Coloring Problem Research Articles

Total Coloring and Total Matching: Polyhedra and Facets

A total coloring of a graph G=(V,E) is an assignment of colors to vertices and edges such that neither two adjacent vertices nor two incident edges get the same color, and, for each edge, the end-points and the edge itself receive different colors. Any valid total coloring induces a partition of the elements of G into total matchings, which are defined as subsets of vertices and edges that can take the same color. In this paper, we propose Integer Linear Programming models for both the Total Coloring and the Total Matching problems, and we study the strength of the corresponding Linear Programming relaxations. The total coloring is formulated as the problem of finding the minimum number of total matchings that cover all the graph elements. This covering formulation can be solved by a Column Generation algorithm, where the pricing subproblem corresponds to the Weighted Total Matching Problem. Hence, we study the Total Matching Polytope. We introduce three families of nontrivial valid inequalities: vertex-clique inequalities based on standard clique inequalities of the Stable Set Polytope, congruent-2k3 cycle inequalities based on the parity of the vertex set induced by the cycle, and even-clique inequalities induced by complete subgraphs of even order. We prove that congruent-2k3 cycle inequalities are facet-defining only when k=4, while the vertex-clique and even-cliques are always facet-defining. Finally, we present preliminary computational results of a Column Generation algorithm for the Total Coloring Problem and a Cutting Plane algorithm for the Total Matching Problem.

On 3-Coloring of (2P_4,C_5)-Free Graphs

The 3-coloring of hereditary graph classes has been a deeply-researched problem in the last decade. A hereditary graph class is characterized by a (possibly infinite) list of minimal forbidden induced subgraphs H_1,H_2,ldots ; the graphs in the class are called (H_1,H_2,ldots )-free. The complexity of 3-coloring is far from being understood, even for classes defined by a few small forbidden induced subgraphs. For H-free graphs, the complexity is settled for any H on up to seven vertices. There are only two unsolved cases on eight vertices, namely 2P_4 and P_8. For P_8-free graphs, some partial results are known, but to the best of our knowledge, 2P_4-free graphs have not been explored yet. In this paper, we show that the 3-coloring problem is polynomial-time solvable on (2P_4,C_5)-free graphs.

Lipid oxidation and antioxidant delivery systems in muscle food.

Lipid oxidation accelerates quality deterioration in muscle-based foods (fish, red meat, and poultry), resulting in off-odors/flavors, color problems, texture defects, and safety concerns. Adding antioxidants is one approach to control lipid oxidation, and several delivery strategies have been applied, such as supplementing antioxidants to the feed, direct mixing into minces, or, for whole muscle pieces; spraying, glazing, and injection. However, some issues linked to these technologies hinder their wide utilization, such as low effectiveness, noncompatibility with clean label, and off-flavor. These shortcomings have promoted the development of new antioxidant delivery technologies. In this review, the main focus is on the principles, characteristics, and implementation of five novel antioxidant delivery methods in different types of muscle food products. Their advantages and drawbacks are also summarized, plus comments about future trends in this area. Among novel routes to deliver antioxidants to muscle foods are, for whole tissues, recyclable dipping solutions; for minces, encapsulation; and, for both minces and whole tissues, cross-processing with nonmuscle antioxidant-containing raw materials as well as applications of edible films/coatings and active packaging. Advantages of these technologies comprise, for example, low price, the possibility to control the antioxidant release rate, overcoming strong aromas from natural antioxidants, and allowing antioxidant-containing raw materials from the food industry to be valorized, providing an opportunity for more circular food production.

On 3-degree 4-chordal graphs

A graph [Formula: see text] is a 3-degree 4-chordal graph if every cycle of length at least five has a chord and the degree of each vertex is at most three. In this paper, we investigate the structure of 3-degree 4-chordal graphs, which is a subclass of 3-degree graphs. We present a structural characterization based on minimal vertex separators and bi-connected components. Many classical problems are known to be NP-complete for 3-degree graphs, and 3-degree 4-chordal graphs are a nontrivial subclass of 3-degree graphs. Using our structural results, we present polynomial-time algorithms for many classical problems which are grouped into (i) subset problems (vertex cover and its variants, feedback vertex set, Steiner tree), (ii) Hamiltonicity and its variants, (iii) graph embedding problems (treewidth, minimum fill-in), and (iv) Coloring problems(rainbow coloring).

Oleg Lazarenko’s Mosaic Color Painting: Features of Plastic Language

The article examines the work of the Kharkiv art school and a member of the art association Burime, artist and designer Oleg Lazarenko. The article highlights the problem of color, which was actively raised by the Impressionists, and was subsequently picked up and comprehended by avant-garde movements. The genesis of color painting as an artistic technique in the art of the twentieth century is traced. Attention is focused on the avant-garde traditions, in particular, collage, suprematism and op-art, which greatly influenced the formation of the artist’s pictorial manner — mosaic color painting. The circle of postmodern innovations is revealed, which can be traced in the author’s manner of painting. It was revealed that in his creative activity the artist uses several pictorial techniques, which can be classified as follows: “plein air painting”, “mosaic color painting”, “oil color painting”. In addition, the art history analysis of the works showed his potential as a color painter and demonstrated the artist’s ability to go beyond the framework of a two-dimensional canvas with the help of optical illusions, color transitions, and influence the psychological state of the viewer. The origins of the design component in the master’s painting, which originate from the time of study at the “Khudprom” (Kharkiv State Academy of Design and Fine Arts) and have a significant impact on the author’s writing technique. The connection of the artist’s pictorial language with the ancient artistic culture is traced, which is expressed through Lazarenko’s appeal to the Trypillian ornamentation and Ukrainian folk traditions. The author reveals the relationship between religious art and icon-painting reminiscences of the master, which are transmitted through mosaic and oil color painting and illuminated in sacramental images on canvas. An art history analysis of O. Lazarenko’s selected works, performed in the technique of mosaic and oil color painting, is carried out, and the peculiarities of their structural-compositional and figurative-meaningful solutions are revealed.

Spatially Consistent Transformer for Colorization in Monochrome-Color Dual-Lens System.

We study the colorization problem in monochrome-color dual-lens camera systems, i.e. colorizing the gray image from the monochrome camera using the color image from the color camera as reference. In related methods, cost volume based CNN methods achieve the state-of-the-art results, but they are costly in GPU memory due to building the 4D cost volume. Recently, some slice-wise cross-attention based methods are proposed for related problems. The slice-wise cross-attention has much less costs in GPU memory but directly using them for this colorization problem cannot generate competing results. We make use of the non-local computation property of cross-attention to propose a transformer based method. To overcome the limitations of straight-forward slice-wise cross-attention, we propose the spatially consistent cross-attention (SCCA) block to encourage pixels of slices across different epipolar lines in the gray image to find spatially consistent correspondence with pixels of the reference color image. And, to further reduce the memory cost while keeping the colorization accuracy, we design a pyramid processing strategy to cascade a series of SCCA blocks with smaller slice size and perform the colorization from coarse to fine. To extract more powerful image features, we use several regional self-attention (RSA) blocks with U-style connections. Experimental results show that we outperform the state-of-the-art methods largely on the synthesized datasets of Cityscapes, Sintel, and SceneFlow, and the real monochrome-color dual-lens dataset.

Underwater Images Enhancement by Revised Underwater Images Formation Model

In this paper, we proposed the efficient and appealing technique for underwater images enhancement. Underwater images often suffer from haze, color distortion, low contrast and loss of the human acuity due to light scattering and absorption. To tackle these issues, proposed precise model is presented expressively showed that: (1) the estimation of the transmission map in atmospheric scatter model is divided into two cases, which are more applicable to underwater images in different situations, and make the enhanced results more robust; (2) model not only removes haze but also restores lost colors of underwater images in the image de-hazing step instead of color correction. First, we proposed a revised underwater dehazing model aiming to eliminate the color of water directly while solving the problem of haze in the underwater images. Then proposed color correction method can adaptively address the problem of color shifting without any additional information. Furthermore, we design a multi-scale illumination fusion to reveal more details and low illumination parts of the image. Experimental results demonstrate that our proposed method outperforms other methods significantly with 5%~77% quantitative improvement on all four evaluation performance indices and shows more obvious detailed underwater images. Our method can be applied to underwater detection and exploration as the pre-processing step.

Adjacent Upper Triangular Matrix Algorithm for Vertex Colouring Problem

Adjacent Upper Triangular Matrix Algorithm for Vertex Colouring Problem

Resorting to Context-Aware Background Knowledge for Unveiling Semantically Related Social Media Posts

Social media networks have become a prime source for sharing news, opinions, and research accomplishments in various domains, and hundreds of millions of posts are announced daily. Given this wealth of information in social media, finding related announcements has become a relevant task, particularly in trending news (e.g., COVID-19 or lung cancer). To facilitate the search of connected posts, social networks enable users to annotate their posts, e.g., with hashtags in tweets. Albeit effective, an annotation-based search is limited because results will only include the posts that share the same annotations. This paper focuses on retrieving context-related posts based on a specific topic, and presents PINYON, a knowledge-driven framework, that retrieves associated posts effectively. PINYON implements a two-fold pipeline. First, it encodes, in a graph, a CORPUS of posts and an input post; posts are annotated with entities for existing knowledge graphs and connected based on the similarity of their entities. In a decoding phase, the encoded graph is used to discover communities of related posts. We cast this problem into the Vertex Coloring Problem, where communities of similar posts include the posts annotated with entities colored with the same colors. Built on results reported in the graph theory, PINYON implements the decoding phase guided by a heuristic-based method that determines relatedness among posts based on contextual knowledge, and efficiently groups the most similar posts in the same communities. PINYON is empirically evaluated on various datasets and compared with state-of-the-art implementations of the decoding phase. The quality of the generated communities is also analyzed based on multiple metrics. The observed outcomes indicate that PINYON accurately identifies semantically related posts in different contexts. Moreover, the reported results put in perspective the impact of known properties about the optimality of existing heuristics for vertex graph coloring and their implications on PINYON scalability.

A Grover Search-Based Algorithm for the List Coloring Problem

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 general question: given a list of available colors for each vertex in a graph, does it admit a proper coloring? We propose a quantum algorithm based on Grover search to quadratically speed up exhaustive search. Our algorithm loses in complexity to classical ones in specific restricted cases, but improves exhaustive search for cases where the lists and graphs considered are arbitrary in nature.

Solving Graph Coloring Problem Using Graph Adjacency Matrix Algorithm

Solving Graph Coloring Problem Using Graph Adjacency Matrix Algorithm

INVESTIGATION of COLOR REMOVAL in REAL TEXTILE INDUSTRY WASTEWATER with MEMBRANE BIOREACTOR-ACTIVE CARBON SYSTEM

The textile industry is an industry that consumes large amounts of water during production, contains various chemicals in its wastewater, conventional treatment methods are insufficient to reduce the wastewater pollution level, and has colloidal substances and color problems. Membrane bioreactor systems provide high efficiency in the treatment of textile wastewater and dyestuff removal. Removal of dyestuffs and turbidity in real textile wastewater by using a laboratory-scale membrane bioreactor system was studied. Chemical precipitation was not applied before the biological treatment for the removal of color and other pollutant parameters. A hollow fiber microfiltration membrane module was used in the system. Then a combination with an active carbon filter was created to take the color removal to a higher level. The development of the microorganism composition adapted to the textile industry was observed in the biological reactor. The system was operated with an endless sludge age and a hydraulic retention time of 24 hours. Color measurement transparency index parameter DFZ (DurchsichtsFarbZahl) was measured in a spectrophotometer at wavelengths of 436, 525, and 620 nm (nanometers) according to EN ISO 7887 standards. In the microfiltration permeate water, the color removal were found in 436 nm: 91-95%, 525 nm: 94-98%, 620 nm: 96-99%, and in activated carbon permeate water, the color removal in 436 nm: 96-99% at 525 nm: 95-99%, 620 nm: 96-99%, respectively. Due to the physical separation of the membrane, which is the simplest definition, high efficiencies in color removal have been achieved in the system. The activated carbon system combined with the membrane was found higher efficiency in color removal than the microfiltration output.

DESIGN OF WEB-BASED UYU STORE ATTENDANCE INFORMATION SYSTEM USING COLORING METHOD

Attendance in the world of work is sometimes still done manually. At the Uyu shop, there are still problems that occur in recording and making attendance reports manually, such as mistakes in biodata, forgetting to record the date. Because the Uyu store still doesn't use a computerized employee or staff absence information system in managing data, so the information that can be processed is quite long and storage is not guaranteed safe. The purpose of this researcher is to create an information system that can manage attendance data for employees who work at the computerized Uyu Store and also implement a coloring method on attendance reports that generate reports based on the attendance coloring method according to employee attendance hours that are easy to understand. This method uses the coloring method as a solution to solving problems that can be solved in the greedy method, namely the color problem and the waterfall model as a system development process that uses UML design. The result of this research is that the system can operate attendance data collection as well as report employee data more efficiently and integrated.

Locally-iterative Distributed (Δ + 1)-coloring and Applications

We consider graph coloring and related problems in the distributed message-passing model. Locally-iterative algorithms are especially important in this setting. These are algorithms in which each vertex decides about its next color only as a function of the current colors in its 1-hop-neighborhood . In STOC’93 Szegedy and Vishwanathan showed that any locally-iterative Δ + 1-coloring algorithm requires Ω (Δ log Δ + log * n ) rounds, unless there exists “a very special type of coloring that can be very efficiently reduced” [ 44 ]. No such special coloring has been found since then. This led researchers to believe that Szegedy-Vishwanathan barrier is an inherent limitation for locally-iterative algorithms and to explore other approaches to the coloring problem [ 2 , 3 , 19 , 32 ]. The latter gave rise to faster algorithms, but their heavy machinery that is of non-locally-iterative nature made them far less suitable to various settings. In this article, we obtain the aforementioned special type of coloring. Specifically, we devise a locally-iterative Δ + 1-coloring algorithm with running time O (Δ + log * n ), i.e., below Szegedy-Vishwanathan barrier. This demonstrates that this barrier is not an inherent limitation for locally-iterative algorithms. As a result, we also achieve significant improvements for dynamic, self-stabilizing, and bandwidth-restricted settings. This includes the following results: We obtain self-stabilizing distributed algorithms for Δ + 1-vertex-coloring, (2Δ - 1)-edge-coloring, maximal independent set, and maximal matching with O (Δ + log * n ) time. This significantly improves previously known results that have O(n) or larger running times [ 23 ]. We devise a (2Δ - 1)-edge-coloring algorithm in the CONGEST model with O (Δ + log * n ) time and O (Δ)-edge-coloring in the Bit-Round model with O (Δ + log n ) time. The factors of log * n and log n are unavoidable in the CONGEST and Bit-Round models, respectively. Previously known algorithms had superlinear dependency on Δ for (2Δ - 1)-edge-coloring in these models. We obtain an arbdefective coloring algorithm with running time O (√ Δ + log * n ). Such a coloring is not necessarily proper, but has certain helpful properties. We employ it to compute a proper (1 + ε)Δ-coloring within O (√ Δ + log * n ) time and Δ + 1-coloring within O (√ Δ log Δ log * Δ + log * n ) time. This improves the recent state-of-the-art bounds of Barenboim from PODC’15 [ 2 ] and Fraigniaud et al. from FOCS’16 [ 19 ] by polylogarithmic factors. Our algorithms are applicable to the SET-LOCAL model [ 25 ] (also known as the weak LOCAL model). In this model a relatively strong lower bound of Ω (Δ 1/3 ) is known for Δ + 1-coloring. However, most of the coloring algorithms do not work in this model. (In Reference [ 25 ] only Linial’s O (Δ 2 )-time algorithm and Kuhn-Wattenhofer O (Δ log Δ)-time algorithms are shown to work in it.) We obtain the first linear-in-Δ Δ + 1-coloring algorithms that work also in this model.

Structural Parameterizations of Clique Coloring

A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with q colors. For fixed q ge 2, we give an mathscr {O}^{star }(q^{{mathsf {tw}}})-time algorithm when the input graph is given together with one of its tree decompositions of width {mathsf {tw}} . We complement this result with a matching lower bound under the Strong Exponential Time Hypothesis. We furthermore show that (when the number of colors is unbounded) Clique Coloring is mathsf {XP} parameterized by clique-width.

Optimization of the dynamic transition in the continuous coloring problem

Random constraint satisfaction problems (CSPs) can exhibit a phase where the number of constraints per variable α makes the system solvable in theory on the one hand, but also makes the search for a solution hard, meaning that common algorithms such as Monte Carlo (MC) method fail to find a solution. The onset of this hardness is deeply linked to the appearance of a dynamical phase transition where the phase space of the problem breaks into an exponential number of clusters. The exact position of this dynamical phase transition is not universal with respect to the details of the Hamiltonian one chooses to represent a given problem. In this paper, we develop some theoretical tools in order to find a systematic way to build a Hamiltonian that maximizes the dynamic α d threshold. To illustrate our techniques, we will concentrate on the problem of continuous coloring, where one tries to set an angle x i ∈ [0; 2π] on each node of a network in such a way that no adjacent nodes are closer than some threshold angle θ, that is cos(x i − x j )⩽ cos θ. This problem can be both seen as a continuous version of the discrete graph coloring problem or as a one-dimensional version of the Mari–Krzakala–Kurchan model. The relevance of this model stems from the fact that continuous CSPs on sparse random graphs remain largely unexplored in statistical physics. We show that for sufficiently small angle θ this model presents a random first order transition and compute the dynamical, condensation and Kesten–Stigum transitions; we also compare the analytical predictions with MC simulations for values of θ = 2π/q, . Choosing such values of q allows us to easily compare our results with the renowned problem of discrete coloring.

A New Multi-Objective Evolutionary Approach to Graph Coloring and Channel Allocation Problems

A New Multi-Objective Evolutionary Approach to Graph Coloring and Channel Allocation Problems

Eliminate obstacles of use the solar systems as buildings facades using multilayers optical interference filters

The Building design in a correct way and totalitarian requires integration of using solar energy technologies in the architectural design stage of the roofs and facades as the most appropriate places to obtain solar energy because it greatly affects the architectural aesthetic. This integration has to be taken into account at the design stage, which leads to effective and attractive solutions. Architecture needs the energy to complete its functions to increases human effectiveness and ability to do its tasks better, solar energy is the main factor of providing the necessary energy due to its abundance as well as being clean energy and does not cause polluting emissions to the environment. To provide a comfortable indoor environment for the occupants, Solar Thermal Collectors (STC) and Photovoltaics Cells (PV) used, which convert solar energy into thermal energy and electrical energy, respectively. The main problem of this study is concerning with the problems of the black color, visible tubes, metallic strip gradients (absorption strip), and welding points of the solar systems which gives the facades of the buildings an undesirable view and weakens the aesthetic aspect of the buildings and limits the abilities of architects to use because of their black color and undesirable aspect. The aim of this study is a design of optical interference filter (multilayer coatings) prepared by RF magnetron sputtering as a solution to the problem of black color, visible tubes, metallic strip gradients (absorption strip), and welding points in solar thermal collectors and photovoltaic cells, which are the main reasons for not using solar systems as building facades, this technique works to increase the efficiency of the solar systems and increase the amount of clean energy generated, also enhancing the expressive and aesthetic aspect of facades of buildings. In the NIR region this filter works as an anti-reflective coating. Also the coating includes a high color reflection at a certain wavelength in the VIS region to give the solar system an aesthetic feature, which is used as building facades by using appropriate dielectric substances with high and low reflective indexes likes SiO2 and MgF2 respectively. The results of the study showed that the increase in the number of layers will lead to an increase in the visible reflectivity peak, while near of infrared region remains an anti-reflective with a high Transmission of solar rays, thus increasing solar systems efficiency.

The dyeability and after-dyeing wearability of TPU-based 3D-printed fabrics

PurposeThe purpose of the paper is to study the dyeing process of three-dimensional-printed (3DP) fabrics, and then study the wearability of the fabrics before and after dyeing to provide a feasible dyeing method of 3DP clothes.Design/methodology/approachIn this regard, the thermoplastic polyurethane (TPU) was applied during the process of 3DP. Then, the imitation twill weave (ITW) was printed with fused deposition modeling (FDM) technology using TPU and the suspension of Disperse Blue 2BLN (as a dye) was prepared. After that, the single factor analysis and orthogonal experiment of dyeing were combined to obtain the optimized dyeing process. And then, ITW fabrics were dyed through the weak acid-low temperature dyeing method. In the end, in order to discuss the wearability of ITW fabrics, the dyeing experiments, including permeability, wrinkle recovery angle, bending rigidity, crock fastness and washing colorfastness were carried out.FindingsThe surface morphology of TPU before and after spinning was established by field emission scanning electron microscopy (FE-SEM), which was confirmed the surface of TPU getting smoother after spinning. The wearability of the fabric after dyeing was not affected compared with before dyeing. Moreover, both colorfastness grades were above 4–5 with high colorfastness.Originality/valueThe article provides a method for 3DP dyeing, which can solve the problem of a single color. And the wearability demonstrates that 3DP fabrics after dyeing-based TPU have more value for clothing than before dyeing.

Colorization by Matrix Completion

Given a monochrome image and some manually labeled pixels, the colorization problem is a computer-assisted process of adding color to the monochrome image. This paper proposes a novel approach to the colorization problem by formulating it as a matrix completion problem. In particular, taking a monochrome image and parts of the color pixels (labels) as inputs, we develop a robust colorization model and resort to an augmented Lagrange multiplier algorithm for solving the model. Our approach is based on the fact that a matrix can be represented as a low-rank matrix plus a sparse matrix. Our approach is effective because it is able to handle the potential noises in the monochrome image and outliers in the labels. To improve the performance of our method, we further incorporate a so-called local-color-consistency idea into our method. Empirical results on real data sets are encouraging.