相关论文: Stochastic matching model on the general graphical…
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair…
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…
The \emph{generalized sorting problem} is a restricted version of standard comparison sorting where we wish to sort $n$ elements but only a subset of pairs are allowed to be compared. Formally, there is some known graph $G = (V, E)$ on the…
In recent years, network models have gained prominence for their ability to capture complex associations. In statistical omics, networks can be used to model and study the functional relationships between genes, proteins, and other types of…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New particles appear subject to a neighbourhood exclusion…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree \mth{c} is larger than \mth{2.7183}, groups of max-matching patterns which differ greatly from…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…
Complex systems in nature and in society are often represented as networks, describing the rich set of interactions between objects of interest. Many deterministic and probabilistic clustering methods have been developed to analyze such…
Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…
Hypergraph is the most general model for complex networks involving group interactions. Taking the ideas of path homology from Alexander Grigor'yan, Yong Lin, Yuri Muranov and Shing-Tung Yau [18-22], Stephane Bressan, Jingyan Li and the…
Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…
For $t \in \mathbb{N}$ and every $i\in[t]$, let $H_i$ be a $d_i$-regular connected graph, with $1<|V(H_i)|\le C$ for some integer $C\ge 2$. Let $G=\square_{i=1}^tH_i$ be the Cartesian product of $H_1, \ldots, H_t$. We show that if $t\ge 5C$…
Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity,…
The Subgraph Matching (SM) problem consists of finding all the embeddings of a given small graph, called the query, into a large graph, called the target. The SM problem has been widely studied for simple graphs, i.e. graphs where there is…