Resilient dictionaries

Abstract

We address the problem of designing data structures in the presence of faults that may arbitrarily corrupt memory locations. More precisely, we assume that an adaptive adversary can arbitrarily overwrite the content of up to δ memory locations, that corrupted locations cannot be detected, and that only O(1) memory locations are safe. In this framework, we call a data structure resilient if it is able to operate correctly (at least) on the set of uncorrupted values. We present a resilient dictionary, implementing search, insert and delete operations. Our dictionary has O(log n + δ) expected amortized time per operation, and O(n) space complexity, where n denotes the current number of keys in the dictionary. We also describe a deterministic resilient dictionary, with the same amortized cost per operation over a sequence of at least δ ǫ operations, where ǫ > 0 is an arbitrary constant. Finally, we show that any resilient comparison-based dictionary must take Ω(log n+δ) expected time per search. Our results are achieved by means of simple, new techniques, which might be of independent interest for the design of other resilient algorithms.

Engineering a Delegatable and Error-Tolerant Algorithm for Counting Small Subgraphs

“…Conversely, a number of works study algorithms that are resilient to errors but do not in general produce a correctness proof. For example, Caminiti, Finocchi, Fusco, and Silvetri [30] study resilient dynamic programming, Chen, Grigorescy, and de Wolf [33] study error-correcting data structures for membership queries and polynomial evaluation, Cicalese [37] studies fault-tolerant search algorithms, and Finocchi, Grandoni, and Italiano [48] present sorting and searching algorithms robust against memory errors. Herault and Robert [62] review fault-tolerance techniques in high-performance computing, including work on algorithm-based fault tolerance introduced by Huang and Abraham [66].…”

Online bit flip detection for in-memory B-trees on unreliable hardware

“…There exist already several works that discuss resilient data structures. Finocchi et al [6] proposes resilient search trees that allow search, insert, and delete operations. The key idea of their approach is to form groups of keys and basically store for each group, the interval in which the group's assigned keys reside.…”

Lossless Fault-Tolerant Data Structures with Additive Overhead

“…We adopt the notion of prejudice numbers from [10]. In their setting, each variable is copied 2δ + 1 times, and the prejudice number p represents the minimal "trusted index."…”

“…Our construction is similar in spirit to the resilient dictionaries of [10]. The main difference is that we use error-correcting codes within the leaves of our structure rather than accepting a small number of errors.…”

“…On the one hand, a single word can be reliably stored by maintaining Θ(δ) copies-the resilient variables of [10]. A resilient variable can be accessed quickly, but requires Θ(δ) multiplicative space overhead.…”