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In this paper we present a strategy to maintain a dynamic optimal binary search tree. The algorithms for insertion and deletion use swapping as the basic operation. Since in average situations the tree reorganization is limited to local changes, it can be favourably compared with the local balancing algorithms. The present algorithms dynamically maintain the optimal tree with an amortized time of O(log₂ n), where n is the total number of nodes in the tree. In the worst case situations, the algorithms take only O(n) time. This is significant when they are compared to the algorithms producing static optimal binary search trees.