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Journal articles on the topic 'Geometric packing problems'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Stoyan, Yu G., N. I. Gil’, T. E. Romanova, and M. V. Zlotnik. "Decomposition algorithm for geometric objects in 2D packing and cutting problems." Cybernetics and Systems Analysis 47, no. 6 (2011): 854–62. http://dx.doi.org/10.1007/s10559-011-9364-9.

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2

Xu, Jie, Tao Wu, Jianwei Zhang, Hao Chen, Wei Sun, and Chuang Peng. "Microstructure Measurement and Microgeometric Packing Characterization of Rigid Polyurethane Foam Defects." Cellular Polymers 36, no. 4 (2017): 183–204. http://dx.doi.org/10.1177/026248931703600402.

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Streak and blister cell defects pose extensive surface problems for rigid polyurethane foams. In this study, these morphological anomalies were visually inspected using 2D optical techniques, and the cell microstructural coefficients including degree of anisotropy cell circumdiameter, and the volumetric isoperimetric quotient were calculated from the observations. A geometric regular polyhedron approximation method was developed based on relative density equations, in order to characterize the packing structures of both normal and anomalous cells. The reversely calculated cell volume constant,

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3

Zheng, Pengfei, Jingjing Lou, Dajun Lin, and Qi An. "Descending Packing Algorithm for Irregular Graphics Based on Geometric Feature Points." Mathematical Problems in Engineering 2020 (November 3, 2020): 1–12. http://dx.doi.org/10.1155/2020/8854838.

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The packing for two-dimensional irregular graphics is one of the NP-complete problems and widely used in industrial applications. In this paper, a descending nesting algorithm for a two-dimensional irregular graph based on geometric feature points is proposed. Before the packing, the parts to be packed are sorted, matched, and spliced, and the matching of the rectangular pieces and the rectangular-like pieces is carried out according to the plate size. On this basis, the geometric feature points of the parts are used to construct the packing baseline, and the packing is accurately carried out

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4

Chan, Timothy M., and Elyot Grant. "Exact algorithms and APX-hardness results for geometric packing and covering problems." Computational Geometry 47, no. 2 (2014): 112–24. http://dx.doi.org/10.1016/j.comgeo.2012.04.001.

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5

Trao, Hazim, Niran Ali, Gek Chia, and Adem Kilicman. "Packing 1-plane Hamiltonian cycles in complete geometric graphs." Filomat 33, no. 6 (2019): 1561–74. http://dx.doi.org/10.2298/fil1906561t.

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Counting the number of Hamiltonian cycles that are contained in a geometric graph is #P-complete even if the graph is known to be planar. A relaxation for problems in plane geometric graphs is to allow the geometric graphs to be 1-plane, that is, each of its edges is crossed at most once. We consider the following question: For any set P of n points in the plane, how many 1-plane Hamiltonian cycles can be packed into a complete geometric graph Kn? We investigate the problem by taking three different situations of P, namely, when P is in convex position and when P is in wheel configurations pos

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6

Yakovlev, S. V. "On a combinatorial structure of the problems of optimal packing of geometric objects." Reports of the National Academy of Sciences of Ukraine, no. 9 (September 14, 2017): 26–32. http://dx.doi.org/10.15407/dopovidi2017.09.026.

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7

Yakovlev, S. V. "The Method of Artificial Space Dilation in Problems of Optimal Packing of Geometric Objects." Cybernetics and Systems Analysis 53, no. 5 (2017): 725–31. http://dx.doi.org/10.1007/s10559-017-9974-y.

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8

Tyrin, Grigory, and Vladimir Frolovsky. "Research and application of the crow search algorithm for geometric covering optimization problems." Proceedings of the Russian higher school Academy of sciences, no. 1 (July 8, 2021): 54–61. http://dx.doi.org/10.17212/1727-2769-2021-1-54-61.

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The problem of geometric covering is a special case of the optimal design problem and belongs to the class of cutting and packing problems. The challenge is to position some geometric objects on the surface to be coated so that the entire surface is covered. The complexity of the problems under consideration is due to their belonging to the class of NP-hard problems, which excludes the possibility of solving them by exact methods and requires the development of approximate optimization methods and algorithms. This article discusses the problem of geometric covering of an area with circles from

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9

Chekanin, Vladislav, and Alexander Chekanin. "Application of Algorithms for Placement of Orthogonal Polyhedrons for Solving the Problems of Packing Objects of Complex Geometric Shape." EPJ Web of Conferences 248 (2021): 02001. http://dx.doi.org/10.1051/epjconf/202124802001.

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The article is devoted to the development and research of algorithms for placing objects of complex geometric shapes. To solve the placement problem is proposed an approach which consists in transforming the shape of all objects and further application of the developed algorithm for placing orthogonal polyhedrons of arbitrary dimension to the resulting transformed objects. In the process of transforming the shape of the objects being placed, they are initially voxelized, after which the developed decomposition algorithm is applied to the resulting voxelized objects, which provides the formatio

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10

Yin, Yan Fang, and Zhen Hui Tian. "Optimizing Flow for the Two Color Injection Mould Design." Applied Mechanics and Materials 441 (December 2013): 627–30. http://dx.doi.org/10.4028/www.scientific.net/amm.441.627.

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Commercial CAD/CAM systems provide semi-automatic tools to assist the designer in the dimensioning process. Analytical solutions to injection molding problems are very rare due to thecomplexities of the governing equations, the material behavior and the cavity geometry. Study of window frame fabrication by injection moulding process was carried out with the aid of Moldflow® software. Ejector plate designs were created to compare the pros and cons of each design. The investigations were carried out on flowing, packing, cooling and costing of injection moulded window frame. Using the method, goo

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11

Garzon, Max H., and Kiran C. Bobba. "Geometric Approaches to Gibbs Energy Landscapes and DNA Oligonucleotide Design." International Journal of Nanotechnology and Molecular Computation 3, no. 3 (2011): 42–56. http://dx.doi.org/10.4018/ijnmc.2011070104.

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DNA codeword design has been a fundamental problem since the early days of DNA computing. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves, to each other or to others' complements. Such strands represent so-called domains, particularly in the language of chemical reaction networks (CRNs). The problem has shown to be of interest in other areas as well, including DNA memories and phylogenetic analyses because of their error correction and prevention properties. In prior work, a theoretical framework to analyze this problem has been developed

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12

Jim, Chi Yung. "Soil Compaction as a Constraint to Tree Growth in Tropical & Subtropical Urban Habitats." Environmental Conservation 20, no. 1 (1993): 35–49. http://dx.doi.org/10.1017/s0376892900037206.

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Of the many forms of above- and below-ground stresses facing urban trees, physical soil limitations are generally among the most persistent and least amenable to amelioration. Soil compaction is a common soil malady that afflicts many planting-sites and causes tree decline. The concept of soil structure in terms of porosity and moisture-suction is reviewed, to provide a basis for the interpretation of compaction as structural degradation. The reorganization of solid and interstitial void constituents, which can result in increased dentity of packing, is related to some fundamental physical and

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13

A.M., Chugay, and Alyokhina S.V. "Using of optimization geometric design methods for the problems of the spent nuclear fuel safe storage." Artificial Intelligence 25, no. 3 (2020): 51–63. http://dx.doi.org/10.15407/jai2020.03.051.

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Packing optimization problems have a wide spectrum of real-word applications. One of the applications of the problems is problem of placement of containers with spent nuclear fuel (SNF) on the storage platform. The solution of the problem can be reduced to the solution of the problem of finding the optimal placement of a given set of congruent circles into a multiconnected domain taking into account technological restrictions. A mathematical model of the prob-lem is constructed and its peculiarities are considered. Our approach is based on the mathematical modelling of rela-tions between geome

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14

Казаков, А. Л., А. А. Лемперт, and Г. Л. Нгуен. "An algorithm of packing congruent circles in a multiply connected set with non-Euclidean metrics." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 2 (May 26, 2016): 177–88. http://dx.doi.org/10.26089/nummet.v17r216.

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Рассматривается задача об упаковке конгруэнтных кругов в ограниченное множество (контейнер) в двумерном метрическом пространстве: требуется найти такое расположение кругов в контейнере, при котором они заполнят как можно большую долю последнего. В случае, когда пространство является евклидовым, эта задача достаточно хорошо изучена, однако существует ряд прикладных задач, в частности в области инфраструктурной логистики, которые приводят нас к необходимости использовать специальные неевклидовые метрики. Исследованию таких задач и посвящена данная работа, причем рассматриваются как односвязные,

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15

Garzon, Max H. "DNA Codeword Design: Theory and Applications." Parallel Processing Letters 24, no. 02 (2014): 1440001. http://dx.doi.org/10.1142/s0129626414400015.

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This is a survey of the origin, current progress and applications of a major roadblock to the development of analytic models for DNA computing (a massively parallel programming methodology) and DNA self-assembly (a nanofabrication methodology), namely the so-called CODEWORD DESIGN problem. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves or to their complements and has been recognized as an important problem in DNA computing, self-assembly, DNA memories and phylogenetic analyses because of their error correction and prevention properties.

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16

Johnson, Jerome B., and Mark A. Hopkins. "Identifying microstructural deformation mechanisms in snow using discrete-element modeling." Journal of Glaciology 51, no. 174 (2005): 432–42. http://dx.doi.org/10.3189/172756505781829188.

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AbstractA dynamic model of dry snow deformation is developed using a discrete-element technique to identify microstructural deformation mechanisms and simulate creep densification processes. The model employs grain-scale force models, explicit geometric representations of individual ice grains, and snow microstructure using assemblies of grains. Ice grains are randomly oriented cylinders of random length with hemispherical ends. Particle contacts are detected using a novel and efficient method based on the dilation operation in mathematical morphology. Grain-scale ice interaction algorithms, b

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17

Faina, Loris. "A survey on the cutting and packing problems." Bollettino dell'Unione Matematica Italiana 13, no. 4 (2020): 567–72. http://dx.doi.org/10.1007/s40574-020-00253-6.

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Abstract This paper presents a unified approach, based on a geometrical method (see Faina in Eur J Oper Res 114:542–556, 1999; Eur J Oper Res 126:340–354, 2000), which reduces the general two and three dimensional cutting and packing type problems to a finite enumeration scheme.

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18

Valevskaya, L., and O. Sokolovskaya. "DETERMINATION OF PHYSICAL AND TECHNOLOGICAL PROPERTIES OF QUINO GRAIN - THE MAIN STAGES OF JUSTIFICATION OF STORAGE AND PROCESSING TECHNOLOGY." Grain Products and Mixed Fodder’s 21, no. 1 (2021): 4–8. http://dx.doi.org/10.15673/gpmf.v21i1.2089.

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The work is devoted to determining the physical and technological properties of quinoa grain. Quinoa is an unconventional crop for Ukraine, but experiments on its cultivation have been successfully completed in the Sumy region. Due to its unique chemical composition, quinoa is used in dietary and functional products.Quinoa contains about 20% protein, which makes it an excellent dietary supplement for people who do not eat animal products. The amino acid composition of quinoa proteins is very balanced and is characterized by a high content of such essential amino acids. Feature of the fatty aci

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19

Schurmann, Achill, and Frank Vallentin. "Computational Approaches to Lattice Packing and Covering Problems." Discrete & Computational Geometry 35, no. 1 (2005): 73–116. http://dx.doi.org/10.1007/s00454-005-1202-2.

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20

Mityushev, Vladimir, and Zhanat Zhunussova. "Optimal Random Packing of Spheres and Extremal Effective Conductivity." Symmetry 13, no. 6 (2021): 1063. http://dx.doi.org/10.3390/sym13061063.

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A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delau

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21

Hasanov, Ilman, Ibrahim Abbasov, and Nurlan Gurbanov. "Stress-Deformed State of a Packing Ring with Eccentric Holes." Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences. 74, no. 4 (2020): 287–92. http://dx.doi.org/10.2478/prolas-2020-0044.

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AbstractCurrently, various variants of physical and geometrical non-linear calculation of anisotropic bodies have been developed. In spite of the large and increasing number of studies on the theory of shells there are still many unsufficiently developed problems important both in scientific and applied fields, for example, development of practically convenient methods for calculating of anisotropic sealing composite materials weakened by eccentric holes under the influence of local loadings. Stress-deformed state of a packing ring with eccentric holes of sealing materials was studied. In comp

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22

Dubejko, T. "Discrete Solutions of Dirichlet Problems, Finite Volumes, and Circle Packings." Discrete & Computational Geometry 22, no. 1 (1999): 19–39. http://dx.doi.org/10.1007/pl00009447.

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23

Xie, Kuo Jun, Chang Shun Jiang, Lin Zhu, and Hai Feng Xu. "Thermal Stress Analysis of MCM Package Using Diamond Material." Key Engineering Materials 353-358 (September 2007): 2904–7. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.2904.

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With the increasing of packaging integration the power and the quantity of heat of integrate circuit will increase, it will bring more and more temperature distributions and problems about thermal stresses in package. In this paper a finite element thermal stress model of substrate-adhesive-chip is established, thermal stress distribution of substrate-chip interfaces and the affects of geometrical structure on thermal stresses are analyzed by finite element method, especially discuss interfacial thermal stresses distributions on chip-adhesive interface and adhesinve-substrate interface.

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24

Huang, Lei, Shibin Shen, Fei Xie, Jing Zhao, Jianing Han, and Kai Feng. "A Novel Multi-Pattern Solder Joint Simultaneous Segmentation Algorithm for PCB Selective Packaging Systems." International Journal of Pattern Recognition and Artificial Intelligence 33, no. 13 (2019): 2058005. http://dx.doi.org/10.1142/s0218001420580057.

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To prevent any negative electromagnetic influence of high-density integrated circuits, an insulation package needs to be specially designed to shield it. Aiming at the low efficiency and material waste in traditional packaging methods, a printed circuit board (PCB) selective packaging system based on a multi-pattern solder joint simultaneous segmentation algorithm and three-dimensional printing technology is introduced in this paper. Firstly, the structure of PCB selective packaging system is designed. Secondly, to solve the existing problems, such as multi-pattern solder joints which are loca

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25

Zarbov, Martin, David Brandon, Assaf Thon, and Nissim Cohen. "Engineering Tolerances & Performance in Applied EPD." Key Engineering Materials 314 (July 2006): 245–50. http://dx.doi.org/10.4028/www.scientific.net/kem.314.245.

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For the past 10 years Cerel has been engaged in the development of prototype, EPDprocessed, micro-components, primarily for the microelectronics industry. In this contribution we summarize some of the problems of integrating EPD into the production process, and discuss the parameters that need to be considered and controlled. Suitable dispersion media and additives can usually be found for powder of any chemical composition to be deposited by EPD, providing the particle size and size distribution, and their surface to volume ratio are suitable. So it is the geometrical requirements and the dim

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26

Yang, Taolue, Huaping Wang, and Xingzhe Wang. "Strain Transfer Characteristics of Multi-Layer Optical Fiber Sensors with Temperature-Dependent Properties at Low Temperature." Sensors 21, no. 2 (2021): 495. http://dx.doi.org/10.3390/s21020495.

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Optical fiber sensors have been potentially expected to apply in the extreme environment for their advantages of measurement in a large temperature range. The packaging measure which makes the strain sensing fiber survive in these harsh conditions will commonly introduce inevitable strain transfer errors. In this paper, the strain transfer characteristics of a multi-layer optical fiber sensing structure working at cryogenic environment with temperature gradients have been investigated theoretically. A generalized three-layer shear lag model incorporating with temperature-dependent properties o

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27

Kieu, Phan Thuy, Van Thanh Nguyen, Viet Tinh Nguyen, and Thanh Phong Ho. "A Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Combined Compromise Solution (CoCoSo) Algorithm in Distribution Center Location Selection: A Case Study in Agricultural Supply Chain." Axioms 10, no. 2 (2021): 53. http://dx.doi.org/10.3390/axioms10020053.

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Logistics is an important service sector, contributing to improving the competitiveness of the economy. Therefore, along with increasing the application of technology and effective business models, it is necessary to increase the connectivity of the infrastructure systems of industrial parks, roads, and seaports of regions and the country. Over the past decades, Vietnamese businesses have been step-by-step going through many stages from production, packaging, quality, hygiene, and safety to grasping new stages in the domestic and global value chain. In many industries, businesses are increasin

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28

Krauth, Werner, and Martin Loebl. "Jamming and Geometric Representations of Graphs." Electronic Journal of Combinatorics 13, no. 1 (2006). http://dx.doi.org/10.37236/1082.

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We expose a relationship between jamming and a generalization of Tutte's barycentric embedding. This provides a basis for the systematic treatment of jamming and maximal packing problems on two-dimensional surfaces.

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29

Peddada, Satya R. T., Kai A. James, and James T. Allison. "A Novel Two-Stage Design Framework for Two-Dimensional Spatial Packing of Interconnected Components." Journal of Mechanical Design 143, no. 3 (2020). http://dx.doi.org/10.1115/1.4048817.

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Abstract Packing and routing separately are each challenging NP-hard problems. Therefore, solving the coupled packing and routing problem simultaneously will require disruptive methods to better address pressing-related challenges, such as system volume reduction, interconnect length reduction, ensuring non-intersection, and physics (thermal, hydraulic, or electromagnetic) considerations. Here we present a novel two-stage sequential design framework to perform simultaneous physics-based packing and routing optimization. Stage 1 generates interference-free initial layouts that are fed to stage

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30

Chekanin, Vladislav. "Solving the Problem of Packing Objects of Complex Geometric Shape into a Container of Arbitrary Dimension." Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2, December 17, 2020, paper50–1—paper50–13. http://dx.doi.org/10.51130/graphicon-2020-2-3-50.

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The article is devoted to algorithms developed for solving the problem of placement orthogonal polyhedrons of arbitrary dimension into a container. To describe all free areas of a container of complex geometric shape is applied the developed model of potential containers. Algorithms for constructing orthogonal polyhedrons and their subsequent placement are presented. The decomposition algorithm intended to reduce the number of orthogonal objects forming an orthogonal polyhedron is described in detail. The proposed placement algorithm is based on the application of intersection operations to ob

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31

Balogh, József, Alexandr Kostochka, and Andrew Treglown. "On Perfect Packings in Dense Graphs." Electronic Journal of Combinatorics 20, no. 1 (2013). http://dx.doi.org/10.37236/3173.

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We say that a graph $G$ has a perfect $H$-packing if there exists a set of vertex-disjoint copies of $H$ which cover all the vertices in $G$. We consider various problems concerning perfect $H$-packings: Given $n, r , D \in \mathbb N$, we characterise the edge density threshold that ensures a perfect $K_r$-packing in any graph $G$ on $n$ vertices and with minimum degree $\delta (G) \geq D$. We also give two conjectures concerning degree sequence conditions which force a graph to contain a perfect $H$-packing. Other related embedding problems are also considered. Indeed, we give a structural re

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32

Burstein, Alexander, Peter Hästö, and Toufik Mansour. "Packing Patterns into Words." Electronic Journal of Combinatorics 9, no. 2 (2003). http://dx.doi.org/10.37236/1692.

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In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns.

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33

Zhang, Yuqin, and Yonghui Fan. "Packing and Covering a Unit Equilateral Triangle with Equilateral Triangles." Electronic Journal of Combinatorics 12, no. 1 (2005). http://dx.doi.org/10.37236/1952.

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Packing and covering are elementary but very important in combinatorial geometry, they have great practical and theoretical significance. In this paper, we discuss a problem on packing and covering a unit equilateral triangle with smaller triangles which is originated from one of Erdős' favorite problems.

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34

Quistorff, Jörn. "A Survey on Packing and Covering Problems in the Hamming Permutation Space." Electronic Journal of Combinatorics 13, no. 1 (2006). http://dx.doi.org/10.37236/1161.

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35

Hästö, Peter A. "The Packing Density of Other Layered Permutations." Electronic Journal of Combinatorics 9, no. 2 (2002). http://dx.doi.org/10.37236/1673.

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In this paper the packing density of various layered permutations is calculated, thus solving some problems suggested by Albert, Atkinson, Handley, Holton $\&$ Stromquist [Electron. J. Combin. 9 (2002), $\#$R5]. Specifically, the density is found for layered permutations of type $[m_1, \ldots, m_r]$ when $\log(r+1)\le \min\{ m_i\}$. It is also shown how to derive good estimates for the packing density of permutations of type $[k,1,k]$ when $k\ge 3$. Both results are based on establishing the number of layers in near optimal permutations using a layer-merging technique.

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36

Lu, Linyuan, and László Székely. "Using Lovász Local Lemma in the Space of Random Injections." Electronic Journal of Combinatorics 14, no. 1 (2007). http://dx.doi.org/10.37236/981.

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The Lovász Local Lemma is known to have an extension for cases where independence is missing but negative dependencies are under control. We show that this is often the case for random injections, and we provide easy-to-check conditions for the non-trivial task of verifying a negative dependency graph for random injections. As an application, we prove existence results for hypergraph packing and Turán type extremal problems. A more surprising application is that tight asymptotic lower bounds can be obtained for asymptotic enumeration problems using the Lovász Local Lemma.

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37

Aronov, Boris, Vida Dujmović, Pat Morin, Aurélien Ooms, and Luı́s Fernando Schultz Xavier da Silveira. "More Turán-Type Theorems for Triangles in Convex Point Sets." Electronic Journal of Combinatorics 26, no. 1 (2019). http://dx.doi.org/10.37236/7224.

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We study the following family of problems: Given a set of $n$ points in convex position, what is the maximum number triangles one can create having these points as vertices while avoiding certain sets of forbidden configurations. As forbidden configurations we consider all 8 ways in which a pair of triangles in such a point set can interact. This leads to 256 extremal Turán-type questions. We give nearly tight (within a $\log n$ factor) bounds for 248 of these questions and show that the remaining 8 questions are all asymptotically equivalent to Stein's longstanding tripod packing problem.

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38

Pollicott, Mark, and Mariusz Urbanski. "Asymptotic Counting in Conformal Dynamical Systems." Memoirs of the American Mathematical Society 271, no. 1327 (2021). http://dx.doi.org/10.1090/memo/1327.

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In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We deal with two classes of such systems: attracting and parabolic. The latter being treated by means of the former. We prove fairly complete asymptotic counting results for multipliers and diameters associated with preimages or periodic orbits ordered by a natural geometric weighting. We also prove the corresponding Central Limit Theorems describing the further features of the distribution of their weights. These results have direct applica

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39

Schwartz, Lawrence M. "Transport Properties of Granular Porous Media." MRS Proceedings 195 (1990). http://dx.doi.org/10.1557/proc-195-537.

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ABSTRACTThis paper is concerned with two related problems: (1) the construction of geometrical models of porous media relevant to granular composites and (2) the description of transport processes in these model systems. We will show that a variety of interesting porous media can be generated by the packing and subsequent modification of spherical grains. This modification may involve a change in either the grain's size, shape, or both. Steady state transport processes such as the flow of electrical current or viscous fluids are controlled by the distribution of pore throat sizes and, within t

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40

Martínez-Bernal, José, Edwin O'Shea, and Rafael H. Villarreal. "Ehrhart Clutters: Regularity and Max-Flow Min-Cut." Electronic Journal of Combinatorics 17, no. 1 (2010). http://dx.doi.org/10.37236/324.

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If $\mathcal{C}$ is a clutter with $n$ vertices and $q$ edges whose clutter matrix has column vectors ${\mathcal A} = \{v_1, \ldots, v_q\}$, we call $\mathcal{C}$ an Ehrhart clutter if $\{(v_1,1),\ldots,(v_q,1)\} \subset \{ 0,1 \}^{n+1}$ is a Hilbert basis. Letting $A(P)$ be the Ehrhart ring of $P={\rm conv}(\mathcal{A})$, we are able to show that if $\mathcal{C}$ is a uniform unmixed MFMC clutter, then $\mathcal{C}$ is an Ehrhart clutter and in this case we provide sharp upper bounds on the Castelnuovo-Mumford regularity and the $a$-invariant of $A(P)$. Motivated by the Conforti-Cornuéjols co

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