arXiv subjects

Stefano Coniglio

Publications and source records attributed to Stefano Coniglio.

At least 19 recordsLinked to original sources

arXiv2026

An Integer Programming Approach to Compute Lower Bounds for Ramsey Numbers Using Circulant Graphs

The Ramsey number $R(m,n)$ is the smallest order at which every red-blue edge coloring of a complete graph must contain a blue clique (a complete subgraph) of size $m$ or a red clique of size $n$. Determining these numbers exactly is extremely hard, and even certifying a lower bound requires exhibiting an explicit coloring that avoids both cliques. We develop an integer programming framework for certifying such lower bounds, restricting the search to circulant graphs, whose rotational symmetry lets us reformulate the problem in a projected distance space, reducing the number of binary variables from quadratic to linear in the graph order. We strengthen this projected model through coefficient reduction and solve it with a branch-and-cut algorithm whose separation routine exploits the common neighborhood structure of circulant graphs, combining heuristic and exact maximum-clique algorithms. In an extensive computational campaign on circulant graphs with up to 410 vertices, we improve the best lower bounds previously obtained by other methods by up to 11 points for 25 values of $R(3,n)$ with $24\le n\le49$ and $n\neq27$, each backed by an explicit graph certificate that can be independently verified with a stand-alone exact clique solver. To the best of our knowledge, our method also provides the first reproducible optimization-based procedure for certifying circulant Ramsey numbers $R_C(m,n)$, which we use to establish eight new values of $R_C(3,n)$ with $13\le n\le20$. Our framework, graph certificates, and stand-alone checker are provided as supplementary material to support independent verification and reuse.

math.OC↗

arXiv2026

Artificial Effort

Real-effort tasks, in which participants perform cognitively costly activities whose outcomes depend on actual performance, are widely used in experimental economics. Their validity, however, rests on the assumption that a human performs them. We study whether this assumption still holds in the era of Artificial Intelligence (AI) and Large Language Models (LLMs). Using 8 canonical real-effort tasks and 23 LLMs from three major providers, we show that most tasks can now be solved accurately and at a negligible cost, while only a few resist automation. Performance improves with each model generation, and midtier models are rapidly closing the gap with frontier ones, broadening the set of widely accessible models that can automate these tasks. Additionally, we show that verbally offering monetary incentives has no effect on LLM performance. Our findings establish a boundary condition for the use of real-effort tasks in unsupervised settings: when participants can cheaply outsource task completion to an LLM, observed performance may no longer reflect genuine human effort.

cs.CY↗

arXiv2025

A Tight 2-Approximation Algorithm for the Bin Packing Problem with Setups

We study approximation algorithms for the Bin Packing Problem with Setups (BPPS), a generalization of the classical Bin Packing Problem (BPP) in which items are partitioned into classes and activating a class in a bin consumes a setup weight and incurs a setup cost. We show that direct adaptations of Next Fit (NF), First Fit (FF), Best Fit (BF), and Worst Fit (WF), as well as their decreasing-order variants, have unbounded absolute worst-case performance ratios, even with unit-weight items and zero setup costs. We then introduce a two-phase algorithm, $\mathrm{TP}_{\mathcal{A}}$ , that packs each class independently with a BPP algorithm and subsequently merges compatible packing patterns. We prove that the solution returned by $\mathrm{TP}_{\mathcal{A}}$ has cost at most twice the optimum under the assumption that produces pairwise merge-maximal solutions, i.e., such that no two packing patterns in the class-wise solution can be feasibly merged. If also runs in polynomial time, this yields a 2-approximation algorithm for the BPPS. The factor is tight: the absolute worst-case performance ratio of $\mathrm{TP}_{\mathcal{A}}$ is exactly 2, even when solves every class-wise BPP instance optimally. Since every Any Fit algorithm returns pairwise merge-maximal solutions, it follows that $\mathrm{TP}_{\mathrm{FF}}$ , $\mathrm{TP}_{\mathrm{BF}}$ , $\mathrm{TP}_{\mathrm{WF}}$ , and their decreasing-order variants all have an absolute worst-case performance ratio exactly 2. If, in addition, is an $\alpha$-approximation algorithm with $\alpha \leq 2$, we obtain a finer, component-wise guarantee with factor 2 for the bin-opening cost and factor $\alpha$ for the setup-cost component.

math.OC↗

arXiv2025

Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs

Hypergraphs provide a natural way to represent higher-order interactions among multiple entities. While undirected hypergraphs have been extensively studied, the case of directed hypergraphs, which can model oriented group interactions, remains largely under-explored despite its relevance for many applications. Recent approaches in this direction often exhibit an implicit bias toward homophily, which limits their effectiveness in heterophilic settings. Rooted in the algebraic topology notion of Cellular Sheaves, Sheaf Neural Networks (SNNs) were introduced as an effective solution to circumvent such a drawback. While a generalization to hypergraphs is known, it is only suitable for undirected hypergraphs, failing to tackle the directed case. In this work, we introduce Directional Sheaf Hypergraph Networks (DSHN), a framework integrating sheaf theory with a principled treatment of asymmetric relations within a hypergraph. From it, we construct the Directed Sheaf Hypergraph Laplacian, a complex-valued operator by which we unify and generalize many existing Laplacian matrices proposed in the graph- and hypergraph-learning literature. Across 7 real-world datasets and against 13 baselines, DSHN achieves relative accuracy gains from 2% up to 20%, showing how a principled treatment of directionality in hypergraphs, combined with the expressive power of sheaves, can substantially improve performance.

cs.LG↗

arXiv2025

Adversarial training with restricted data manipulation

Adversarial machine learning concerns situations in which learners face attacks from active adversaries. Such scenarios arise in applications such as spam email filtering, malware detection and fake image generation, where security methods must be actively updated to keep up with the everimproving generation of malicious data. Pessimistic Bilevel optimisation has been shown to be an effective method of training resilient classifiers against such adversaries. By modelling these scenarios as a game between the learner and the adversary, we anticipate how the adversary will modify their data and then train a resilient classifier accordingly. However, since existing pessimistic bilevel approaches feature an unrestricted adversary, the model is vulnerable to becoming overly pessimistic and unrealistic. When finding the optimal solution that defeats the classifier, it is possible that the adversary's data becomes nonsensical and loses its intended nature. Such an adversary will not properly reflect reality, and consequently, will lead to poor classifier performance when implemented on real-world data. By constructing a constrained pessimistic bilevel optimisation model, we restrict the adversary's movements and identify a solution that better reflects reality. We demonstrate through experiments that this model performs, on average, better than the existing approach.

cs.LG↗

arXiv2025

The Bin Packing Problem with Setups: Formulations, Structural Properties and Computational Insights

We introduce the Bin Packing Problem with Setups (BPPS), a generalization of the classical Bin Packing Problem with applications in production planning and logistics. In this problem, the items are partitioned into classes, and packing items of a class in a bin incurs a setup weight and cost. We propose a natural Integer Linear Programming (ILP) formulation for the BPPS and analyze its Linear Programming relaxation. We show that the resulting lower bound can be arbitrarily weak and introduce the Minimum Classes Inequalities (MCIs), which guarantee a worst-case ratio of 1/2 with respect to the optimal objective function value of the BPPS. We also derive the Minimum Bins Inequality (MBI) and an upper bound on the number of bins in any optimal solution, substantially reducing the formulation size. We further develop an arc-flow formulation for the BPPS based on a tailored graph construction and compression procedure. Its LP relaxation dominates that of the natural formulation, and both the MCIs and the MBI are extended to the arc-flow model. Finally, we introduce a benchmark comprising 576 randomly generated instances and 36 real-world instances derived from a vehicle-routing application, and conduct extensive computational experiments. Results show that the natural formulation performs best on instances with small or medium item weights, whereas the arc-flow formulation is more effective for large item weights and on the real-world testbed.

math.CO↗

arXiv2025

Sheaves Reloaded: A Directional Awakening

Sheaf Neural Networks (SNNs) represent a powerful generalization of Graph Neural Networks (GNNs) that significantly improve our ability to model complex relational data. While directionality has been shown to substantially boost performance in graph learning tasks and is key to many real-world applications, existing SNNs fall short in representing it. To address this limitation, we introduce the Directed Cellular Sheaf, a special type of cellular sheaf designed to explicitly account for edge orientation. Building on this structure, we define a new sheaf Laplacian, the Directed Sheaf Laplacian, which captures both the graph's topology and its directional information. This operator serves as the backbone of the Directed Sheaf Neural Network (DSNN), the first SNN model to embed a directional bias into its architecture. Extensive experiments on nine real-world benchmarks show that DSNN consistently outperforms baseline methods.

cs.LG↗

arXiv2024

Classification under strategic adversary manipulation using pessimistic bilevel optimisation

Adversarial machine learning concerns situations in which learners face attacks from active adversaries. Such scenarios arise in applications such as spam email filtering, malware detection and fake-image generation, where security methods must be actively updated to keep up with the ever improving generation of malicious data.We model these interactions between the learner and the adversary as a game and formulate the problem as a pessimistic bilevel optimisation problem with the learner taking the role of the leader. The adversary, modelled as a stochastic data generator, takes the role of the follower, generating data in response to the classifier. While existing models rely on the assumption that the adversary will choose the least costly solution leading to a convex lower-level problem with a unique solution, we present a novel model and solution method which do not make such assumptions. We compare these to the existing approach and see significant improvements in performance suggesting that relaxing these assumptions leads to a more realistic model.

cs.LG↗

arXiv2024

DLGNet: Hyperedge Classification through Directed Line Graphs for Chemical Reactions

Graphs and hypergraphs provide powerful abstractions for modeling interactions among a set of entities of interest and have been attracting a growing interest in the literature thanks to many successful applications in several fields. In particular, they are rapidly expanding in domains such as chemistry and biology, especially in the areas of drug discovery and molecule generation. One of the areas witnessing the fasted growth is the chemical reactions field, where chemical reactions can be naturally encoded as directed hyperedges of a hypergraph. In this paper, we address the chemical reaction classification problem by introducing the notation of a Directed Line Graph (DGL) associated with a given directed hypergraph. On top of it, we build the Directed Line Graph Network (DLGNet), the first spectral-based Graph Neural Network (GNN) expressly designed to operate on a hypergraph via its DLG transformation. The foundation of DLGNet is a novel Hermitian matrix, the Directed Line Graph Laplacian, which compactly encodes the directionality of the interactions taking place within the directed hyperedges of the hypergraph thanks to the DLG representation. The Directed Line Graph Laplacian enjoys many desirable properties, including admitting an eigenvalue decomposition and being positive semidefinite, which make it well-suited for its adoption within a spectral-based GNN. Through extensive experiments on chemical reaction datasets, we show that DGLNet significantly outperforms the existing approaches, achieving on a collection of real-world datasets an average relative-percentage-difference improvement of 33.01%, with a maximum improvement of 37.71%.

cs.LG↗

arXiv2023

Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs

We introduce QuaterGCN, a spectral Graph Convolutional Network (GCN) with quaternion-valued weights at whose core lies the Quaternionic Laplacian, a quaternion-valued Laplacian matrix by whose proposal we generalize two widely-used Laplacian matrices: the classical Laplacian (defined for undirected graphs) and the complex-valued Sign-Magnetic Laplacian (proposed to handle digraphs with weights of arbitrary sign). In addition to its generality, our Quaternionic Laplacian is the only Laplacian to completely preserve the topology of a digraph, as it can handle graphs and digraphs containing antiparallel pairs of edges (digons) of different weights without reducing them to a single (directed or undirected) edge as done with other Laplacians. Experimental results show the superior performance of QuaterGCN compared to other state-of-the-art GCNs, particularly in scenarios where the information the digons carry is crucial to successfully address the task at hand.

cs.LG↗

arXiv2023

SigMaNet: One Laplacian to Rule Them All

This paper introduces SigMaNet, a generalized Graph Convolutional Network (GCN) capable of handling both undirected and directed graphs with weights not restricted in sign nor magnitude. The cornerstone of SigMaNet is the Sign-Magnetic Laplacian ($L^σ$), a new Laplacian matrix that we introduce ex novo in this work. $L^σ$ allows us to bridge a gap in the current literature by extending the theory of spectral GCNs to (directed) graphs with both positive and negative weights. $L^σ$ exhibits several desirable properties not enjoyed by other Laplacian matrices on which several state-of-the-art architectures are based, among which encoding the edge direction and weight in a clear and natural way that is not negatively affected by the weight magnitude. $L^σ$ is also completely parameter-free, which is not the case of other Laplacian operators such as, e.g., the Magnetic Laplacian. The versatility and the performance of our proposed approach is amply demonstrated via computational experiments. Indeed, our results show that, for at least a metric, SigMaNet achieves the best performance in 15 out of 21 cases and either the first- or second-best performance in 21 cases out of 21, even when compared to architectures that are either more complex or that, due to being designed for a narrower class of graphs, should -- but do not -- achieve a better performance.

cs.LG↗

arXiv2021

A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.

math.OC↗

arXiv2021

Deep learning methods for screening patients' S-ICD implantation eligibility

Subcutaneous Implantable Cardioverter-Defibrillators (S-ICDs) are used for prevention of sudden cardiac death triggered by ventricular arrhythmias. T Wave Over Sensing (TWOS) is an inherent risk with S-ICDs which can lead to inappropriate shocks. A major predictor of TWOS is a high T:R ratio (the ratio between the amplitudes of the T and R waves). Currently patients' Electrocardiograms (ECGs) are screened over 10 seconds to measure the T:R ratio, determining the patients' eligibility for S-ICD implantation. Due to temporal variations in the T:R ratio, 10 seconds is not long enough to reliably determine the normal values of a patient's T:R ratio. In this paper, we develop a convolutional neural network (CNN) based model utilising phase space reconstruction matrices to predict T:R ratios from 10-second ECG segments without explicitly locating the R or T waves, thus avoiding the issue of TWOS. This tool can be used to automatically screen patients over a much longer period and provide an in-depth description of the behaviour of the T:R ratio over that period. The tool can also enable much more reliable and descriptive screenings to better assess patients' eligibility for S-ICD implantation.

cs.LG↗

arXiv2021

Infrequent adverse event prediction in low carbon energy production using machine learning

We address the problem of predicting the occurrence of infrequent adverse events in the context of predictive maintenance. We cast the corresponding machine learning task as an imbalanced classification problem and propose a framework for solving it that is capable of leveraging different classifiers in order to predict the occurrence of an adverse event before it takes place. In particular, we focus on two applications arising in low-carbon energy production: foam formation in anaerobic digestion and condenser tube leakage in the steam turbines of a nuclear power station. The results of an extensive set of omputational experiments show the effectiveness of the techniques that we propose.

cs.LG↗

arXiv2019

Bayesian Persuasion with Sequential Games

We study an information-structure design problem (a.k.a. persuasion) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the case where the receivers interact in a sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ in the time at which the receivers commit to following the sender's signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the sender's expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. In contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to a novel algorithm based on the ellipsoid method which we propose.

cs.AI↗

arXiv2019

Computing Optimal Coarse Correlated Equilibria in Sequential Games

We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the hardness results on the computation of normal-form correlated equilibria, we introduce the notion of normal-form coarse correlated equilibrium, extending the definition of coarse correlated equilibrium to sequential games. We show that, in two-player games without chance moves, an optimal (e.g., social welfare maximizing) normal-form coarse correlated equilibrium can be computed in polynomial time, and that in general multi-player games (including two-player games with Chance), the problem is NP-hard. For the former case, we provide a polynomial-time algorithm based on the ellipsoid method and also propose a more practical one, which can be efficiently applied to problems of considerable size. Then, we discuss how our algorithm can be extended to games with Chance and games with more than two players.

cs.GT↗

arXiv2018

Leadership in Singleton Congestion Games: What is Hard and What is Easy

We study the problem of computing Stackelberg equilibria Stackelberg games whose underlying structure is in congestion games, focusing on the case where each player can choose a single resource (a.k.a. singleton congestion games) and one of them acts as leader. In particular, we address the cases where the players either have the same action spaces (i.e., the set of resources they can choose is the same for all of them) or different ones, and where their costs are either monotonic functions of the resource congestion or not. We show that, in the case where the players have different action spaces, the cost the leader incurs in a Stackelberg equilibrium cannot be approximated in polynomial time up to within any polynomial factor in the size of the game unless P = NP, independently of the cost functions being monotonic or not. We show that a similar result also holds when the players have nonmonotonic cost functions, even if their action spaces are the same. Differently, we prove that the case with identical action spaces and monotonic cost functions is easy, and propose polynomial-time algorithm for it. We also improve an algorithm for the computation of a socially optimal equilibrium in singleton congestion games with the same action spaces without leadership, and extend it to the computation of a Stackelberg equilibrium for the case where the leader is restricted to pure strategies. For the cases in which the problem of finding an equilibrium is hard, we show how, in the optimistic setting where the followers break ties in favor of the leader, the problem can be formulated via mixed-integer linear programming techniques, which computational experiments show to scale quite well.

cs.GT↗

arXiv2018

Computing a Pessimistic Leader-Follower Equilibrium with Multiple Followers: the Mixed-Pure Case

The search problem of computing a \textit{leader-follower equilibrium} has been widely investigated in the scientific literature in, almost exclusively, the single-follower setting. Although the \textit{optimistic} and \ textit{pessimistic} versions of the problem are solved with different methodologies, both cases allow for efficient, polynomial-time algorithms based on linear programming. The situation is different with multiple followers, where results are only sporadic and depend strictly on the nature of the followers' game. In this paper, we investigate the setting of a normal-form game with a single leader and multiple followers who, after observing the leader's commitment, play a Nash equilibrium. The corresponding search problem, both in the optimistic and pessimistic versions, is known to be not in Poly-$\textsf{APX}$ unless $\textsf{P}=\textsf{NP}$ and exact algorithms are known only for the optimistic case. We focus on the case where the followers play in pure strategies under the assumption of pessimism. After casting this search problem as a \italic{pessimistic bilevel programming problem}, we show that, with two followers, the problem is $\textsf{NP}$-hard and, with three or more followers, it is not in Poly-$\textsf{APX}$ unless $\textsf{P}=\textsf{NP}$. We propose a single-level mathematical programming reformulation which calls for the maximisation of a nonconcave quadratic function over an unbounded nonconvex feasible region defined by linear and quadratic constraints. Since, due to admitting a supremum but not a maximum, only a restricted version of this formulation can be solved to optimality with state-of-the-art methods, we propose an exact \textit{ad hoc} algorithm, which we also embed within a branch-and-bound scheme, capable of computing the supremum of the problem.

cs.GT↗