Lossless fault-tolerant data structures with additive overhead

12th International Symposium, WADS 2011, New York, NY, USA, August 15-17, 2011. ProceedingsWe develop the first dynamic data structures that tolerate δ memory faults, lose no data, and incur only an O(δ ) additive overhead in overall space and time per operation. We obtain such data structures for arrays, linked lists, binary search trees, interval trees, predecessor search, and suffix trees. Like previous data structures, δ must be known in advance, but we show how to restore pristine state in linear time, in parallel with queries, making δ just a bound on the rate of memory faults. Our data structures require Θ(δ) words of safe memory during an operation, which may not be theoretically necessary but seems a practical assumption.Center for Massive Data Algorithmics (MADALGO

A watchdog processor to detect data and control flow errors

A watchdog processor for the MOTOROLA M68040 microprocessor is presented. Its main task is to protect from transient faults caused by SEUs the transmission of data between the processor and the system memory, and to ensure a correct instructions' flow, just monitoring the external bus, without modifying the internal architecture of the M68040. A description of the principal procedures is given, together with the method used for monitoring the instructions' flow

Error-Correcting Data Structures

We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been corrupted by a constant fraction of errors. This new model is the common generalization of (static) data structures and locally decodable error-correcting codes. The main issue is the tradeoff between the space used by the data structure and the time (number of probes) needed to answer a query about the encoded object. We prove a number of upper and lower bounds on various natural error-correcting data structure problems. In particular, we show that the optimal length of error-correcting data structures for the Membership problem (where we want to store subsets of size s from a universe of size n) is closely related to the optimal length of locally decodable codes for s-bit strings.Comment: 15 pages LaTeX; an abridged version will appear in the Proceedings of the STACS 2009 conferenc

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

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.Comment: To appear in Theoretical Computer Science, 201

Efficient and Error-Correcting Data Structures for Membership and Polynomial Evaluation

We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder with high probability either answers correctly or declares "don't know." Furthermore, if there is no noise on the data structure, it answers all queries correctly with high probability. Our model is the common generalization of a model proposed recently by de Wolf and the notion of "relaxed locally decodable codes" developed in the PCP literature. We measure the efficiency of a data structure in terms of its length, measured by the number of bits in its representation, and query-answering time, measured by the number of bit-probes to the (possibly corrupted) representation. In this work, we study two data structure problems: membership and polynomial evaluation. We show that these two problems have constructions that are simultaneously efficient and error-correcting.Comment: An abridged version of this paper appears in STACS 201

A watchdog processor to detect data and control flow errors

A watchdog processor for the MOTOROLA M68040 microprocessor is presented. Its main task is to protect from transient faults caused by SEUs the transmission of data between the processor and the system memory, and to ensure a correct instructions' flow, just monitoring the external bus, without modifying the internal architecture of the M68040. A description of the principal procedures is given, together with the method used for monitoring the instructions' flow