Francesco Silvestri

Matteo Ceccarello, Francesco Pio Monaco, Francesco Silvestri

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.

Luca Fantin, Marco Antonelli, Margherita Cesetti et al.

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.

Martin Aumüller, Sariel Har-Peled, Sepideh Mahabadi et al.

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.

Rezaul Chowdhury, Francesco Silvestri, Flavio Vella

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.

Francesco Silvestri, Gerhard Reinelt, Christoph Schnörr

We consider clustering problems where the goal is to determine an optimal partition of a given point set in Euclidean space in terms of a collection of affine subspaces. While there is vast literature on heuristics for this kind of problem, such approaches are known to be susceptible to poor initializations and getting trapped in bad local optima. We alleviate these issues by introducing a semidefinite relaxation based on Lasserre's method of moments. While a similiar approach is known for classical Euclidean clustering problems, a generalization to our more general subspace scenario is not straightforward, due to the high symmetry of the objective function that weakens any convex relaxation. We therefore introduce a new mechanism for symmetry breaking based on covering the feasible region with polytopes. Additionally, we introduce and analyze a deterministic rounding heuristic.