Complexity of Layered Binary Search Trees with Relaxed Balance
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
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{\it Relaxed} balancing means that, in a dictionary stored as a balanced tree, the necessary rebalancing after updates may be delayed. This is in contrast to {\it strict} balancing meaning that rebalancing is performed immediately after the update. Relaxed balancing is important for efficiency in highly dynamic applications where updates can occur in bursts. The rebalancing tasks can be performed gradually after all urgent updates, allowing the concurrent use of the dictionary even though the underlying tree structure is not completely in balance. The contribution of the present paper is that we introduce a new scheme for relaxed balancing, which is obtained by a simple generalization of strict balancing. Our approach implies a simple proof of the fact that the number of the needed rebalancing operations (to put the tree in balance) for relaxed balancing is the same as for strict balancing.