Exploring Differential Obliviousness

In a recent paper, Chan et al. [SODA \u2719] proposed a relaxation of the notion of (full) memory obliviousness, which was introduced by Goldreich and Ostrovsky [J. ACM \u2796] and extensively researched by cryptographers. The new notion, differential obliviousness, requires that any two neighboring inputs exhibit similar memory access patterns, where the similarity requirement is that of differential privacy. Chan et al. demonstrated that differential obliviousness allows achieving improved efficiency for several algorithmic tasks, including sorting, merging of sorted lists, and range query data structures. In this work, we continue the exploration of differential obliviousness, focusing on algorithms that do not necessarily examine all their input. This choice is motivated by the fact that the existence of logarithmic overhead ORAM protocols implies that differential obliviousness can yield at most a logarithmic improvement in efficiency for computations that need to examine all their input. In particular, we explore property testing, where we show that differential obliviousness yields an almost linear improvement in overhead in the dense graph model, and at most quadratic improvement in the bounded degree model. We also explore tasks where a non-oblivious algorithm would need to explore different portions of the input, where the latter would depend on the input itself, and where we show that such a behavior can be maintained under differential obliviousness, but not under full obliviousness. Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness

Exploring Differential Obliviousness

In a recent paper Chan et al. [SODA '19] proposed a relaxation of the notion of (full) memory obliviousness, which was introduced by Goldreich and Ostrovsky [J. ACM '96] and extensively researched by cryptographers. The new notion, differential obliviousness, requires that any two neighboring inputs exhibit similar memory access patterns, where the similarity requirement is that of differential privacy. Chan et al. demonstrated that differential obliviousness allows achieving improved efficiency for several algorithmic tasks, including sorting, merging of sorted lists, and range query data structures. In this work, we continue the exploration and mapping of differential obliviousness, focusing on algorithms that do not necessarily examine all their input. This choice is motivated by the fact that the existence of logarithmic overhead ORAM protocols implies that differential obliviousness can yield at most a logarithmic improvement in efficiency for computations that need to examine all their input. In particular, we explore property testing, where we show that differential obliviousness yields an almost linear improvement in overhead in the dense graph model, and at most quadratic improvement in the bounded degree model. We also explore tasks where a non-oblivious algorithm would need to explore different portions of the input, where the latter would depend on the input itself, and where we show that such a behavior can be maintained under differential obliviousness, but not under full obliviousness. Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness

Testing Booleanity and the Uncertainty Principle

Let f:{-1,1}^n -> R be a real function on the hypercube, given by its discrete Fourier expansion, or, equivalently, represented as a multilinear polynomial. We say that it is Boolean if its image is in {-1,1}. We show that every function on the hypercube with a sparse Fourier expansion must either be Boolean or far from Boolean. In particular, we show that a multilinear polynomial with at most k terms must either be Boolean, or output values different than -1 or 1 for a fraction of at least 2/(k+2)^2 of its domain. It follows that given oracle access to f, together with the guarantee that its representation as a multilinear polynomial has at most k terms, one can test Booleanity using O(k^2) queries. We show an \Omega(k) queries lower bound for this problem. Our proof crucially uses Hirschman's entropic version of Heisenberg's uncertainty principle.Comment: 15 page

Adaptive Mechanisms for Mobile Spatio-Temporal Applications

Mobile spatio-temporal applications play a key role in many mission critical fields, including Business Intelligence, Traffic Management and Disaster Management. They are characterized by high data volume, velocity and large and variable number of mobile users. The design and implementation of these applications should not only consider this variablility, but also support other quality requirements such as performance and cost. In this thesis we propose an architecture for mobile spatio-temporal applications, which enables multiple angles of adaptivity. We also introduce a two-level adaptation mechanism that ensures system performance while facilitating scalability and context-aware adaptivity. We validate the architecture and adaptation mechanisms by implementing a road quality assessment mobile application as a use case and by performing a series of experiments on cloud environment. We show that our proposed architecture can adapt at runtime and maintain service level objectives while offering cost-efficiency and robustness

Deep Understanding of Technical Documents : Automated Generation of Pseudocode from Digital Diagrams & Analysis/Synthesis of Mathematical Formulas

The technical document is an entity that consists of several essential and interconnected parts, often referred to as modalities. Despite the extensive attention that certain parts have already received, per say the textual information, there are several aspects that severely under researched. Two such modalities are the utility of diagram images and the deep automated understanding of mathematical formulas. Inspired by existing holistic approaches to the deep understanding of technical documents, we develop a novel formal scheme for the modelling of digital diagram images. This extends to a generative framework that allows for the creation of artificial images and their annotation. We contribute on the field with the creation of a novel synthetic dataset and its generation mechanism. We propose the conversion of the pseudocode generation problem to an image captioning task and provide a family of techniques based on adaptive image partitioning. We address the mathematical formulas’ semantic understanding by conducting an evaluating survey on the field, published in May 2021. We then propose a formal synthesis framework that utilized formula graphs as metadata, reaching for novel valuable formulas. The synthesis framework is validated by a deep geometric learning mechanism, that outsources formula data to simulate the missing a priori knowledge. We close with the proof of concept, the description of the overall pipeline and our future aims

Incremental Processing and Optimization of Update Streams

Over the recent years, we have seen an increasing number of applications in networking, sensor networks, cloud computing, and environmental monitoring, which monitor, plan, control, and make decisions over data streams from multiple sources. We are interested in extending traditional stream processing techniques to meet the new challenges of these applications. Generally, in order to support genuine continuous query optimization and processing over data streams, we need to systematically understand how to address incremental optimization and processing of update streams for a rich class of queries commonly used in the applications. Our general thesis is that efficient incremental processing and re-optimization of update streams can be achieved by various incremental view maintenance techniques if we cast the problems as incremental view maintenance problems over data streams. We focus on two incremental processing of update streams challenges currently not addressed in existing work on stream query processing: incremental processing of transitive closure queries over data streams, and incremental re-optimization of queries. In addition to addressing these specific challenges, we also develop a working prototype system Aspen, which serves as an end-to-end stream processing system that has been deployed as the foundation for a case study of our SmartCIS application. We validate our solutions both analytically and empirically on top of our prototype system Aspen, over a variety of benchmark workloads such as TPC-H and LinearRoad Benchmarks