Luca Becchetti

Luca Becchetti, Andrea Clementi, Amos Korman et al.

We investigate opinion dynamics in a fully-connected system, consisting of $n$ identical and anonymous agents, where one of the opinions (which is called correct) represents a piece of information to disseminate. In more detail, one source agent initially holds the correct opinion and remains with this opinion throughout the execution. The goal for non-source agents is to quickly agree on this correct opinion, and do that robustly, i.e., from any initial configuration. The system evolves in rounds. In each round, one agent chosen uniformly at random is activated: unless it is the source, the agent pulls the opinions of $\ell$ random agents and then updates its opinion according to some rule. We consider a restricted setting, in which agents have no memory and they only revise their opinions on the basis of those of the agents they currently sample. As restricted as it is, this setting encompasses very popular opinion dynamics, such as the voter model and best-of-$k$ majority rules. Qualitatively speaking, we show that lack of memory prevents efficient convergence. Specifically, we prove that no dynamics can achieve correct convergence in an expected number of steps that is sub-quadratic in $n$, even under a strong version of the model in which activated agents have complete access to the current configuration of the entire system, i.e., the case $\ell=n$. Conversely, we prove that the simple voter model (in which $\ell=1$) correctly solves the problem, while almost matching the aforementioned lower bound. These results suggest that, in contrast to symmetric consensus problems (that do not involve a notion of correct opinion), fast convergence on the correct opinion using stochastic opinion dynamics may indeed require the use of memory. This insight may reflect on natural information dissemination processes that rely on a few knowledgeable individuals.

Luca Becchetti, Andrea Clementi, Luciano Gualà et al.

The Approximate Near Neighbor (ANN) problem is a cornerstone in high-dimensional data analysis, with applications ranging from information retrieval to data mining. Among the most successful paradigms for solving ANN in high-dimensional metric spaces is Locality Sensitive Hashing (LSH), alongside the more recent Locality Sensitive Filtering (LSF). Since the seminal work of Indyk and Motwani, literature has expanded into a complex landscape of variants, often presented under different perspectives and adopting different notation. In this work, we address the technical challenge of navigating this landscape, by providing a self-contained, unified view of the essential algorithmic ingredients governing LSH-based and LSF-based solutions for angular distance -- a case of particular relevance in modern applications. In doing so, we touch on deep connections between LSF and LSH strategies. Our contribution is twofold. First, we design and analyze an LSF-based data structure for the Angular ANN problem, serving as a "guided tour" through fundamental techniques and results in the area. Second, we provide a streamlined analysis that, piecing together technical ingredients and results appeared throughout previous literature, proves optimality of the proposed data structure. In doing so, we revisit and strengthen a key technical lemma central to this body of work. The result is a critical and cohesive review that identifies core mechanisms of proximity search, offering both a streamlined entry point for researchers and a refined perspective on the state of the art.

Michele Gentili, Leonardo Martini, Manuela Petti et al.

This work proposes a unified framework to leverage biological information in network propagation-based gene prioritization algorithms. Preliminary results on breast cancer data show significant improvements over state-of-the-art baselines, such as the prioritization of genes that are not identified as potential candidates by interactome-based algorithms, but that appear to be involved in/or potentially related to breast cancer, according to a functional analysis based on recent literature.

Aris Anagnostopoulos, Luca Becchetti, Adriano Fazzone et al.

Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. We complement several recent papers in this line of research by introducing a general method to reduce bias in the data through random projections in a "fair" subspace. We apply this method to densest subgraph problem. For densest subgraph, our approach based on fair projections allows to recover both theoretically and empirically an almost optimal, fair, dense subgraph hidden in the input data. We also show that, under the small set expansion hypothesis, approximating this problem beyond a factor of 2 is NP-hard and we show a polynomial time algorithm with a matching approximation bound.