Related papers: Computing The Analytic Connectivity of A Uniform H…
We propose a tensor product structure that is compatible with the hypergraph structure. We define the algebraic connectivity of the $(m+1)$-uniform hypergraph in this product, and prove the relationship with the vertex connectivity. We…
In this paper, we study the analytic connectivity of a $k$-uniform hypergraph $H$, denoted by $\alpha(H)$. In addition to computing the analytic connectivity of a complete $k$-graph, we present several bounds on analytic connectivity that…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
Algebraic connectivity is one way to quantify graph connectivity, which in turn gauges robustness as a network. In this paper, we consider the problem of maximising algebraic connectivity both local and globally over all simple, undirected,…
Random hypergraph is a broad concept used to describe probability distributions over hypergraphs, which are mathematical structures with applications in various fields, e.g., complex systems in physics, computer science, social sciences,…
Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model…
The connectivity is an important parameter to evaluate the robustness of a network. As a generalization, structure connectivity and substructure connectivity of graphs were proposed. For connected graphs $G$ and $H$, the $H$-structure…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
Current distributed data fabrics lack a rigorous mathematical foundation, often relying on ad-hoc architectures that struggle with consistency, lineage, and scale. We propose a mathematical framework for data fabrics, unifying heterogeneous…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
A fundamental question that shrouds the emergence of massively parallel computing (MPC) platforms is how can the additional power of the MPC paradigm be leveraged to achieve faster algorithms compared to classical parallel models such as…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…
A standard question in real algebraic geometry is to compute the number of connected components of a real algebraic variety in affine space. By adapting an approach for determining connectivity in complements of real hypersurfaces by Hong,…
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
In this paper we extend the known results of analytic connectivity to non-uniform hypergraphs. We prove a modified Cheeger's inequality and also give a bound on analytic connectivity with respect to the degree sequence and diameter of a…
Spectral algorithms, such as principal component analysis and spectral clustering, typically require careful data transformations to be effective: upon observing a matrix $A$, one may look at the spectrum of $\psi(A)$ for a properly chosen…