相关论文: General solution to nonlinear optical quantum grap…

This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…

In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…

Partitioning is a known problem in computer science and is critical in chip design workflows, as advancements in this area can significantly influence design quality and efficiency. Deep Learning (DL) techniques, particularly those…

In this paper, a new graph partitioning problem is introduced. The depth of each part is constrained, i.e., the node count in the longest path of the corresponding sub-graph is no more than a predetermined positive integer value p. An…

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image…

Proving the existence of an operator that connects non-perturbed states to perturbed states, an alternative derivation of the Dalgarno-Lewis method is given. To illustrate that the Dalgarno-Lewis method is an apt tool for algebraic…

In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…

Subgraph representation learning has been effective in solving various real-world problems. However, current graph neural networks (GNNs) produce suboptimal results for subgraph-level tasks due to their inability to capture complex…

Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…

We demonstrate that a quantum annealer can be used to solve the NP-complete problem of graph partitioning into subgraphs containing Hamiltonian cycles of constrained length. We present a method to find a partition of a given directed graph…

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver…

We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…

Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the…

We present three sublinear randomized algorithms for vertex-coloring of graphs with maximum degree $\Delta$. The first is a simple algorithm that extends the idea of Morris and Song to color graphs with maximum degree $\Delta$ using…

Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…

This paper introduces an efficient quantum computing method for reducing special graphs in the context of the graph coloring problem. The special graphs considered include both symmetric and non-symmetric graphs where the axis passes…

Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…

Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…

In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…