Related papers: Computing The Analytic Connectivity of A Uniform H…

An abstract topological graph (AT-graph) is a pair $A=(G,\mathcal{X})$, where $G=(V,E)$ is a graph and $\mathcal{X} \subseteq {E \choose 2}$ is a set of pairs of edges of $G$. A realization of $A$ is a drawing $\Gamma_A$ of $G$ in the plane…

Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…

Large-scale decentralized learning frameworks such as federated learning (FL), require both communication efficiency and strong data security, motivating the study of secure aggregation (SA). While information-theoretic SA is well…

Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate…

An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic substructure. The locally graphic behaviors are formalized in…

We consider the action of the (combinatorial) Laplacian of a finite and simple graph on integer vectors. By a \emph{Laplacian monopole} we mean an image vector negative at exactly one coordinate associated with a vertex. We consider a…

We consider the incomplete multi-graph matching problem, which is a generalization of the NP-hard quadratic assignment problem for matching multiple finite sets. Multi-graph matching plays a central role in computer vision, e.g., for…

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can…

We study the problem of determining the optimal low dimensional projection for maximising the separability of a binary partition of an unlabelled dataset, as measured by spectral graph theory. This is achieved by finding projections which…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

Here, we show a method to reconstruct connectivity hypermatrices of a general hypergraph (without any self loop or multiple edge) using tensor. We also study the different spectral properties of these hypermatrices and find that these…

We show that (i) any constrained polynomial optimization problem (POP) has an equivalent formulation on a variety contained in an Euclidean sphere and (ii) the resulting semidefinite relaxations in the moment-SOS hierarchy have the constant…

In the 20th century, newly invented technical artifacts were connected to form large-scale complex engineering systems. Furthermore, the interactions found within these networked systems has grown in both degree as well as heterogeneity.…

The algebraic connectivity of a network characterizes the lower-bound of the exponential convergence rate of consensus processes. This paper investigates the problem of accelerating the convergence of consensus processes by adding links to…

In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of…

Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize…

In this paper, we settle a long-standing problem on the connectivity of spaces of finite unit norm tight frames (FUNTFs), essentially affirming a conjecture first appearing in [Dykema and Strawn, 2003]. Our central technique involves…

Decentralized and asynchronous communications are two popular techniques to speedup communication complexity of distributed machine learning, by respectively removing the dependency over a central orchestrator and the need for…

The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…

We present a novel theoretical framework connecting k-component edge connectivity with spectral graph theory and homology theory to pro vide new insights into the resilience of real-world networks. By extending classical edge connectivity…