Amortization Results for Chromatic Search Trees, with an Application to Priority Queues.

Joan Boyar, Rolf Fagerberg, and Kim S. Larsen.
Journal of Computer and System Sciences, 55(3): 504-521, 1997.

The intention in designing data structures with relaxed balance, such as chromatic search trees, is to facilitate fast updating on shared-memory asynchronous parallel architectures. To obtain this, the updating and rebalancing have been uncoupled, so extensive locking in connection with updates is avoided.

In this paper, we prove that only an amortized constant amount of rebalancing is necessary after an update in a chromatic search tree. We also prove that the amount of rebalancing done at any particular level decreases exponentially, going from the leaves towards the root. These results imply that, in principle, a linear number of processes can access the tree simultaneously.

We have included one interesting application of chromatic trees. Based on these trees, a priority queue with possibilities for a greater degree of parallelism than previous proposals can be implemented.

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