  Motivated by recent developments in optical switching and reconfigurable
network design, we study dynamic binary search trees (BSTs) in the matching
model. In the classical dynamic BST model, the cost of both link traversal and
basic reconfiguration (rotation) is $O(1)$. However, in the matching model, the
BST is defined by two optical switches (that represent two matchings in an
abstract way), and each switch (or matching) reconfiguration cost is $\alpha$
while a link traversal cost is still $O(1)$. In this work, we propose
Arithmetic BST (A-BST), a simple dynamic BST algorithm that is based on dynamic
Shannon-Fano-Elias coding, and show that A-BST is statically optimal for
sequences of length $\Omega(n \alpha \log \alpha)$ where $n$ is the number of
nodes (keys) in the tree.
