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Motivated by recent developments in optical switching and reconfigurablenetwork design, we study dynamic binary search trees (BSTs) in the matchingmodel. In the classical dynamic BST model, the cost of both link traversal andbasic reconfiguration (rotation) is $O(1)$. However, in the matching model, theBST is defined by two optical switches (that represent two matchings in anabstract way), and each switch (or matching) reconfiguration cost is $\alpha$while a link traversal cost is still $O(1)$. In this work, we proposeArithmetic BST (A-BST), a simple dynamic BST algorithm that is based on dynamicShannon-Fano-Elias coding, and show that A-BST is statically optimal forsequences of length $\Omega(n \alpha \log \alpha)$ where $n$ is the number ofnodes (keys) in the tree.

Arithmetic Binary Search Trees: Static Optimality in the Matching Model