lock-free skiplist with rank operation

Question

Is anyone aware of any lock-free skiplist implimentations and/or research papers that support the rank operation (i.e. find kth element)? Alternatively, is anyone aware of a fundamental reason why such an operation could never work?

Bonus points:

An implimentation that does not assume garbage collection. It has been my experience quite a few research papers ignore memory management.

Support:

For a description of how the rank operation may be done in a regular skiplist: "A Skip List Cookbook" by William Pugh

For one of the better lock-free skiplist descriptions: "Practical lock-freedom" by Keir Fraser

One of the better lock-free skiplist implimentations: http://www.1024cores.net/home/parallel-computing/concurrent-skip-list

Answer 1

Unlike key, value and level, which are local properties of an element in a skiplist and are not affected by operations with other elements, rank of an element, i.e. its position in the list, is a property that changes with insertion and removal of elements with lower rank. Therefore, for a concurrent skiplist, rank of an element is very ephemeral because it may be changed in any moment by a concurrently running operation that inserts or delets a lower rank element.

For example, suppose you do linear search of k-th element through the level 1 list. At the moment you did k steps, concurrent modifications might add or remove any number of prior elements, so the current rank of the element you just find is in fact unknown. Moreover, while the thread is performing the k forward iterations, concurrent changes can be done between its current position and the element that was k-th when it started the search. So what the search ends up with is neither the element with the current rank of k nor the one that has the rank of k when the search started. It's just some random element!

To say it short, for concurrent list, rank of an element is an ill-defined concept and searching by rank is an ill-defined operation. This is the fundamental reason why it could never work, and why implementers should never bother with providing such operation.