On Self-stabilizing Search Trees

We introduce a self-stabilizing data structure, which we call either a min-max search tree or a max-min search tree (both abbreviated M2ST), depending on whether the root has the minimum or the maximum value in the tree. Our structure is a refinement of the standard min-max heap (or max-min heap), with additional property that every value in the left subtree of a node is less than or equal to every value in the right subtree of that node. The M2ST has all the power of a binary search tree and all the power of a min-max heap, combined; with the additional feature that maintaining balance is easy. We give a self-stabilizing algorithm for reorganizing the values of an asynchronous network with a binary tree topology into an M2ST in O(n) rounds. We then give an algorithm for reorganizing an asynchronous network with a binary tree topology, which is already in M2ST order, into binary search tree order in O(h) rounds. This result answers an open problem posed in [3].