arXiv subjects

Costanza Catalano

Publications and source records attributed to Costanza Catalano.

8 recordsLinked to original sources

arXiv2025

Chase Anonymisation: Privacy-Preserving Knowledge Graphs with Logical Reasoning

We propose a novel framework to enable Knowledge Graphs (KGs) sharing while ensuring that information that should remain private is not directly released nor indirectly exposed via derived knowledge, maintaining at the same time the embedded knowledge of the KGs to support business downstream tasks. Our approach produces a privacy-preserving KG as an augmentation of the input one via controlled addition of nodes and edges as well as re-labeling of nodes and perturbation of weights. We introduce a novel privacy measure for KGs, which considers derived knowledge, a new utility metric that captures the business semantics we want to preserve, and propose two novel anonymisation algorithms. Our extensive experimental evaluation, with both synthetic graphs and real-world datasets, confirms the effectiveness of our approach.

cs.DB↗

arXiv2023

On Computing Optimal Temporal Branchings and Spanning Subgraphs

In this work we extend the concept of out/in-branchings spanning the vertices of a digraph (also called directed spanning trees) to temporal graphs, which are digraphs where arcs are available only at prescribed times. While the literature has focused on minimum weight/earliest arrival time Temporal Out-Branchings (TOB), we solve the problem for other optimization criteria. In particular, we define five different types of TOBs based on the optimization of the travel duration (FT-TOB), of the departure time (LD-TOB), of the number of transfers (MT-TOB), of the total waiting time (MW-TOB), and of the travelling time (ST-TOB). For D$\in \{$LD,MT,ST$\}$, we provide necessary and sufficient conditions for the existence of a spanning D-TOB; when it does not exist, we characterize the maximum vertex set that a D-TOB can span. Moreover, we provide a log linear algorithm for computing such branchings. For D$\in \{$FT,MW$\}$, we prove that deciding the existence of a spanning D-TOB is NP-complete; we also show that the same results hold for optimal temporal in-branchings. Finally, we investigate the related problem of computing a spanning temporal subgraph with the minimum number of arcs and optimizing a chosen criterion D. This problem turns out to be NP-hard for any D. The hardness results are quite surprising, as computing optimal paths between nodes can always be done in polynomial time.

cs.DS↗

arXiv2023

On a Network Centrality Maximization Game

We study a network formation game where $n$ players, identified with the nodes of a directed graph to be formed, choose where to wire their outgoing links in order to maximize their PageRank centrality. Specifically, the action of every player $i$ consists in the wiring of a predetermined number $d_i$ of directed out-links, and her utility is her own PageRank centrality in the network resulting from the actions of all players. We show that this is a potential game and that the best response correspondence always exhibits a local structure in that it is never convenient for a node $i$ to link to other nodes that are at incoming distance more than $d_i $ from her. We then study the equilibria of this game determining necessary conditions for a graph to be a (strict, recurrent) Nash equilibrium. Moreover, in the homogeneous case, where players all have the same number $d$ of out-links, we characterize the structure of the potential maximizing equilibria and, in the special cases $ d=1 $ and $ d=2 $, we provide a complete classification of the set of (strict, recurrent) Nash equilibria. Our analysis shows in particular that the considered formation mechanism leads to the emergence of undirected and disconnected or loosely connected networks.

cs.SI↗

arXiv2021

A linear bound on the k-rendezvous time for primitive sets of NZ matrices

A set of nonnegative matrices is called primitive if there exists a product of these matrices that is entrywise positive. Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest product of a primitive set having a column or a row with k positive entries, called its k-rendezvous time (k-RT}), in the case of sets of matrices having no zero rows and no zero columns. We prove that the k-RT is at most linear w.r.t. the matrix size n for small k, while the problem is still open for synchronizing automata. We provide two upper bounds on the k-RT: the second is an improvement of the first one, although the latter can be written in closed form. We then report numerical results comparing our upper bounds on the k-RT with heuristic approximation methods.

cs.DM↗

arXiv2020

On a Centrality Maximization Game

The Bonacich centrality is a well-known measure of the relative importance of nodes in a network. This notion is, for example, at the core of Google's PageRank algorithm. In this paper we study a network formation game where each player corresponds to a node in the network to be formed and can decide how to rewire his m out-links aiming at maximizing his own Bonacich centrality, which is his utility function. We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the set of NE when m=1 and a fairly complete classification of the NE when m=2. Our analysis shows that the centrality maximization performed by each node tends to create undirected and disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special "Butterfly"-shaped graph when m=2. Our results build on locality property of the best response function in such game that we formalize and prove in the paper.

cs.SI↗

arXiv2019

The Synchronizing Probability Function for Primitive Sets of Matrices

Motivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns. We formulate the primitivity process in the setting of a two-player probabilistic game and we make use of convex optimization techniques to describe its behavior. We develop a tool for approximating and upper bounding the exponent of any primitive set and supported by numerical results we state a conjecture that, if true, would imply a quadratic upper bound on the reset threshold of a new class of automata.

cs.FL↗

arXiv2018

On random primitive sets, directable NDFAs and the generation of slowly synchronizing DFAs

We tackle the problem of the randomized generation of slowly synchronizing deterministic automata (DFAs) by generating random primitive sets of matrices. We show that when the randomized procedure is too simple the exponent of the generated sets is O(n log n) with high probability, thus the procedure fails to return DFAs with large reset threshold. We extend this result to random nondeterministic automata (NDFAs) by showing, in particular, that a uniformly sampled NDFA has both a 2-directing word and a 3-directing word of length O(n log n) with high probability. We then present a more involved randomized algorithm that manages to generate DFAs with large reset threshold and we finally leverage this finding for exhibiting new families of DFAs with reset threshold of order $ Ω(n^2/4) $.

cs.FL↗

arXiv2018

On randomized generation of slowly synchronizing automata

Motivated by the randomized generation of slowly synchronizing automata, we study automata made of permutation letters and a merging letter of rank $ n\!-\!1 $. We present a constructive randomized procedure to generate synchronizing automata of that kind with (potentially) large alphabet size based on recent results on \textit{primitive} sets of matrices. We report numerical results showing that our algorithm finds automata with much larger reset threshold than a mere uniform random generation and we present new families of automata with reset threshold of $ Ω(n^2/4) $. We finally report theoretical results on randomized generation of primitive sets of matrices: a set of permutation matrices with a $ 0 $ entry changed into a $ 1 $ is primitive and has exponent of $ O(n\log n) $ with high probability in case of uniform random distribution and the same holds for a random set of binary matrices where each entry is set, independently, equal to $ 1 $ with probability $ p $ and equal to $ 0 $ with probability $ 1-p $, when $ np-\log n\rightarrow\infty $ as $ n\rightarrow\infty $.

cs.FL↗