Related papers: Factor system for graphs and combinatorial HHS

We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…

Girth-regular graphs with equal girth, regular degree and chromatic index are studied for the determination of 1-factorizations with each 1-factor intersecting every girth cycle. Applications to hamiltonian decomposability and to…

Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.

Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…

We show that additive induced-hereditary properties of coloured hypergraphs can be uniquely factorised into irreducible factors. Our constructions and proofs are so general that they can be used for arbitrary concrete categories of…

We present a simple combinatorial framework for establishing approximate tensorization of variance and entropy in the setting of spin systems (a.k.a. undirected graphical models) based on balanced separators of the underlying graph. Such…

Vector quantization(VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution presents a theoretical foundation of…

In this paper we introduce compressed commuting graph of rings. It can be seen as a compression of the standard commuting graph (with the central elements added) where we identify the vertices that generate the same subring. The compression…

An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…

We describe a graph-based neural acceleration technique for nonnegative matrix factorization that builds upon a connection between matrices and bipartite graphs that is well-known in certain fields, e.g., sparse linear algebra, but has not…

Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.

Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization…

A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when…

In this note, we discuss and motivate the use of the terminology ``median graphs'' in place of ``CAT(0) cube complexes'' in geometric group theory.

HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…

A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…

This paper describes a unified method solving for inverse, forward, and hybrid dynamics problems for robotic manipulators with either open kinematic chains or closed kinematic loops based on factor graphs. Manipulator dynamics is considered…

The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping…

A Hamiltonian graph is 2-factor Hamiltonian (2FH) if each of its 2-factors is a Hamiltonian cycle. A similar, but weaker, property is the Perfect-Matching-Hamiltonian property (PMH-property): a graph admitting a perfect matching is said to…

Graph is a ubiquitous structure in many domains. The rapidly increasing data volume calls for efficient and scalable graph data processing. In recent years, designing distributed graph processing systems has been an increasingly important…