Some reformulations for the quadratic assignment problem

Kombinatorisk optimering handlar om att hitta en bra eller rent av den bästa möjliga lösningen från ett känt antal lösningar eller kombinationer. Ofta är antalet lösningar så enormt att en genomgång av alla olika lösningar inte är möjlig. En av huvudorsakerna till att det forskas inom kombinatorisk optimering är att liknande frågeställningar eller problem uppkommer inom så många olika områden. Påståendet stämmer speciellt bra för kvadratiska tilldelningsproblem(eng. Quadratic Assignment Problem). Sådana problem uppstår då man försöker beskriva en stor mängd tillämpade frågeställningar. Vilken gate skall väljas för flygen på större flygplatser för att minimera den totala väg människorna behöver gå och bagaget förflyttas? Var skall olika avdelningar på en fabrik placeras för att minimera materialförflyttningar mellan avdelningarna? Hur ser ett optimalt tangentbord ut för olika språk? Var skall komponenterna placeras på ett kretskort? De här är alla frågor som kan besvaras genom att lösa kvadratiska tilldelningsproblem. Kvadratiska tilldelningsproblem är dock mycket svåra att lösa. Det beror på att problemet i den standardform det matematiskt formuleras i huvudsak består av produkter av binära variabler. I denna avhandling har problemet omformulerats till en linjär diskret form som innehåller färre variabler. Med omformuleringen har bland annat flera tidigare olösta kvadratiska tilldelningsproblem kunnat lösas till globalt optimum, den bästa möjliga lösningen, för första gången någonsin.

NIR-Vis Up-Conversion Luminescence in the Yb3+,Er3+ Doped Y2O2S, ZrO2, and NaYF4 Nanomaterials

Since the discovery of the up-conversion phenomenon, there has been an ever increasing interest in up-converting phosphors in which the absorption of two or more low energy photons is followed by emission of a higher energy photon. Most up-conversion luminescence materials operate by using a combination of a trivalent rare earth (lanthanide) sensitizer (e.g. Yb or Er) and an activator (e.g. Er, Ho, Tm or Pr) ion in a crystal lattice. Up-converting phosphors have a variety of potential applications as lasers and displays as well as inks for security printing (e.g. bank notes and bonds). One of the most sophisticated applications of lanthanide up-conversion luminescence is probably in medical diagnostics. However, there are some major problems in the use of photoluminescence based on the direct UV excitation in immunoassays. Human blood absorbs strongly UV radiation as well as the emission of the phosphor in the visible. A promising way to overcome the problems arising from the blood absorption is to use a long wavelength excitation and benefit from the up-conversion luminescence. Since there is practically no absorption by the whole-blood in the near IR region, it has no capability for up-conversion in the excitation wavelength region of the conventional up-converting phosphor based on the Yb3+ (sensitizer) and Er3+ (activator) combination. The aim of this work was to prepare nanocrystalline materials with high red (and green) up-conversion luminescence efficiency for use in quantitative whole-blood immunoassays. For coupling to biological compounds, nanometer-sized (crystallite size below 50 nm) up-converting phosphor particles are required. The nanocrystalline ZrO2:Yb3+,Er3+, Y2O2S:Yb3+,Er3+, NaYF4:Yb3+,Er3+ and NaRF4-NaR’F4 (R: Y, Yb, Er) materials, prepared with the combustion, sol-gel, flux, co-precipitation and solvothermal synthesis, were studied using the thermal analysis, FT-IR spectroscopy, transmission electron microscopy, EDX spectroscopy, XANES/EXAFS measurements, absorption spectroscopy, X-ray powder diffraction, as well as up-conversion and thermoluminescence spectroscopies. The effect of the impurities of the phosphors, crystallite size, as well as the crystal structure on the up-conversion luminescence intensity was analyzed. Finally, a new phenomenon, persistent up-conversion luminescence was introduced and discussed. For efficient use in bioassays, more work is needed to yield nanomaterials with smaller and more uniform crystallite sizes. Surface modifications need to be studied to improve the dispersion in water. On the other hand, further work must be carried out to optimize the persistent up-conversion luminescence of the nanomaterials to allow for their use as efficient immunoassay nanomaterials combining the advantages of both up-conversion and persistent luminescence.

The effect of porphyrins on normal and transformed mouse cell lines in the presence of visible light

Photodynamic therapy consists of the uptake of a photosensitizing dye, often a porphyrin, by tumor tissue and subsequent irradiation of the tumor with visible light of an appropriate wavelength matched to the absorption spectrum of the photosensitizing dye. This class of molecules produces reactive oxygen species when activated by light, resulting in a direct or indirect cytotoxic effect on the target cells. Photodynamic therapy has been used in the treatment of cancer but the technology has a potential for the treatment of several disease conditions mainly because of its selectivity. However, it is not clear why the porphyrins are retained preferentially by abnormal tissue. This paper describes a study of the effect of the association of porphyrin and visible light on two mouse fibroblast cell lines: A31, normal cells and B61, an EJ-ras transformed variant of A31. Two water-soluble porphyrins were used, a positively charged one, tetra(N-methyl-4-pyridyl)porphyrin chloride, and a negatively charged one, tetra(4-sulfonatophenyl)porphyrin-Na salt (TPPS4) in order to assess the effect on cell survival. The results suggest that the B61 cell line is more sensitive to incubation with the anionic porphyrin (TPPS4) followed by light irradiation and that the anionic porphyrin is more efficient in killing the cells than the cationic porphyrin.

Low-intensity red and infrared laser effects at high fluences on Escherichia coli cultures

Semiconductor laser devices are readily available and practical radiation sources providing wavelength tenability and high monochromaticity. Low-intensity red and near-infrared lasers are considered safe for use in clinical applications. However, adverse effects can occur via free radical generation, and the biological effects of these lasers from unusually high fluences or high doses have not yet been evaluated. Here, we evaluated the survival, filamentation induction and morphology of Escherichia coli cells deficient in repair of oxidative DNA lesions when exposed to low-intensity red and infrared lasers at unusually high fluences. Cultures of wild-type (AB1157), endonuclease III-deficient (JW1625-1), and endonuclease IV-deficient (JW2146-1) E. coli, in exponential and stationary growth phases, were exposed to red and infrared lasers (0, 250, 500, and 1000 J/cm2) to evaluate their survival rates, filamentation phenotype induction and cell morphologies. The results showed that low-intensity red and infrared lasers at high fluences are lethal, induce a filamentation phenotype, and alter the morphology of the E. coli cells. Low-intensity red and infrared lasers have potential to induce adverse effects on cells, whether used at unusually high fluences, or at high doses. Hence, there is a need to reinforce the importance of accurate dosimetry in therapeutic protocols.

Benchmark of routing protocols regarding green considerations

In Mobile Ad-hoc Networks (MANET) the participating nodes have several roles such as sender, receiver and router. Hence there is a lot of energy consumed by the nodes for the normal working of the network since each node has many different roles. Also in MANET the nodes keep moving constantly and this in turn consumes a lot of energy. Since battery capacity of these nodes is limited it fails to fulfil the high demand of energy. The scarcity of energy makes the energy conservation in mobile ad-hoc networks an important concern. There is several research carried out on the energy consumption of mobile ad-hoc networks these days. Some of this research suggests sleep mode, transmission power control, load balancing etc. In this thesis, we are comparing various proposed energy efficient models for some of the ad-hoc protocols. We compare different energy efficient models for Optimised Linked State Algorithm (OLSR) and Ad-hoc On Demand Distance Vector (AODV). The routing protocols are compared for different parameters such as average remaining energy, number of nodes alive, payload data received and performance with different mobility speed. The simulation results helps in benchmarking the various energy efficient routing models for OLSR and AODV protocols. The benchmarking of the routing protocols can be based on many factors but this thesis concentrates on benchmarking the MANET routing protocols mainly based on the energy efficiency and increased network lifetime.

Helsinki hub – new traffic flows and business networks

This thesis is the Logistics Development Forum's assignment and the work dealing with the development of the Port of Helsinki as part of Helsinki hub. The Forum aims to develop logistics efficiency through public-private co-operation and development of the port is clearly dependent on both factors. Freight volumes in the Port of Helsinki are the biggest single factor in hub and, therefore, the role of the port of the entire hub development is strong. The aim is to look at how the port will develop as a result of changes in the foreign trade of Finland and the Northern European logistics trends in 25 years time period. Work includes the current state analysis and scenario work. The analyses are intended to find out, which trends are the most important in the port volume development. The change and effect of trends is examined through scenarios based on current state. Based on the work, the structure of Finnish export industry and international demand are in the key role in the port volume development. There is significant difference between demands of Finnish exporting products in different export markets and the development between the markets has different impacts on the port volumes by mass and cargo type. On the other hand, the Finnish economy is stuck in a prolonged recession and competition between ports has become a significant factor in the individual port's volume development. Ecological valuesand regulations have changed the competitive landscape and maritime transport emissions reductions has become an important competitive factor for short routes in the Baltic Sea, such as in the link between Helsinki and Tallinn.

Spectral retinal image processing and analysis for ophthalmology

Diabetic retinopathy, age-related macular degeneration and glaucoma are the leading causes of blindness worldwide. Automatic methods for diagnosis exist, but their performance is limited by the quality of the data. Spectral retinal images provide a significantly better representation of the colour information than common grayscale or red-green-blue retinal imaging, having the potential to improve the performance of automatic diagnosis methods. This work studies the image processing techniques required for composing spectral retinal images with accurate reflection spectra, including wavelength channel image registration, spectral and spatial calibration, illumination correction, and the estimation of depth information from image disparities. The composition of a spectral retinal image database of patients with diabetic retinopathy is described. The database includes gold standards for a number of pathologies and retinal structures, marked by two expert ophthalmologists. The diagnostic applications of the reflectance spectra are studied using supervised classifiers for lesion detection. In addition, inversion of a model of light transport is used to estimate histological parameters from the reflectance spectra. Experimental results suggest that the methods for composing, calibrating and postprocessing spectral images presented in this work can be used to improve the quality of the spectral data. The experiments on the direct and indirect use of the data show the diagnostic potential of spectral retinal data over standard retinal images. The use of spectral data could improve automatic and semi-automated diagnostics for the screening of retinal diseases, for the quantitative detection of retinal changes for follow-up, clinically relevant end-points for clinical studies and development of new therapeutic modalities.

The infared optical properties of Sr2RuO4 and SmTiO3 including an object-oriented resistivity interface /

The perovskite crystal structure is host to many different materials from insulating to superconducting providing a diverse range of intrinsic character and complexity. A better fundamental description of these materials in terms of their electronic, optical and magnetic properties undoubtedly precedes an effective realization of their application potential. SmTiOa, a distorted perovskite has a strongly localized electronic structure and undergoes an antiferromagnetic transition at 50 K in its nominally stoichiometric form. Sr2Ru04 is a layered perovskite superconductor (ie. Tc % 1 K) bearing the same structure as the high-tem|>erature superconductor La2_xSrrCu04. Polarized reflectance measurements were carried out on both of these materials revealing several interesting features in the far-infrared range of the spectrum. In the case of SmTiOa, although insulating, evidence indicates the presence of a finite background optical conductivity. As the temperature is lowered through the ordering temperature a resonance feature appears to narrow and strengthen near 120 cm~^ A nearby phonon mode appears to also couple to this magnetic transition as revealed by a growing asymmetry in the optica] conductivity. Experiments on a doped sample with a greater itinerant character and lower Neel temperature = 40 K also indicate the presence of this strongly temperature dependent mode even at twice the ordering temperature. Although the mode appears to be sensitive to the magnetic transition it is unclear whether a magnon assignment is appropriate. At very least, evidence suggests an interesting interaction between magnetic and electronic excitations. Although Sr2Ru04 is highly anisotropic it is metallic in three-dimensions at low temperatures and reveals its coherent transport in an inter-plane Drude-like component to the highest temperatures measured (ie. 90 K). An extended Drude analysis is used to probe the frequency dependent scattering character revealing a peak in both the mass enhancement and scattering rate near 80 cm~* and 100 cm~* respectively. All of these experimental observations appear relatively consistent with a Fermi-liquid picture of charge transport. To supplement the optical measurements a resistivity station was set up with an event driven object oriented user interface. The program controls a Keithley Current Source, HP Nano-Voltmeter and Switching Unit as well as a LakeShore Temperature Controller in order to obtain a plot of the Resistivity as a function of temperature. The system allows for resistivity measurements ranging from 4 K to 290 K using an external probe or between 0.4 K to 295 K using a Helium - 3 Cryostat. Several materials of known resistivity have confirmed the system to be robust and capable of measuring metallic samples distinguishing features of several fiQ-cm.

The normal co-ordinate analysis, vibrational spectra and theoretical infrared intensities of some thiocarbonyl halide molecules /

TITLE: The normal co-ordinate analysis, vibrational spectra and theoretical infrared intensities of some thiocarbonyl halides. AUTHOR: J. L. Brema SUPERVISOR: Dr. D. C. Moule NUMBER OF PAGES: 89 ABSTRACT: The vibrational assignment of the five-in-plane fundamental modes of CSClBr has been made on the basis of infrared gas phase and liquid Raman spectral analyses to supplement our earlier vibrational studies. Even though the one out-of-plane fundamental was not observed spectroscopically an attempt has been made to predict its frequency. The vibrational spectra contained impurity bands and the CSClBr assignment was made only after a thorough analysis of the impurities themselves. A normal co-ordinate analysis calculation was performed assuming a Urey-Bradley force field. This calculation yielded the fundamental frequencies in good agreement with those observed after refinement of the originally transferred force constants. The theoretical frequencies are the eigenvalues of the secular equation and the calculation also gave the corresponding eigenvectors in the form of the very important LLj matrix. The [l] matrix is the transfoirmation between internal co-ordinates and normal co-ordinates and it is essential for Franck-Condon calculations on electronically excited molecules and for infrared Integrated band intensity studies. Using a self-consistent molecular orbital calculation termed "complete neglect of differential overlap" (CNDO/2) , theoretical values of equilibrium bond lengths and angleswere calcuted for a series of carbonyl and thlocarbonyl molecules. From these calculations valence force field force constants were also determined but with limited success. With the CNIX)/2 method theoretical dipole moment derivatives with respect to symmetrized internal co-ordinates were calculated and the results should be useful in a correlation with experimentally determined values.

Confocal and two-photon microscopy : image enhancement /

Confocal and two-photon microcopy have become essential tools in biological research and today many investigations are not possible without their help. The valuable advantage that these two techniques offer is the ability of optical sectioning. Optical sectioning makes it possible to obtain 3D visuahzation of the structiu-es, and hence, valuable information of the structural relationships, the geometrical, and the morphological aspects of the specimen. The achievable lateral and axial resolutions by confocal and two-photon microscopy, similar to other optical imaging systems, are both defined by the diffraction theorem. Any aberration and imperfection present during the imaging results in broadening of the calculated theoretical resolution, blurring, geometrical distortions in the acquired images that interfere with the analysis of the structures, and lower the collected fluorescence from the specimen. The aberrations may have different causes and they can be classified by their sources such as specimen-induced aberrations, optics-induced aberrations, illumination aberrations, and misalignment aberrations. This thesis presents an investigation and study of image enhancement. The goal of this thesis was approached in two different directions. Initially, we investigated the sources of the imperfections. We propose methods to eliminate or minimize aberrations introduced during the image acquisition by optimizing the acquisition conditions. The impact on the resolution as a result of using a coverslip the thickness of which is mismatched with the one that the objective lens is designed for was shown and a novel technique was introduced in order to define the proper value on the correction collar of the lens. The amoimt of spherical aberration with regard to t he numerical aperture of the objective lens was investigated and it was shown that, based on the purpose of our imaging tasks, different numerical apertures must be used. The deformed beam cross section of the single-photon excitation source was corrected and the enhancement of the resolution and image quaUty was shown. Furthermore, the dependency of the scattered light on the excitation wavelength was shown empirically. In the second part, we continued the study of the image enhancement process by deconvolution techniques. Although deconvolution algorithms are used widely to improve the quality of the images, how well a deconvolution algorithm responds highly depends on the point spread function (PSF) of the imaging system applied to the algorithm and the level of its accuracy. We investigated approaches that can be done in order to obtain more precise PSF. Novel methods to improve the pattern of the PSF and reduce the noise are proposed. Furthermore, multiple soiu'ces to extract the PSFs of the imaging system are introduced and the empirical deconvolution results by using each of these PSFs are compared together. The results confirm that a greater improvement attained by applying the in situ PSF during the deconvolution process.

The electronic spectra and the determination of the excited state geometry of 3A" propynal /|nby Chhiu-Tsu Lin. -- 260 St. Catharines, Ont. : [s. n.],

Impurity free eluission spectra of HCCCHO and DCCCHO have been rephotographed using the electronic-energy-exchange method with benzene as a carrier gas. The near ultraviolet spectra of ReeCHO and DCCCHO were photographed in a sorption under conditions of high resolution with absorption path lengths up to 100 meters. The emission and absorption spectra of Propynal resulting from 3 n 1 t 1\ - A excitation has been reanalyzed in som.e detail. Botrl of the eH out-of-plane wagging modes were found to have negative anharmonicity. A barrier height of 56.8/0.0 cm- 1 and a nonplanar oft , , equilibrium angle of 17 3 /30 are calculated for the V 10/ lJ 11 modes. The in-plane and out-of-plane v1. brational modes in the 3A." and 1a~. ' elec ronic states of Propynal were subjected to a normal coordinate treatment in the approximat :on of tIle Urey-Bradley force field. From the relative oscillator strengths of the trans1·t1·0ns connect i ng t he v ibrat1•0n1ess lA' , state and t,he V1· bron1·C 3· if levels of the A state, the differences in equilibrium configuration were evaluated from an approximate Franck-Condon analysis based on the ground state normal coordinates. As this treatment gave 512 possible geometrical structures for the upper state, it 4 was necessary to resort to a comparison of the observed and calculated moments of inertia along with chemical intuition to isolate the structure. A test of the correctness of the calculated structure change and the vibrational assignment was raade by evaluating the intensities of the inplane and out-oi-plane fundarnental, sequence, and cross sequellce transitions y the exact Franck-Condon method.

The measurement of the optical absorption cross section of photosystem 1 and photosystem 2 from whole live cells of porphyridium cruentum, in light state 1 and light state 2

The optical cross section of PS I in whole cells of Porphyridium cruentum (UTEX 161), held in either state 1 or state 2, was determined by measuring the change in absorbance at 820nm, an indication of P700+; the X-section of PS2 was determined by measuring the variable fluorescence, (Fv-Fo)/Fo, from PS2. Both cross-sections were 7 determined by fitting Poisson distribution equations to the light saturation curves obtained with single turnover laser flashes which varied in intensity from zero to a level where maximum yield occurred. Flash wavelengths of 574nm, 626nm, and 668nm were used, energy absorbed by PBS, by PBS and chla, and by chla respectively. There were two populations of both PSi and PS2. A fraction of PSi is associated with PBS, and a fraction of PS2 is free from PBS. On the transition S1->S2, only with PBS-absorbed energy (574nm) did the average X-section of PSi increase (27%), and that of PS2 decrease (40%). The fraction of PSi associated with PBS decreased, from 0.65 to 0.35, and the Xsection of this associated PS 1 increased, from 135±65 A2 to 400±300A2. The cross section of PS2 associated with PBS decreased from 150±50 A2 to 85±45 A2, but the fraction of PS2 associated with PBS, approximately 0.75, did not change significantly. The increase in PSi cross section could not be completely accounted for by postulating that several PSi are associated with a single PBS and that in the transition to state2, fewer PSi share the same number of PBS, resulting in a larger X-section. It is postulated that small changes occur in the attachment of PS2 to PBS causing energy to be diverted to the attached PSi. These experiments support neither the mobile-PBS model of state transitions nor that of spillover. From cross section changes there was no evidence of energy transfer from PS2 to PSi with 668nm light. The decrease in PS2 fluorescence which occurred at this wavelength cannot be explained by energy transfer; another explanation must be sought. No explanation was found for an observed decrease in PSi yield at high flash intensities.

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.

Characterization of the state transition in the cyanobacterium synechococcus sp. 7002 and a phycobilisome-less Mutant

ABSTRACT Photosynthetic state transitions were investigated in the cyanobacterium Synechococcus sp. PCC 7002 in both wild-type cells and mutant cells lacking phycobilisomes. Preillumination in the presence of DCMU (3(3,4 dichlorophenyl) 1,1 dimethyl urea) induced state 1 and dark adaptation induced state 2 in both wild-type and mutant cells as determined by 77K fluorescence emission spectroscopy. Light-induced transitions were observed in the wildtype after preferential excitation of phycocyanin (state 2) or preferential excitation of chlorophyll .a. (state 1). The state 1 and 2 transitions in the wild-type had half-times of approximately 10 seconds. Cytochrome f and P-700 oxidation kinetics could not be correlated with any current state transition model as cells in state 1 showed faster oxidation kinetics regardless of excitation wavelength. Light-induced transitions were also observed in the phycobilisomeless mutant after preferential excitation of short wavelength chlorophyll !l. (state 2) or carotenoids and long wavelength chlorophyll it (state 1). One-dimensional electrophoresis revealed no significant differences in phosphorylation patterns of resolved proteins between wild-type cells in state 1 and state 2. It is concluded that the mechanism of the light state transition in cyanobacteria does not require the presence of the phycobilisome. The results contradict proposed models for the state transition which require an active role for the phycobilisome.

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.