An irregular coloring of a graph is a proper vertex coloring that distinguishes vertices in the graph either by their own colors or by the colors of their neighbors. In algebraic graph theory, graphs with a certain amount of symmetry can sometimes be specified in terms of a group and a smaller graph called a voltage graph. In [3], Radcliffe and Zhang found a bound for the irregular chromatic nu...

We consider simple labeled graphs, with non-zero labels in a ring. If the adjacency matrix of a labeled graph is invertible, the inverse matrix is a (labeled) adjacency matrix of another graph, called the inverse of the original graph. If the labeling takes place in an ordered ring, then balanced inverses—those with positive products of labels along every cycle—are of interest. We introduce the...

Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent inhibition as well as in networks with mixed recurrent inhibition and excitation. Here we analytically investigate this irregular dynamics in finite networks...

In this paper we present a method for the application of Convolutional Neural Network (CNN) operators for use in domains which exhibit irregular spatial geometry by use of the spectral domain of a graph Laplacian, Figure 1. This allows learning of localized features in irregular domains by defining neighborhood relationships as edge weights between vertices in graph G. By formulating the domain...

Edge Vertex Push Edge Edge The Problem: We want the fastest graph processing! • High-performance graph processing is very interesting for data science • High-performance computing is increasingly GPU/accelerator based • Mapping irregular (graph) algorithms to GPU is hard • Performance of irregular algorithms is data-dependent Thesis Goals • Quantify performance impact of data dependence • Model...

Many image analysis tasks lead to or make use of graph structures that are related through the analysis process with the planar layout of a digital image. This paper presents a theory that allows to build diierent types of hierarchies on top of such image graphs. The theory is based on the properties of a pair of dual image graphs that the reduction process should preserve, e.g. the structure o...

The graph-coloring metaphor leads to elegant algorithms for register allocation that have been shown to be quite effective for regular architectures with plenty of registers. Published attempts to make these algorithms applicable to architectures that are irregular in their use of registers have yielded several incompatible extensions that handle only a small subset of the irregularities seen i...

A group-labeled graph is a graph whose vertices and edges have been assigned labels from some abelian group. The weight of a subgraph of a group-labeled graph is the sum of the labels of the vertices and edges in the subgraph. A group-labeled graph is said to be balanced if the weight of every cycle in the graph is zero. We give a characterization of balanced group-labeled graphs that generaliz...