arXiv subjects

Francesco Silvestri

Publications and source records attributed to Francesco Silvestri.

At least 19 recordsLinked to original sources

arXiv2026

Dimensionality Reduction on Complex Vector Spaces for Euclidean Distance with Dynamic Weights

The weighted Euclidean norm $\|x\|_w$ of a vector $x\in \mathbb{R}^d$ with weights $w\in \mathbb{R}^d$ is the Euclidean norm where the contribution of each dimension is scaled by a given weight. Approaches to dimensionality reduction that satisfy the Johnson-Lindenstrauss (JL) lemma can be easily adapted to the weighted Euclidean distance if weights are known and fixed: it suffices to scale each dimension of the input vectors according to the weights, and then apply any standard approach. However, this is not the case when weights are unknown during the dimensionality reduction or might dynamically change. In this paper, we address this issue by providing a linear function that maps vectors into a smaller complex vector space and allows to retrieve a JL-like estimate for the weighted Euclidean distance once weights are revealed. Our results are based on the decomposition of the complex dimensionality reduction into several Rademacher chaos random variables, which are studied using novel concentration inequalities for sums of independent Rademacher chaoses.

cs.DS↗

arXiv2026

Accelerating Triangle Counting with Real Processing-in-Memory Systems

Triangle Counting (TC) is a procedure that involves enumerating the number of triangles within a graph. It has important applications in numerous fields, such as social or biological network analysis and network security. TC is a memory-bound workload that does not scale efficiently in conventional processor-centric systems due to several memory accesses across large memory regions and low data reuse. However, recent Processing-in-Memory (PIM) architectures present a promising solution to alleviate these bottlenecks. Our work presents the first TC algorithm that leverages the capabilities of the UPMEM system, the first commercially available PIM architecture, while at the same time addressing its limitations. We use a vertex coloring technique to avoid expensive communication between PIM cores and employ reservoir sampling to address the limited amount of memory available in the PIM cores' DRAM banks. In addition, our work makes use of the Misra-Gries summary to speed up counting triangles on graphs with high-degree nodes and uniform sampling of the graph edges for quicker approximate results. Our PIM implementation surpasses state-of-the-art CPU-based TC implementations when processing dynamic graphs in Coordinate List format, showcasing the effectiveness of the UPMEM architecture in addressing TC's memory-bound challenges.

cs.AR↗

arXiv2026

MOMENTI: Scalable Motif Mining in Multidimensional Time Series

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least $1-δ$, where $δ$ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

cs.DS↗

arXiv2026

How many users have been here for a long time? Efficient solutions for counting long aggregated visits

This paper addresses the Counting Long Aggregated Visits problem, which is defined as follows. We are given $n$ users and $m$ regions, where each user spends some time visiting some regions. For a parameter $k$ and a query consisting of a subset of $r$ regions, the task is to count the number of distinct users whose aggregate time spent visiting the query regions is at least $k$. This problem is motivated by queries arising in the analysis of large-scale mobility datasets. We present several exact and approximate data structures for supporting counting long aggregated visits, as well as conditional and unconditional lower bounds. First, we describe an exact data structure that exhibits a space-time tradeoff, as well as efficient approximate solutions based on sampling and sketching techniques. We then study the problem in geometric settings where regions are points in $\mathbb{R}^d$ and queries are hyperrectangles, and derive exact data structures that achieve improved performance in these structured spaces.

cs.DS↗

arXiv2025

Design and testing of an agent chatbot supporting decision making with public transport data

Assessing the quality of public transportation services requires the analysis of large quantities of data on the scheduled and actual trips and documents listing the quality constraints each service needs to meet. Interrogating such datasets with SQL queries, organizing and visualizing the data can be quite complex for most users. This paper presents a chatbot offering a user-friendly tool to interact with these datasets and support decision making. It is based on an agent architecture, which expands the capabilities of the core Large Language Model (LLM) by allowing it to interact with a series of tools that can execute several tasks, like performing SQL queries, plotting data and creating maps from the coordinates of a trip and its stops. This paper also tackles one of the main open problems of such Generative AI projects: collecting data to measure the system's performance. Our chatbot has been extensively tested with a workflow that asks several questions and stores the generated query, the retrieved data and the natural language response for each of them. Such questions are drawn from a set of base examples which are then completed with actual data from the database. This procedure yields a dataset for the evaluation of the chatbot's performance, especially the consistency of its answers and the correctness of the generated queries.

cs.AI↗

arXiv2025

Differentially Private High-Dimensional Approximate Range Counting, Revisited

Locality Sensitive Filters are known for offering a quasi-linear space data structure with rigorous guarantees for the Approximate Near Neighbor search (ANN) problem. Building on Locality Sensitive Filters, we derive a simple data structure for the Approximate Near Neighbor Counting (ANNC) problem under differential privacy (DP). Moreover, we provide a simple analysis leveraging a connection with concomitant statistics and extreme value theory. Our approach produces a simple data structure with a tunable parameter that regulates a trade-off between space-time and utility. Through this trade-off, our data structure achieves the same performance as the recent findings of Andoni et al. (NeurIPS 2023) while offering better utility at the cost of higher space and query time. In addition, we provide a more efficient algorithm under pure $\varepsilon$-DP and elucidate the connection between ANN and differentially private ANNC. As a side result, the paper provides a more compact description and analysis of Locality Sensitive Filters for Fair Near Neighbor Search, improving a previous result in Aumüller et al. (TODS 2022).

cs.DS↗

arXiv2025

Differentially Private Release of Hierarchical Origin/Destination Data with a TopDown Approach

This paper presents a novel method for generating differentially private tabular datasets for hierarchical data, specifically focusing on origin-destination (O/D) trips. The approach builds upon the TopDown algorithm, a constraint-based mechanism developed by the U.S. Census to incorporate invariant queries into tabular data. O/D hierarchical data refers to datasets representing trips between geographical areas organized in a hierarchical structure (e.g., region $\rightarrow$ province $\rightarrow$ city). The proposed method is designed to improve the accuracy of queries covering broader geographical areas, which are derived through aggregation. This feature provides a "zoom-in" effect on the dataset, ensuring that when zoomed back out, the overall picture is preserved. Furthermore, the approach aims to reduce false positive detection. These characteristics can strengthen practitioners' and decision-makers' confidence in adopting differential privacy datasets. The main technical contribution of this paper includes a novel TopDown algorithm that employs constrained optimization with Chebyshev distance minimization, with theoretical guarantees on the maximum absolute error. Additionally, we propose a new integer optimization algorithm that significantly reduces the incidence of false positives. The effectiveness of the proposed approach is validated using real-world and synthetic O/D datasets, demonstrating its ability to generate private data with high utility and a reduced number of false positives. Our experiments focus on O/D datasets with a single trip as a unit of privacy: nevertheless, the proposed approach supports other units of privacy and also applies to any tabular data with a hierarchical structure.

cs.DS↗

arXiv2022

Understanding the Role of Non-Fullerene Acceptors Crystallinity on the Charge Transport Properties and Performance of Organic Solar Cells

The active layer crystallinity has long been associated with favourable organic solar cells (OSCs) properties such as high mobility and Fill Factor. In particular, this applies to acceptor materials such as fullerene-derivatives and the most recent Non-Fullerene Acceptors (NFAs), which are now surpassing 19% of Power Conversion Efficiency. Despite these advantages are being commonly attributed to their 3-dimensional crystal packing motif in the single crystal, the bridge that links the acceptor crystal packing from single crystals to solar cells has not clearly been shown yet. In this work, we investigate the molecular organisation of seven NFAs (o-IDTBR, IDIC, ITIC, m-ITIC, 4TIC, 4TICO, m-4TICO), following the evolution of their packing motif in single-crystals, powder and thin films made with pure NFAs and donor:NFA blends. In general, we observed a good correlation between the NFA single crystal packing and their molecular arrangement in the bulk heterojunction. However, the NFA packing motif is not directly affecting the device parameters but it provide an impact on the material propensity to form highly crystalline domain in the blend. Although that NFA crystallinity is required to obtain high mobility, the domain purity is more important to limit the bimolecular recombination and to obtain high efficiency organic solar cells.

cond-mat.mtrl-sci↗

arXiv2022

Blocking Techniques for Sparse Matrix Multiplication on Tensor Accelerators

Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since their features are specifically designed for tensor algebra (typically dense matrix-product), it is commonly assumed that they are not suitable for applications with sparse data. To challenge this viewpoint, we discuss methods and present solutions for accelerating sparse matrix multiplication on such architectures. In particular, we present a 1-dimensional blocking algorithm with theoretical guarantees on the density, which builds dense blocks from arbitrary sparse matrices. Experimental results show that, even for unstructured and highly-sparse matrices, our block-based solution which exploits Nvidia Tensor Cores is faster than its sparse counterpart. We observed significant speed-ups of up to two orders of magnitude on real-world sparse matrices.

cs.DC↗

arXiv2021

On the Bike Spreading Problem

A free-floating bike-sharing system (FFBSS) is a dockless rental system where an individual can borrow a bike and returns it anywhere, within the service area. To improve the rental service, available bikes should be distributed over the entire service area: a customer leaving from any position is then more likely to find a near bike and then to use the service. Moreover, spreading bikes among the entire service area increases urban spatial equity since the benefits of FFBSS are not a prerogative of just a few zones. For guaranteeing such distribution, the FFBSS operator can use vans to manually relocate bikes, but it incurs high economic and environmental costs. We propose a novel approach that exploits the existing bike flows generated by customers to distribute bikes. More specifically, by envisioning the problem as an Influence Maximization problem, we show that it is possible to position batches of bikes on a small number of zones, and then the daily use of FFBSS will efficiently spread these bikes on a large area. We show that detecting these zones is NP-complete, but there exists a simple and efficient $1-1/e$ approximation algorithm; our approach is then evaluated on a dataset of rides from the free-floating bike-sharing system of the city of Padova.

cs.DS↗

arXiv2021

Sampling a Near Neighbor in High Dimensions -- Who is the Fairest of Them All?

Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. Given a set of points $S$ and a radius parameter $r>0$, the $r$-near neighbor ($r$-NN) problem asks for a data structure that, given any query point $q$, returns a point $p$ within distance at most $r$ from $q$. In this paper, we study the $r$-NN problem in the light of individual fairness and providing equal opportunities: all points that are within distance $r$ from the query should have the same probability to be returned. In the low-dimensional case, this problem was first studied by Hu, Qiao, and Tao (PODS 2014). Locality sensitive hashing (LSH), the theoretically strongest approach to similarity search in high dimensions, does not provide such a fairness guarantee. In this work, we show that LSH based algorithms can be made fair, without a significant loss in efficiency. We propose several efficient data structures for the exact and approximate variants of the fair NN problem. Our approach works more generally for sampling uniformly from a sub-collection of sets of a given collection and can be used in a few other applications. We also develop a data structure for fair similarity search under inner product that requires nearly-linear space and exploits locality sensitive filters. The paper concludes with an experimental evaluation that highlights the inherent unfairness of NN data structures and shows the performance of our algorithms on real-world datasets.

cs.DS↗

arXiv2020

A Computational Model for Tensor Core Units

To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature of these architectures is a hardware circuit for efficiently computing a dense matrix multiplication of a given small size. In order to broaden the class of algorithms that exploit these systems, we propose a computational model, named the TCU model, that captures the ability to natively multiply small matrices. We then use the TCU model for designing fast algorithms for several problems, including matrix operations (dense and sparse multiplication, Gaussian Elimination), graph algorithms (transitive closure, all pairs shortest distances), Discrete Fourier Transform, stencil computations, integer multiplication, and polynomial evaluation. We finally highlight a relation between the TCU model and the external memory model.

cs.DS↗

arXiv2020

Similarity Search with Tensor Core Units

Tensor Core Units (TCUs) are hardware accelerators developed for deep neural networks, which efficiently support the multiplication of two dense $\sqrt{m}\times \sqrt{m}$ matrices, where $m$ is a given hardware parameter. In this paper, we show that TCUs can speed up similarity search problems as well. We propose algorithms for the Johnson-Lindenstrauss dimensionality reduction and for similarity join that, by leveraging TCUs, achieve a $\sqrt{m}$ speedup up with respect to traditional approaches.

cs.DS↗

arXiv2020

Fair Near Neighbor Search: Independent Range Sampling in High Dimensions

Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. There are several variants of the similarity search problem, and one of the most relevant is the $r$-near neighbor ($r$-NN) problem: given a radius $r>0$ and a set of points $S$, construct a data structure that, for any given query point $q$, returns a point $p$ within distance at most $r$ from $q$. In this paper, we study the $r$-NN problem in the light of fairness. We consider fairness in the sense of equal opportunity: all points that are within distance $r$ from the query should have the same probability to be returned. In the low-dimensional case, this problem was first studied by Hu, Qiao, and Tao (PODS 2014). Locality sensitive hashing (LSH), the theoretically strongest approach to similarity search in high dimensions, does not provide such a fairness guarantee. To address this, we propose efficient data structures for $r$-NN where all points in $S$ that are near $q$ have the same probability to be selected and returned by the query. Specifically, we first propose a black-box approach that, given any LSH scheme, constructs a data structure for uniformly sampling points in the neighborhood of a query. Then, we develop a data structure for fair similarity search under inner product that requires nearly-linear space and exploits locality sensitive filters. The paper concludes with an experimental evaluation that highlights (un)fairness in a recommendation setting on real-world datasets and discusses the inherent unfairness introduced by solving other variants of the problem.

cs.DS↗

arXiv2019

FRESH: Fréchet Similarity with Hashing

This paper studies the $r$-range search problem for curves under the continuous Fréchet distance: given a dataset $S$ of $n$ polygonal curves and a threshold $r>0$, construct a data structure that, for any query curve $q$, efficiently returns all entries in $S$ with distance at most $r$ from $q$. We propose FRESH, an approximate and randomized approach for $r$-range search, that leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and on a subsequent pruning step based on a cascade of curve simplifications. We experimentally compare \fresh to exact and deterministic solutions, and we show that high performance can be reached by suitably relaxing precision and recall.

cs.CG↗

arXiv2018

Distance-Sensitive hashing

Locality-sensitive hashing (LSH) is an important tool for managing high-dimensional noisy or uncertain data, for example in connection with data cleaning (similarity join) and noise-robust search (similarity search). However, for a number of problems the LSH framework is not known to yield good solutions, and instead ad hoc solutions have been designed for particular similarity and distance measures. For example, this is true for output-sensitive similarity search/join, and for indexes supporting annulus queries that aim to report a point close to a certain given distance from the query point. In this paper we initiate the study of distance-sensitive hashing (DSH), a generalization of LSH that seeks a family of hash functions such that the probability of two points having the same hash value is a given function of the distance between them. More precisely, given a distance space $(X, \text{dist})$ and a "collision probability function" (CPF) $f\colon \mathbb{R}\rightarrow [0,1]$ we seek a distribution over pairs of functions $(h,g)$ such that for every pair of points $x, y \in X$ the collision probability is $\Pr[h(x)=g(y)] = f(\text{dist}(x,y))$. Locality-sensitive hashing is the study of how fast a CPF can decrease as the distance grows. For many spaces, $f$ can be made exponentially decreasing even if we restrict attention to the symmetric case where $g=h$. We show that the asymmetry achieved by having a pair of functions makes it possible to achieve CPFs that are, for example, increasing or unimodal, and show how this leads to principled solutions to problems not addressed by the LSH framework. This includes a novel application to privacy-preserving distance estimation. We believe that the DSH framework will find further applications in high-dimensional data management.

cs.DS↗

arXiv2018

Adaptive MapReduce Similarity Joins

Similarity joins are a fundamental database operation. Given data sets S and R, the goal of a similarity join is to find all points x in S and y in R with distance at most r. Recent research has investigated how locality-sensitive hashing (LSH) can be used for similarity join, and in particular two recent lines of work have made exciting progress on LSH-based join performance. Hu, Tao, and Yi (PODS 17) investigated joins in a massively parallel setting, showing strong results that adapt to the size of the output. Meanwhile, Ahle, Aumüller, and Pagh (SODA 17) showed a sequential algorithm that adapts to the structure of the data, matching classic bounds in the worst case but improving them significantly on more structured data. We show that this adaptive strategy can be adapted to the parallel setting, combining the advantages of these approaches. In particular, we show that a simple modification to Hu et al.'s algorithm achieves bounds that depend on the density of points in the dataset as well as the total outsize of the output. Our algorithm uses no extra parameters over other LSH approaches (in particular, its execution does not depend on the structure of the dataset), and is likely to be efficient in practice.

cs.DS↗

arXiv2017

A Lower Bound Technique for Communication in BSP

Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower bound technique for the communication complexity in the bulk-synchronous parallel (BSP) model of a given class of DAG computations. The derived bound is expressed in terms of the switching potential of a DAG, that is, the number of permutations that the DAG can realize when viewed as a switching network. The proposed technique yields tight lower bounds for the fast Fourier transform (FFT), and for any sorting and permutation network. A stronger bound is also derived for the periodic balanced sorting network, by applying this technique to suitable subnetworks. Finally, we demonstrate that the switching potential captures communication requirements even in computational models different from BSP, such as the I/O model and the LPRAM.

cs.DC↗