Abstract
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 M 2 ST 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 M 2 ST order, into binary search tree order in O(h) rounds. This result answers an open problem posed in [3].
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Bein, D., Datta, A.K., Larmore, L.L. (2006). On Self-stabilizing Search Trees. In: Dolev, S. (eds) Distributed Computing. DISC 2006. Lecture Notes in Computer Science, vol 4167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864219_6
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DOI: https://doi.org/10.1007/11864219_6
Publisher Name: Springer, Berlin, Heidelberg
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