Synchronized parallel algorithms on RedBlack trees

We present an approach for designing synchronized parallel algorithms to update RedBlack trees. The resulting algorithms update k keys with k processors on trees of size n in time O(log n + log k) which is very close to the optimal speedup of O(log n) (sequential time for one search or update). The algorithms are designed as a pipeline of waves of processors, which are created at the bottom of the tree and flow up to the root. The design is made following the E.W.Dijkstra approach by first choosing the invariant properties and then the rules to update the tree.Preprin