Exploiting non-constant safe memory in resilient algorithms and data structures

TL;DR

This paper extends the Faulty RAM model by incorporating safe memory, enabling the development of more efficient resilient algorithms for sorting and priority queues that outperform previous methods by leveraging safe memory to reduce time complexity.

Contribution

It introduces a new resilient sorting algorithm that exploits safe memory to improve performance and derives a resilient priority queue based on this sorting method.

Findings

Resilient sorting algorithm with $O(n ext{log} n + rac{ ext{alpha}( ext{delta}}{S} + ext{log} S)$ time.

Resilient priority queue with $O( ext{log} n + rac{ ext{delta}}{S})$ amortized time per operation.

Outperforms previous resilient algorithms that do not utilize safe memory.

Abstract

We extend the Faulty RAM model by Finocchi and Italiano (2008) by adding a safe memory of arbitrary size $S$, and we then derive tradeoffs between the performance of resilient algorithmic techniques and the size of the safe memory. Let $\delta$ and $\alpha$ denote, respectively, the maximum amount of faults which can happen during the execution of an algorithm and the actual number of occurred faults, with $\alpha \leq \delta$. We propose a resilient algorithm for sorting $n$ entries which requires $O\left(n\log n+\alpha (\delta/S + \log S)\right)$ time and uses $\Theta(S)$ safe memory words. Our algorithm outperforms previous resilient sorting algorithms which do not exploit the available safe memory and require $O\left(n\log n+ \alpha\delta\right)$ time. Finally, we exploit our sorting algorithm for deriving a resilient priority queue. Our implementation uses $\Theta(S)$ safe memory words and $\Theta(n)$ faulty memory words for storing $n$ keys, and requires $O\left(\log n + \delta/S\right)$ amortized time for each insert and deletemin operation. Our resilient priority queue improves the $O\left(\log n + \delta\right)$ amortized time required by the state of the art.