Concurrent rebalancing on HyperRed-Black trees

The HyperRed-Black trees are a relaxed version of Red-Black trees accepting a high degree of concurrency. In the Red-Black trees, consecutive red nodes are forbidden. This restriction has been withdrawn in the Chromatic trees introduced by O. Nurni and E. Soisalon-Soininen (1996). These trees have been designed to deal concurrently with insertions and deletions. A major motivation of Chromatic trees seems to be a good performance of the concurrent deletions algorithm. However, concurrent insertions have a serious drawback: in a big cluster of red nodes only the top node can be updated. Direct updating inside the cluster is forbidden. This approach gives us a limited degree of concurrency. The HyperRed-Black trees were designed to solve this problem. It is possible to update red nodes in the inside of a red cluster. In a HyperRed-Black tree, nodes can have a multiplicity of colors; they can be red, black or hyper-red.