Available and Stabilizing 2-3 Trees

Abstract

Transient faults corrupt the content and organization of data structures. A recovery technique dealing with such faults is stabilization, which guarantees, following some number of operations on the data structure, that content of the data structure is legitimate. Another notion of fault tolerance is availability, which is the property that operations continue to be applied during the period of recovery after a fault, and successful updates are not lost while the data structure stabilizes to a legitimate state. The available, stabilizing 2-3 tree supports find, insert, and delete operations, each with O(lg n) complexity when the tree's state is legitimate and contains n items. For an illegitimate state, these operations have O(lg K) complexity where K is the maximum capacity of the tree. Within O(t) operations, the state of the tree is guaranteed to be legitimate, where t is the number of nodes accessible via some path from the tree's root at the initial state. This paper resolves, for the first time, issues of dynamic allocation and pointer organization in a stabilizing data structure.