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Cell formation is a critical step in the design of cellular manufacturing systems. Recently, it was tackled using a cut-based-graph-partitioning model. This model meets real-life production systems requirements as it uses the actual amount…
The problem of efficiently coloring $3$-colorable graphs with few colors has received much attention on both the algorithmic and inapproximability fronts. We consider exponential time approximations, in which given a parameter $r$, we aim…
We consider a variation of the prototype combinatorial-optimisation problem known as graph-colouring. Our optimisation goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximise the number of different…
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper $r$-coloring $\varphi$ of a graph $G$. We investigate the problem of finding a proper $r$-coloring of $G$, which is "the…
Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…
Edge-coloring problems with forbidden patterns are decision problems asking to find an edge-coloring of the input graph which avoids a homomorphism from a fixed forbidden family of edge-colored graphs. In the precolored version of these…
We live in a period where bio-informatics is rapidly expanding, a significant quantity of genomic data has been produced as a result of the advancement of high-throughput genome sequencing technology, raising concerns about the costs…
We introduce a novel method to analyse complete genomes and recognise some distinctive features by means of an adaptive compression algorithm, which is not DNA-oriented. We study the Information Content as a function of the number of…
This work investigates structural and computational aspects of list-based graph coloring under interval constraints. Building on the framework of analogous and p-analogous problems, we show that classical List Coloring, $\mu$-coloring, and…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Advances in deep-learning-based pipelines have led to breakthroughs in a variety of microscopy image diagnostics. However, a sufficiently big training data set is usually difficult to obtain due to high annotation costs. In the case of…
Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ for $k\ge 5$. The list coloring problem asks the following more…
We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics…
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire…
In the Coloured Clustering problem, we wish to colour vertices of an edge coloured graph to produce as many stable edges as possible, i.e., edges with the same colour as their ends. In this paper, we reveal that the problem is in fact a…
Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by $k$: (1) Given a graph $G$, a clique modulator $D$ (a clique modulator is a set of vertices, whose…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…