Computer Science – Data Structures and Algorithms
Scientific paper
2012-04-23
Computer Science
Data Structures and Algorithms
18 pages
Scientific paper
This paper focuses on solving the selection problem in the faulty memory RAM (FRAM) model. In the selection problem the goal is to locate the k-th smallest element in an unsorted array of size n. The FRAM model, introduced by Finocchi and Italiano in [11], is a variant of the RAM model in which the content of memory cells may become corrupted, and corrupted cells are indistinguishable from uncorrupted cells. The model assumes knowledge of an upper bound {\delta} on the number of corruptions that may occur, and O(1) reliable memory cells which will never become corrupted. In this model, an algorithm solving the selection problem is said to be correct if the element returned has rank between k - {\alpha} and k + {\alpha} in the input array, where {\alpha} is the number of corruptions that occurred during the execution of the algorithm. One of the major difficulties in this model is dealing with recursion, because if the stack is too large, memory corruptions can cause the system to behave unexpectedly. To this end, this paper develops techniques for the recursion stack in the FRAM model which allow to sometimes use non-tail recursion algorithms, as is the case with the solution to the selection problem presented within. This, together with several other techniques, leads to an O(n) worst case deterministic algorithm for the selection problem in the FRAM model. Interestingly, the running time does not depend on the number of faults. Moreover, the algorithm does not need to know {\delta} explicitly. In addition, a new randomized in-place resilient sorting algorithm is developed, which is based on a simple randomized selection algorithm in the FRAM model. This is the first inplace sorting algorithm presented in this model with expected running time O(n log n + {\alpha}{\delta}).
Kopelowitz Tsvi
Talmon Nimrod
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