Related papers: Fractional Graph Coloring for Functional Compressi…

In parallel computing, a valid graph coloring yields a lock-free processing of the colored tasks, data points, etc., without expensive synchronization mechanisms. However, coloring is not free and the overhead can be significant. In…

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…

Several authors modelled networks ad hoc by oriented or disoriented graphs, whereby the problem of allowance (allocation) of the frequencies at the level of the network was transformed into coloring problem of nodes in the graph. Graph…

An $(a:b)$-coloring of a graph $G$ is a function $f$ which maps the vertices of $G$ into $b$-element subsets of some set of size $a$ in such a way that $f(u)$ is disjoint from $f(v)$ for every two adjacent vertices $u$ and $v$ in $G$. The…

Large alphabet source coding is a basic and well-studied problem in data compression. It has many applications such as compression of natural language text, speech and images. The classic perception of most commonly used methods is that a…

For spin systems, such as the $q$-colorings and independent-set models, approximating the partition function in the so-called non-uniqueness region, where the model exhibits long-range correlations, is typically computationally hard for…

A new algorithm to obtain the chromatic number of a finite, connected graph is proposed in this paper. The algorithm is based on contraction of non adjacent vertices.

Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…

In this paper, we suggest new SAT encodings of the partial-ordering based ILP model for the graph coloring problem (GCP) and the bandwidth coloring problem (BCP). The GCP asks for the minimum number of colors that can be assigned to the…

We develop a heuristic graph coloring approximation algorithm that uses the D-Wave 2X as an independent set sampler and evaluate its performance against a fully classical implementation. A randomly generated set of small but hard graph…

The randomized technique of color coding is behind state-of-the-art algorithms for estimating graph motif counts. Those algorithms, however, are not yet capable of scaling well to very large graphs with billions of edges. In this paper we…

Graph signals arise in various applications, ranging from sensor networks to social media data. The high-dimensional nature of these signals implies that they often need to be compressed in order to be stored and transmitted. The common…

The coming quantum computation is forcing us to reexamine the cryptosystems people use. We are applying graph colorings of topological coding to modern information security and future cryptography against supercomputer and quantum computer…

Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each…

Let $2\le k\in\mathbb{Z}$. A total coloring of a$k$-regular simple graph via $k+1$ colors is an efficient total coloring if each color yields an efficient dominating set, where the efficient domination condition applies to the restriction…

We show how to couple phase-oscillators on a graph so that collective dynamics "searches" for the coloring of that graph as it relaxes toward the dynamical equilibrium. This translates a combinatorial optimization problem (graph coloring)…

A graph G is (a:b)-colorable if there exists an assignment of b-element subsets of {1,...,a} to vertices of G such that sets assigned to adjacent vertices are disjoint. We first show that for every triangle-free planar graph G and a vertex…

Various graphs such as web or social networks may contain up to trillions of edges. Compressing such datasets can accelerate graph processing by reducing the amount of I/O accesses and the pressure on the memory subsystem. Yet, selecting a…

Higher dimensional graphs can be used to colour two-dimensional geometric graphs. If G the boundary of a three dimensional graph H for example, we can refine the interior until it is colourable with 4 colours. The later goal is achieved if…

With neural networks growing deeper and feature maps growing larger, limited communication bandwidth with external memory (or DRAM) and power constraints become a bottleneck in implementing network inference on mobile and edge devices. In…