Notes of Range Queries in Non-blocking k-ary Search Trees

Approaches to Range Queries

  • STM
  • Lock
  • Persistent data structures
  • Snapshot
    • Ctrie
    • Snap

Range Query in k-ary Search Trees

dirty field

The dirty field is set to dirty when the leaf is affected by some update operations (helpInsert and helpMark).


The Validate check all leaves stored in snap. If any dirty field is true, than Validate returns false.

Range Query

The abridged RangeQuery follows few steps,

  1. Use DFS to populate snap with all leaves that may contain a key in range.
  2. Invoke Validate to check all the leaves stored in snap. If Validate returns false, than retry.
  3. Extract all keys in range from snap and return.

Differences between snaphots in BST and range query in k-ary search trees

- snapshots in BST range query in k-ary search trees
Efficiency low (iterate all nodes while checking) high
Scope global partial

Just personal opinion, may contain errors.

Some Doubts

Theorem 3 in Proof

In the paper,

Theorem 3. All operations are non-blocking.

After discussing this with Keren, both of us feel it should be a bug.

But actually it’s correct.

My question:
If the update operations are always exist (insertion and deletion are frequently invoked), than RangeQuery cannot return. So the RangeQuery is actually blocked by these update operations.

Answer from Brown:
However, your intuition about range queries blocking is not quite correct. What you are referring to is starvation. Starvation can happen in any algorithm that is not wait-free. In order to be non-blocking, the algorithm simply needs to guarantee that, if operations are performed infinitely often, then operations will succeed infinitely often. (I.e., the system, as a whole, makes progress, even if some thread(s) starve.) Equivalently, a non-blocking progress guarantee simply states that it is impossible for /all/ threads to block forever. In your example, the fact that a range query is blocked by updates is not a problem, because the updates make progress.


  1. Non-blocking k-ary Search Trees, Trevor Brown, Joanna Helga
  2. Range Queries in Non-blocking k-ary Search Trees, Trevor Brown, Hillel Avni