED
 
+#include <my_global.h>
 #include "queues.h"
 
 /**
   A typesafe wrapper of QUEUE, a priority heap
 */
-template<typename Element, typename Key, typename Param=void>
+template<typename Element, typename Param=void>
 class Queue
 {
 public:
-  typedef int (*Queue_compare)(Param *, Key *, Key *);
+  typedef int (*Queue_compare)(Param *, const Element *, const Element *);
 
   Queue() { m_queue.root= 0; }
   ~Queue() { delete_queue(&m_queue); }
-  int init(uint max_elements, uint offset_to_key, bool max_at_top,
-           Queue_compare compare, Param *param= 0)
+  int init(uint max_elements, bool max_at_top, Queue_compare compare,
+           Param *param= 0)
   {
-    return init_queue(&m_queue, max_elements, offset_to_key, max_at_top,
-                      (queue_compare)compare, param, 0, 0);
+    return init_queue(&m_queue, max_elements, 0, max_at_top,
+                      (queue_compare)compare, (void *)param, 0, 0);
   }
 
   size_t elements() const { return m_queue.elements; }
@@ -42,11 +43,11 @@ public:
   bool is_empty() const { return elements() == 0; }
   Element *top() const { return (Element*)queue_top(&m_queue); }
 
-  void push(Element *element) { queue_insert(&m_queue, (uchar*)element); }
+  void push(const Element *element) { queue_insert(&m_queue, (uchar*)element); }
   Element *pop() { return (Element *)queue_remove_top(&m_queue); }
   void clear() { queue_remove_all(&m_queue); }
   void propagate_top() { queue_replace_top(&m_queue); }
-  void replace_top(Element *element)
+  void replace_top(const Element *element)
   {
     queue_top(&m_queue)= (uchar*)element;
     propagate_top();
diff --git a/sql/vector_mhnsw.cc b/sql/vector_mhnsw.cc
index 4efec9d8bc9..9fe5378f177 100644
--- a/sql/vector_mhnsw.cc
+++ b/sql/vector_mhnsw.cc
@@ -78,21 +78,21 @@ int mhnsw_insert(TABLE *table, KEY *keyinfo)
   return err == HA_ERR_END_OF_FILE ? 0 : err;
 }
 
-static int cmp_float(void *, float *a, float *b)
-{
-  return *a < *b ? -1 : *a == *b ? 0 : 1;
-}
-
 struct Node
 {
   float distance;
   uchar ref[1000];
 };
 
+static int cmp_float(void *, const Node *a, const Node *b)
+{
+  return a->distance < b->distance ? -1 : a->distance == b->distance ? 0 : 1;
+}
+
 int mhnsw_read_first(TABLE *table, Item *dist, ulonglong limit)
 {
   TABLE *graph= table->hlindex;
-  Queue<Node, float> todo, result;
+  Queue<Node> todo, result;
   Node *cur;
   String *str, strbuf;
   const size_t ref_length= table->file->ref_length;
@@ -105,10 +105,10 @@ int mhnsw_read_first(TABLE *table, Item *dist, ulonglong limit)
 
   DBUG_ASSERT(graph);
 
-  if (todo.init(1000, 0, 0, cmp_float)) // XXX + autoextent
+  if (todo.init(1000, 0, cmp_float)) // XXX + autoextent
     return HA_ERR_OUT_OF_MEM;
 
-  if (result.init(limit, 0, 1, cmp_float))
+  if (result.init(limit, 1, cmp_float))
     return HA_ERR_OUT_OF_MEM;
 
   if ((err= graph->file->ha_index_init(0, 1)))