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 Universal RAM Machine Resistant to Isolated Bursts of Faults

The most natural question of reliable computation, in every computation model and noise model,is whether given a certain level of noise, a machine of that model exists that canperform arbitrarily complex computations under noise of that level. This question has positive answers for circuits, cellular automata, and recently for Turing machines. Here, we raise the question of the existence of a random access machine that---with some moderate slowdown --- can simulate any other random access machine even if the simulator is subjected to constant size bursts of faults separated by a certain minimum number of steps from each other. We will analyze and spell out the problems and difficulties that need to be addressed in such construction

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

Selection in the Presence of Memory Faults, with Applications to In-place Resilient Sorting

The selection problem, where one wishes to locate the $k^{th}$ smallest element in an unsorted array of size $n$, is one of the basic problems studied in computer science. The main focus of this work is designing algorithms for solving the selection problem in the presence of memory faults. These can happen as the result of cosmic rays, alpha particles, or hardware failures. Specifically, the computational model assumed here is a faulty variant of the RAM model (abbreviated as FRAM), which was introduced by Finocchi and Italiano. In this model, the content of memory cells might get corrupted adversarially during the execution, and the algorithm is given an upper bound $\delta$ on the number of corruptions that may occur. The main contribution of this work is a deterministic resilient selection algorithm with optimal O(n) worst-case running time. Interestingly, the running time does not depend on the number of faults, and the algorithm does not need to know $\delta$. The aforementioned resilient selection algorithm can be used to improve the complexity bounds for resilient $k$-d trees developed by Gieseke, Moruz and Vahrenhold. Specifically, the time complexity for constructing a $k$-d tree is improved from $O(n\log^2 n + \delta^2)$ to $O(n \log n)$. Besides the deterministic algorithm, a randomized resilient selection algorithm is developed, which is simpler than the deterministic one, and has $O(n + \alpha)$ expected time complexity and O(1) space complexity (i.e., is in-place). This algorithm is used to develop the first resilient sorting algorithm that is in-place and achieves optimal $O(n\log n + \alpha\delta)$ expected running time.Comment: 26 page

Resiliency in numerical algorithm design for extreme scale simulations

This work is based on the seminar titled ‘Resiliency in Numerical Algorithm Design for Extreme Scale Simulations’ held March 1–6, 2020, at Schloss Dagstuhl, that was attended by all the authors. Advanced supercomputing is characterized by very high computation speeds at the cost of involving an enormous amount of resources and costs. A typical large-scale computation running for 48 h on a system consuming 20 MW, as predicted for exascale systems, would consume a million kWh, corresponding to about 100k Euro in energy cost for executing 1023 floating-point operations. It is clearly unacceptable to lose the whole computation if any of the several million parallel processes fails during the execution. Moreover, if a single operation suffers from a bit-flip error, should the whole computation be declared invalid? What about the notion of reproducibility itself: should this core paradigm of science be revised and refined for results that are obtained by large-scale simulation? Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronously writing checkpoint data all the way to background storage at frequent intervals will create intolerable overheads in runtime and energy consumption. Forecasts show that the mean time between failures could be lower than the time to recover from such a checkpoint, so that large calculations at scale might not make any progress if robust alternatives are not investigated. More advanced resilience techniques must be devised. The key may lie in exploiting both advanced system features as well as specific application knowledge. Research will face two essential questions: (1) what are the reliability requirements for a particular computation and (2) how do we best design the algorithms and software to meet these requirements? While the analysis of use cases can help understand the particular reliability requirements, the construction of remedies is currently wide open. One avenue would be to refine and improve on system- or application-level checkpointing and rollback strategies in the case an error is detected. Developers might use fault notification interfaces and flexible runtime systems to respond to node failures in an application-dependent fashion. Novel numerical algorithms or more stochastic computational approaches may be required to meet accuracy requirements in the face of undetectable soft errors. These ideas constituted an essential topic of the seminar. The goal of this Dagstuhl Seminar was to bring together a diverse group of scientists with expertise in exascale computing to discuss novel ways to make applications resilient against detected and undetected faults. In particular, participants explored the role that algorithms and applications play in the holistic approach needed to tackle this challenge. This article gathers a broad range of perspectives on the role of algorithms, applications and systems in achieving resilience for extreme scale simulations. The ultimate goal is to spark novel ideas and encourage the development of concrete solutions for achieving such resilience holistically.Peer Reviewed"Article signat per 36 autors/es: Emmanuel Agullo, Mirco Altenbernd, Hartwig Anzt, Leonardo Bautista-Gomez, Tommaso Benacchio, Luca Bonaventura, Hans-Joachim Bungartz, Sanjay Chatterjee, Florina M. Ciorba, Nathan DeBardeleben, Daniel Drzisga, Sebastian Eibl, Christian Engelmann, Wilfried N. Gansterer, Luc Giraud, Dominik G ̈oddeke, Marco Heisig, Fabienne Jezequel, Nils Kohl, Xiaoye Sherry Li, Romain Lion, Miriam Mehl, Paul Mycek, Michael Obersteiner, Enrique S. Quintana-Ortiz, Francesco Rizzi, Ulrich Rude, Martin Schulz, Fred Fung, Robert Speck, Linda Stals, Keita Teranishi, Samuel Thibault, Dominik Thonnes, Andreas Wagner and Barbara Wohlmuth"Postprint (author's final draft

Reduce to the Max: A Simple Approach for Massive-Scale Privacy-Preserving Collaborative Network Measurements (Extended Version)

Privacy-preserving techniques for distributed computation have been proposed recently as a promising framework in collaborative inter-domain network monitoring. Several different approaches exist to solve such class of problems, e.g., Homomorphic Encryption (HE) and Secure Multiparty Computation (SMC) based on Shamir's Secret Sharing algorithm (SSS). Such techniques are complete from a computation-theoretic perspective: given a set of private inputs, it is possible to perform arbitrary computation tasks without revealing any of the intermediate results. In fact, HE and SSS can operate also on secret inputs and/or provide secret outputs. However, they are computationally expensive and do not scale well in the number of players and/or in the rate of computation tasks. In this paper we advocate the use of "elementary" (as opposite to "complete") Secure Multiparty Computation (E-SMC) procedures for traffic monitoring. E-SMC supports only simple computations with private input and public output, i.e., it can not handle secret input nor secret (intermediate) output. Such a simplification brings a dramatic reduction in complexity and enables massive-scale implementation with acceptable delay and overhead. Notwithstanding its simplicity, we claim that an E-SMC scheme is sufficient to perform a great variety of computation tasks of practical relevance to collaborative network monitoring, including, e.g., anonymous publishing and set operations. This is achieved by combining a E-SMC scheme with data structures like Bloom Filters and bitmap strings.Comment: This is an extended version of the paper presented at the Third International Workshop on Traffic Monitoring and Analysis (TMA'11), Vienna, 27 April 201

High-performance hardware accelerators for image processing in space applications

Mars is a hard place to reach. While there have been many notable success stories in getting probes to the Red Planet, the historical record is full of bad news. The success rate for actually landing on the Martian surface is even worse, roughly 30%. This low success rate must be mainly credited to the Mars environment characteristics. In the Mars atmosphere strong winds frequently breath. This phenomena usually modifies the lander descending trajectory diverging it from the target one. Moreover, the Mars surface is not the best place where performing a safe land. It is pitched by many and close craters and huge stones, and characterized by huge mountains and hills (e.g., Olympus Mons is 648 km in diameter and 27 km tall). For these reasons a mission failure due to a landing in huge craters, on big stones or on part of the surface characterized by a high slope is highly probable. In the last years, all space agencies have increased their research efforts in order to enhance the success rate of Mars missions. In particular, the two hottest research topics are: the active debris removal and the guided landing on Mars. The former aims at finding new methods to remove space debris exploiting unmanned spacecrafts. These must be able to autonomously: detect a debris, analyses it, in order to extract its characteristics in terms of weight, speed and dimension, and, eventually, rendezvous with it. In order to perform these tasks, the spacecraft must have high vision capabilities. In other words, it must be able to take pictures and process them with very complex image processing algorithms in order to detect, track and analyse the debris. The latter aims at increasing the landing point precision (i.e., landing ellipse) on Mars. Future space-missions will increasingly adopt Video Based Navigation systems to assist the entry, descent and landing (EDL) phase of space modules (e.g., spacecrafts), enhancing the precision of automatic EDL navigation systems. For instance, recent space exploration missions, e.g., Spirity, Oppurtunity, and Curiosity, made use of an EDL procedure aiming at following a fixed and precomputed descending trajectory to reach a precise landing point. This approach guarantees a maximum landing point precision of 20 km. By comparing this data with the Mars environment characteristics, it is possible to understand how the mission failure probability still remains really high. A very challenging problem is to design an autonomous-guided EDL system able to even more reduce the landing ellipse, guaranteeing to avoid the landing in dangerous area of Mars surface (e.g., huge craters or big stones) that could lead to the mission failure. The autonomous behaviour of the system is mandatory since a manual driven approach is not feasible due to the distance between Earth and Mars. Since this distance varies from 56 to 100 million of km approximately due to the orbit eccentricity, even if a signal transmission at the light speed could be possible, in the best case the transmission time would be around 31 minutes, exceeding so the overall duration of the EDL phase. In both applications, algorithms must guarantee self-adaptability to the environmental conditions. Since the Mars (and in general the space) harsh conditions are difficult to be predicted at design time, these algorithms must be able to automatically tune the internal parameters depending on the current conditions. Moreover, real-time performances are another key factor. Since a software implementation of these computational intensive tasks cannot reach the required performances, these algorithms must be accelerated via hardware. For this reasons, this thesis presents my research work done on advanced image processing algorithms for space applications and the associated hardware accelerators. My research activity has been focused on both the algorithm and their hardware implementations. Concerning the first aspect, I mainly focused my research effort to integrate self-adaptability features in the existing algorithms. While concerning the second, I studied and validated a methodology to efficiently develop, verify and validate hardware components aimed at accelerating video-based applications. This approach allowed me to develop and test high performance hardware accelerators that strongly overcome the performances of the actual state-of-the-art implementations. The thesis is organized in four main chapters. Chapter 2 starts with a brief introduction about the story of digital image processing. The main content of this chapter is the description of space missions in which digital image processing has a key role. A major effort has been spent on the missions in which my research activity has a substantial impact. In particular, for these missions, this chapter deeply analizes and evaluates the state-of-the-art approaches and algorithms. Chapter 3 analyzes and compares the two technologies used to implement high performances hardware accelerators, i.e., Application Specific Integrated Circuits (ASICs) and Field Programmable Gate Arrays (FPGAs). Thanks to this information the reader may understand the main reasons behind the decision of space agencies to exploit FPGAs instead of ASICs for high-performance hardware accelerators in space missions, even if FPGAs are more sensible to Single Event Upsets (i.e., transient error induced on hardware component by alpha particles and solar radiation in space). Moreover, this chapter deeply describes the three available space-grade FPGA technologies (i.e., One-time Programmable, Flash-based, and SRAM-based), and the main fault-mitigation techniques against SEUs that are mandatory for employing space-grade FPGAs in actual missions. Chapter 4 describes one of the main contribution of my research work: a library of high-performance hardware accelerators for image processing in space applications. The basic idea behind this library is to offer to designers a set of validated hardware components able to strongly speed up the basic image processing operations commonly used in an image processing chain. In other words, these components can be directly used as elementary building blocks to easily create a complex image processing system, without wasting time in the debug and validation phase. This library groups the proposed hardware accelerators in IP-core families. The components contained in a same family share the same provided functionality and input/output interface. This harmonization in the I/O interface enables to substitute, inside a complex image processing system, components of the same family without requiring modifications to the system communication infrastructure. In addition to the analysis of the internal architecture of the proposed components, another important aspect of this chapter is the methodology used to develop, verify and validate the proposed high performance image processing hardware accelerators. This methodology involves the usage of different programming and hardware description languages in order to support the designer from the algorithm modelling up to the hardware implementation and validation. Chapter 5 presents the proposed complex image processing systems. In particular, it exploits a set of actual case studies, associated with the most recent space agency needs, to show how the hardware accelerator components can be assembled to build a complex image processing system. In addition to the hardware accelerators contained in the library, the described complex system embeds innovative ad-hoc hardware components and software routines able to provide high performance and self-adaptable image processing functionalities. To prove the benefits of the proposed methodology, each case study is concluded with a comparison with the current state-of-the-art implementations, highlighting the benefits in terms of performances and self-adaptability to the environmental conditions