Experimental mole fraction solubilities of several carboxylic acids (2-methoxybenzoic acid, 4-methoxybenzoic acid, 4-nitrobenzoic acid, 4-chloro-3-nitrobenzoic acid, 2-chloro-5-nitrobenzoic acid,2-methylbenzoic acid and ibuprofen) and 9-fluorenone, thianthrene and xanthene were measured in a wide range of solvents of varying polarity and hydrogen-bonding characteristics. Results of these measurements were used to calculate gas-to-organic solvent and water-to-organic solvent solubility ratios, which were then substituted into known Abraham process partitioning correlations. The molecular solute descriptors that were obtained as the result of these computations described the measured solubility data to within an average absolute deviation of 0.2 log units. The calculated solute descriptors also enable one to estimate many chemically, biologically and pharmaceutically important properties for the ten solutes studied using published mathematical correlations.

Nesta dissertação estudamos --- do ponto de vista algorítmico --- o seguinte problema, conhecido como problema da partição conexa balanceada. Dado um grafo conexo G com pesos atribuídos a seus vértices, e um inteiro q >= 2, encontrar uma partição dos vértices de G em q classes, de forma que cada classe da partição induza um grafo conexo e que, ao considerar as somas dos pesos dos vértices de cada classe, a menor das somas seja o maior possível. Em outras palavras, o objetivo é encontrar q classes cujos pesos sejam tão balanceados quanto possível. Sabe-se que este problema é NP-difícil. Mencionamos alguns resultados sobre complexidade computacional e algoritmos que são conhecidos para este problema. Apresentamos algumas heurísticas que desenvolvemos, todas elas baseadas no uso do algoritmo polinomial para árvores, devido a Perl e Schach, que apresentamos com detalhe. Implementamos quatro heurísticas e um algoritmo de 3/4-aproximação conhecido para o caso q=2. Exibimos os resultados obtidos com os vários testes computacionais conduzidos com instâncias aleatórias, com grafos de diferentes pesos e densidades. Os resultados computacionais indicam que o desempenho dessas heurísticas --- todas elas polinomiais --- é bem satisfatório. No caso especial em que q=2, observamos que a heurística mais onerosa sistematicamente produziu soluções melhores ou iguais às do algoritmo de aproximação / In this dissertation we study algorithmic aspects of the following problem, known as the balanced connected partition. Given a connected graph G with weights defined on its vertices, and an integer q >= 2, find a partition of the vertices of G into q classes such that each class induces a connected graph, and furthermore, when we consider the sum of the weights of the vertices in each class, the smallest sum is as large as possible. In other words, the q classes must have weights that are as balanced as possible. This problem is known to be NP-hard. We mention some computational complexity and algorithmic results that are known for this problem. We present some heuristics that we designed, all of them based on the use of the polynomial algorithm for trees, due to Perl and Schach, which we show in detail. We implemented four heuristics and a 3/4-approximation algorithm that is known for q=2. We run tests on many random instances, of graphs with different weights and densities. The computational results indicate that the performance of these heuristics --- all of polynomial time complexity --- are very satisfactory. For q=2, we observed that the most expensive heuristic produced solutions with values which are systematically better or equal to those produced by the approximation algorithm.

[EN] The main objective of this Thesis was to study the energy metabolism in small ruminants under different nutrition sceneries. As methodology we utilized indirect calorimetry instead of direct calorimetry or feeding trials. Within indirect calorimetry we worked with a portable open circuit gas exchange system with a head hood. This open circuit respiration system permitted completed the whole energy balance and evaluate the efficiency of utilization of the energy of the diet for different physiological circumstances as milk production in dairy goats or maintenance in sheep. Besides, we could quantify in each trial some of the wastes related to environmental pollution as CH4 emissions and excretion of nitrogen in feces and urine. In this thesis three experiments were designed, two in dairy goats and other in sheep as we described below. In the first experiment, digestibility, energy balance, carbon and nitrogen balance, milk performance, rumen parameters and milk fatty acids and metabolites were obtained. Metabolic cages and open circuit indirect calorimetry system were the methods applied. Treatments consist in two mixed diets with alfalfa as forage. Within the concentrate, oat grain was replaced with rice bran. No significant differences were found for metabolizable energy intake (MEI), 1254kJ/kg of BW0.75 on average, and heat production (HP); 640 kJ/kg of BW0.75 on average. No differences were obtained for milk production (2.2 kg/d on average) and milk fat was greater in the rice bran diet (6.9% vs. 5.3% for rice bran and oat diets, respectively). Energy balance was positive and milk metabolites correlated these found. Regards to CH4 emissions, determined in vivo by gas exchange indirect calorimetry, goats fed the rice bran significantly reduced methane production (23.2 g/d vs 30.1 g/d). In the second experiment, we also used two types of diets, but in this case we substituted the forage and maintained the same concentrate; in one of the diets a grass (Maralfafa [Pennisetum sp.]- M diet) was used as forage and in the other an extensively used leguminous (Alfalfa [Medicago sativa]- A diet). Methods and analysis were the same that in Experiment 1, and here we include metabolites in urine and blood plasma. The dry matter intake was higher for diet A (1.8 vs 1.6 kg/d, respectively) and digestibility coefficients were higher for diet M. However, no significant differences were shown in MEI (1089 kJ/kg of BW0.75, on average) and HP (639 kJ/kg of BW0.75on average). Higher milk yield was observed in A diet than M diet (1.8 vs. 1.7 kg/d, respectively) and metabolites in urine, plasma and milk indicated better use of diet A than M, while no differences in milk composition were found (5% of fat and 4.3% of protein). Methane production was higher for A diet (28.5 g/d) than M diet (25.9 g/d), although these differences were not statistically significant. In the third experiment, energy partition was compared in two sheep breeds (Manchega vs. Guirra) fed above maintenance. We fed again with mixed diets and metabolic cages, indirect calorimetry, nitrogen balance and integral calculus were the tools used for these energy partitioning approach. An approximation of division of heat production was done. ME for maintenence was estimated at 354 kJ/kg of BW0.75and day, on average for the two breeds. Basal metabolic rate was different between breeds; 270 vs. 247 kJ/kg of BW0.75for Guirra and Manchega, respectively. / [ES] El objetivo principal de esta tesis fue estudiar el metabolismo energético en pequeños rumiantes bajo diferentes escenarios de nutrición. Como metodología se utilizó la calorimetría indirecta en vez de calorimetría directa o pruebas de alimentación. Dentro de la calorimetría indirecta trabajamos con un sistema portátil de circuito abierto de intercambio de gases con una "urna" (Heat hood). Este sistema de circuito abierto de respiración nos permitió completar todo el balance energético y evaluar la eficiencia de la utilización de la energía de la dieta para diferentes estados fisiológicos como producción de leche en cabras u oveja en mantenimiento. Además fue posible cuantificar en cada ensayo algunas perdidas relacionadas con la contaminación ambiental como emisiones de CH4 y la excreción de nitrógeno en heces y orina. En esta tesis se diseñaron tres experimentos, dos en cabras en lactación y otro en ovejas como describimos a continuación. En el primer experimento se han determinado, digestibilidad, balance energético, balance carbono nitrógeno, producción de leche, parámetros ruminales, ácidos grasos y metabolitos en leche. Jaulas metabólicas y un sistema de circuito abierto de calorimetría indirecta fue el método aplicado. Los tratamientos consistieron en dos dietas mixtas con alfalfa como forraje y dentro del concentrado el grano de avena fue reemplazado por cilindro de arroz. No se encontraron diferencias significativas en la energía metabolizable ingerida (MEI) de 1254 kJ/kg PV0.75 en promedio y una producción de calor (HP) de 640 kJ/kg PV0.75 en promedio. La producción de leche no presentó diferencias significativas entre las dos dietas, (2,2 kg/den promedio), la grasa de la leche fue mayor en la dieta de cilindro de arroz (6,9% vs. 5,3% para cilindro de arroz y avena respectivamente). El balance energético fue positivo y correlacionado a los metabolitos en leche determinados. En cuanto a las emisiones de CH4, determinadas en vivo mediante el intercambio de gases por calorimetría indirecta, las cabras alimentadas con el subproducto redujeron significativamente la producción de metano (23,2 g / d vs 30,1 g / d.). En el segundo experimento, también utilizamos dos tipos de dietas, pero en este caso sustituimos los forrajes y mantuvimos el mismo pienso; en una de las dietas se utilizó como forraje una gramínea (Maralfafa [Pennisetum sp.] - dieta M) y en el otro una leguminosa de uso extendido (Alfalfa [Medicago sativa] - dieta A). Los métodos de análisis y análisis fueron los mismos que los utilizados en el Experimento 1, y se incluyeron además análisis de metabolitos en orina y plasma. La materia seca ingerida fue mayor para dieta A (1,8 vs 1,6 kg/d, respectivamente), los coeficientes de digestibilidad fueron mayores para la dieta M. Sin embargo, no se encontraron diferencias significativas en MEI (1089 kJ/kg PV0.75, en promedio) y HP 639 kJ/kg PV0.75, en promedio). La producción de leche fue mayor en la dieta A que la dieta M, (1,8 vs. 1,7 kg/d, respectively) y los metabolitos en orina, plasma y leche indican un mejor aprovechamiento de la dieta A. No se presentaron diferencias en la composición de la leche (5% de grasa and 4.3% de proteína). La producción de metano fue mayor para la dieta A (28,5 g/d) que para la dieta M (25,9 g/d), aunque estas diferencias no fueron estadísticamente significativas. En el tercer experimento se compararon la partición energética en dos razas de ovejas (Manchega vs. Guirra) en mantenimiento. Fueron alimentadas con dietas mixtas en jaulas metabólicas, calorimetría indirecta, balance carbono nitrógeno y cálculos integrales fueron las herramientas utilizadas para un aproximación de la partición energética. Se realizó una aproximación de división de producción de calor. El ME para mantenimiento se estimó en 354 kJ/kg PV0.75/ día, en promedio para las dos razas. Las diferencias en la tasa metabólica basal entre las razas fu / [CAT] El principal objectiu d'aquesta tesi va ser estudiar el metabolism energètic en xicotets ruminants baix diferents escenaris de nutrició. Com a metodologia es va utilitzar la calorimetria indirecta en compte de calorimetria directa o proves d'alimentació. Dins de la calorimetria indirecta treballarem amb un sistema portatil de circuit obert d'intercanvi de gasos amb "urna" (Heat hood). Aquest sistema de respiració de circuit obert ens va permetre completar tot el balanç energètic i avaluar l'eficiència de la utilització de l'energia de la dieta per a diferents circumstàncies fisiològiques com produccion de llet en cabres o manteniment en ovelles. A més va ser possible quantificar en cada assaig algunes perdues relacionades amb la contaminacion ambiental com a emissions de CH4 i l'excreció de nitrogen en femta i orina. En aquesta tesi es van dissenyar tres experiments, dos en cabres en lactación i un altre en ovelles com vam descriure a continuació. En el primer experiment s'han determinat,digestibilidad, balanç energètic, balanç carboni nitrogen, producció de llet, paràmetres ruminales, àcids grassos i metabòlits en llet. Gàbies metabòliques i un sistema de circuit obert de calorimetria indirecta va ser el mètode aplicat. Els tractaments van consistir en dues dietes mixtes amb alfals com a farratge i dins del concentrat el gra de civada va ser reemplaçat per cilindre d'arròs. No es van trobar diferències significatives en l'energia metabolizable ingerida (MEI) de 1254 kJ/kg PV0.75 en mitjana i una producció de calor (HP) de 640 kJ/kg PV0.75 en mitjana. La producció de llet no va presentar diferències significatives entre les dues dietes, (2.2 kg/donen mitjana), el greix de la llet va ser major en la dieta de cilindre d'arròs (6.9% vs. 5.3% per a cilindre d'arròs i civada respectivament). El balanç energètic va ser positiu i correlacionat als metabòlits en llet determinats. Quant a les emissions de CH4, determinades en viu mitjançant l'intercanvi de gasos per calorimetria indirecta, les cabres alimentades amb el subproducte van reduir significativament la producció de metà (23.2 g / d vs 30.1 g / d.).En el segon experiment, també utilitzem dos tipus de dietes, però en aquest cas substituïm els farratges i vam mantenir el mateix pinso; en una de les dietes es va utilitzar com a farratge una gramínea (Maralfafa [Pennisetum sp.] - dieta M) i en l'altre una **leguminosa d'ús estès (Alfals [Medicago sativa] - dieta A). Els mètodes d'anàlisis i anàlisis van ser els mateixos que els utilitzats en l'Experiment 1, i es van incloure a més anàlisi de metabòlits en orina i plasma. La matèria seca ingerida va ser major per a dieta A (1,8 vs 1,6 kg/d, respectivament), els coeficients de digestibilidad van ser majors per a la dieta M. No obstant açò no es van trobar diferències significatives en MEI (1089 kJ/kg PV0.75, en mitjana) i HP 639 kJ/kg PV0.75, en mitjana). La producció de llet va ser major en la dieta Al fet que la dieta M, (1,8 vs. 1,7 kg/d, respectively) i els metabòlits en orina, plasma i llet indiquen un millor aprofitament de la dieta A. No es van presentar diferències en la composició de la llet (5% de greix i 4.3% de proteïna). La producció de metà va ser major per a la dieta A (28,5 g/d) que per a la dieta M (25,9 g/d), encara que aquestes diferències no van anar estadísticament significatives. En el tercer experiment es van comparar la partició energètica en dues races d'ovelles (Manxega vs. Guirra) en manteniment. Van ser alimentades amb dietes mixtes en gàbies metabòliques, calorimetria indirecta, balanç carboni nitrogen i càlculs integrals van ser les eines utilitzades per a un aproximació de la partició energètica. Es va realitzar una aproximació de divisió de producció de calor. L'EM para manteniment es va estimar en 354 kJ/kg PV0.75 / dia, en mitjana per a les dues races. Les diferències en la taxa metabòlica basal entre les races va ser de 2 / Criscioni Ferreira, PF. (2016). Application of an open circuit indirect calorimetry system for gaseous exchange measurements in small ruminant nutrition [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/64069 / TESIS

The substance of present work is to provide standard thermodynamic functions (STF) of small size molecules for the calculation of the composition and thermodynamic properties of low-temperature plasma, and also method for such a calculation applying obtained STF under non-ideal plasma conditions. With a view to further application in modelling the phenomena in thermal plasma the range of pressures is limited to the region from 0.01 bar to 100 bar, and that of temperature to 298.15–50 kK. To obtain STF the method of partition function resulting from statistical mechanics was proposed. State of art in the given scientific area and theoretical basis of the statistical mechanics required for establishing of the proposed method together with discussion of partition function divergence problem have been reviewed. For the calculation of STF of diatomic molecules the method of direct summation has been employed, whereas, as for the larger size molecules, the rigid rotor and harmonic oscillator model have been generally adopted. The spectral data required for the calculations have been taken from literature, or, in selected cases, these have been computed by quantum chemistry ab initio techniques. The resulting STF have been included into already existing database system of thermodynamic properties and those can serve as input data for subsequent thermodynamic calculations. A general method has been worked out for the purpose of the computation of thermodynamic properties and composition of non-ideal homogenous plasma system in thermodynamic equilibrium. The method is based on minimizing total Gibbs energy to compute at constant pressure or Helmholtz energy to compute at constant volume. The computation algorithm was implemented into computer program and subsequently applied to the computation of the composition and thermodynamic properties of SF6 dissociation and ionization products using obtained STF.

<div>The interplay between network topology and traffic dynamics in road networks impacts various performance measures. There are extensive existing researches focusing on link-level fundamental diagrams, traffic assignments under route choice assumptions. However, the underlying coupling of structure and dynamic makes network-level traffic not fully investigated. In this thesis, we build structural and dynamic models to deal with three challenges: 1) describing road network topology and understanding the difference between cities; 2) quantifying network congestion considering both road network topology and traffic flow information; 3) allocating transportation management resources to optimize the road network connectivity.</div><div><br></div><div>The first part of the thesis focuses on structural models for complex road networks. Online road map data platforms, like OpenStreetMap, provide us with reliable road network data of the world. To solve the duplicate node problem, an O(n) time complexity node merging algorithm is designed to pre-process the raw road network with n nodes. Hereafter, we define unweighted and weighted node degree distribution for</div><div>road networks. Numerical experiments present the heterogeneity in node degree distribution for Beijing and Shanghai road network. Additionally, we find that the power law distribution fits the weighted road network under certain parameter settings, extending the current knowledge that degree distribution for the primal road network is not power law.</div><div><br></div><div>In the second part, we develop a road network congestion analysis and management framework. Different from previous methods, our framework incorporates both network structure and dynamics. Moreover, it relies on link speed data only, which is more accessible than previously used link density data. Specifically, we start from the existing traffic percolation theory and critical relative speed to describe network-level traffic congestion level. Based on traffic component curves, we construct Aij for two road segments i and j to quantify the necessity of considering the two road segments in the same traffic zone. Finally, we apply the Louvain algorithm on defined road segment networks to generate road network partition candidates. These candidate partitions will help transportation engineers to control regional traffic.</div><div><br></div><div>The last part formulates and solves a road network management resource allocation optimization. The objective is to maximize critical relative speed, which is defined from traffic component curves and is closely related to personal driving comfort. Budget upper bound serves as one of the constraints. To solve the simulation-based nonlinear optimization problem, we propose a simple allocation and a meta-heuristic method based on the genetic algorithm. Three applications demonstrate that the meta-heuristic method finds better solutions than simple allocation. The results will inform the optimal allocation of resources at each road segment in metropolitan cities to enhance the connectivity of road networks.</div>

Orientador: Liliane Santos de Camargos / Resumo: O manganês é um micronutriente que se enquadra no critério de essencialidade das plantas, no entanto sua presença altera o teor de outros nutrientes como o fósforo, quando aplicado em solo. A leguminosa herbácea tropical Stizolobium aterrimum Piper & Tracy (Mucuna-preta) é uma planta constantemente utilizada em sistema de cultura consorciada para conservação de matéria orgânica, por conta de sua biomassa. Desta forma, o trabalho visa a utilização dessa leguminosa como tolerante e com potencial fitorremediador para a retirada de manganês em concentrações tóxicas do solo. Portanto. foi avaliado seu crescimento e metabolismo em solos com concentrações tóxicas de manganês, analisando massa fresca, seca, indicadores de estresse oxidante, parâmetros da fotossíntese e metabólitos (aminoácidos, açucares solúveis totais, clorofila, ureídeos, proteína, nitrato e amônia), índice de tolerância e quantificação de manganês nos tecidos. Os dados foram avaliados por análise de variância e Soctt-Knott a 5% de probabilidade, utilizando o software SISVAR®. S aterrimum, consegue germinar em solos com altas concentrações de manganês; produz grande quantidade de biomassa seca e fresca mesmo em doses potencialmente tóxicas de manganês, não apresenta indicadores de estresse oxidativo; S. aterrimum é uma planta tolerante e com potencial de fitorremdiador para manganês. / Abstract: Manganese is a micronutrient that meets the criteria of essentiality of plants, however its presence changes the content of other nutrients such as phosphorus, when applied to soil. The tropical herbaceous legume Stizolobium aterrimum Piper & Tracy (Mucuna-preta) is a plant constantly used in a intercropping system for the conservation of organic matter, due to its biomass. Thus, the work aims to use this legume as a tolerant and with phytoremediation potential for the removal of manganese in toxic concentrations of the soil. Therefore. its growth and metabolism in soils with toxic concentrations of manganese was evaluated, analyzing fresh, dry mass, oxidative stress indicators, photosynthesis parameters and metabolites (amino acids, total soluble sugars, chlorophyll, ureides, protein, nitrate and ammonia), tolerance and quantification of manganese in tissues. The data were evaluated by analysis of variance and Soctt-Knott at 5% probability, using the SISVAR® software. S aterrimum, can germinate in soil with high concentrations of manganese; it produces a large amount of dry and fresh biomass even in potentially toxic doses of manganese, it does not show oxidative stress indicators; S. aterrimum is a tolerant plant with potential for phytoremediation for manganese. / Mestre

Introduction: Instrumented gait analysis and inverse dynamics are commonly used in research and clinical practice to calculate lower extremity joint kinetics, such as power and work. However, multisegment foot (MSF) model kinetics have been limited by ground reaction force (GRF) measurements. New technology enables simultaneous capture of plantar pressure and shear stress distributions but has not yet been used with motion capture. Integrating MSF models and pressure/shear measurements will enhance the analysis of foot joint kinetics. The purpose of this study was to develop methodology to integrate these systems, then analyze the effects of speed on foot joint kinetics. Methods: Custom software was developed to synchronize motion capture and pressure/shear data using measured offsets between reference frame origins and time between events. Marker trajectories were used to mask pressure/shear data and construct segment specific GRFs. Inverse dynamics were done in commercial software. Demonstrative data was from 5 healthy adults walking unshod at 3 fixed speeds (1.0, 1.3, and 1.6 m/s, respectively) wearing retroreflective markers according to an MSF model. Plantar shear forces and ankle, midtarsal, and first metatarsophalangeal (MTP) joint kinetics were reported. Speed effects on joint net work were evaluated with a repeated measures ANOVA. Results: Plantar shear forces during stance showed some spreading effects (directionally opposing shear forces) that relatively were unaffected by walking speed. Midtarsal joint power seemed to slightly lag behind the ankle, particularly in late stance. Net work at the ankle (p = 0.024), midtarsal (p = 0.023), and MTP (p = 0.009) joints increased with speed. Conclusions: Functionally, the ankle and midtarsal joints became more motorlike with increasing speed by generating more energy than they absorbed, while the MTP joint became more damperlike by absorbing more energy than it generated. System integration appears to be an overall success. Limitations and suggestions for future work are presented.

No description available.

Dans cette thèse nous étudions un problème fondamental, le partitionnement de graphe, dans le contexte de la croissance rapide des données, le volume des données continues à augmenter, allant des réseaux sociaux à l'internet des objets. En particulier, afin de vaincre les propriétés intraitables existant dans de nombreuses graphies, par exemple, la distribution des degrés en loi de puissance, nous appliquons un nouveau mode pour coupe de sommet, à la place de la méthode traditionnelle (coupe de bord), ainsi que pour assurer une charge de travail équilibrée et raisonnablement dans le traitement de graphe distribué. En outre, pour réduire le coût de communication inter-partitions, nous proposons une méthode de partition de bord basée sur les blocs, qui peut explorer efficacement les structures graphiques sous-jacentes au niveau local. , afin d'optimiser l'exécution de l'algorithme de graphe. Par cette méthode, le temps d'exécution et des communications généraux peuvent être considérablement réduits par rapport aux approches existantes. Les challenges qui se posent dans les grands graphiques comprennent également leur grande variété. Comme nous le savons, la plupart des applications graphiques au monde réel produisent des ensembles de données hétérogènes, dans lesquels les sommets et / ou les arêtes peuvent avoir des différents types ou des différentes étiquettes. De nombreuses algorithmes de fouille de graphes sont également proposés avec beaucoup d'intérêt pour les attributs d'étiquette. Pour cette raison, notre travail est étendu aux graphes de multicouches en prenant en compte la proximité des arêtes et la distribution des étiquettes lors du processus de partitionnement. En fin de cette thèse, Nous démontré à la ses performances exceptionnelles sur les ensembles de données du monde réel. / In this thesis, we mainly focus on a fundamental problem, graph partitioning, in the context of unexpectedly fast growth of data sources, ranging from social networks to internet of things. Particularly, to conquer intractable properties existing in many graphs, e.g. power-law degree distribution, we apply the novel fashion vertex-cut, instead of the traditional edge-cut method, for achieving balanced workload in distributed graph processing. Besides, to reduce the inter-partition communication cost, we present a block-based edge partition method who can efficiently explore the locality underlying graphical structures, to enhance the execution of graph algorithm. With this method, the overhead of both communication and runtime can be decreased greatly, compared to existing approaches. The challenges arising in big graphs also include their high-variety. As we know, most of real life graph applications produce heterogenous datasets, in which the vertices and/or edges are allowed to have different types or labels. A big number of graph mining algorithms are also proposed with much concern for the label attributes. For this reason, our work is extended to multi-layer graphs with taking into account the edges closeness and labels distribution during partitioning process. Its outstanding performance over real-world datasets is demonstrated finally.

This report aimed to develop algorithms for solving the optimization problem of matchingbuy and sell orders in call auctions while minimizing the number of transactions. The developed algorithms were evaluated based on their execution time and solution accuracy.The study found that the problem was more difficult to solve than initially anticipated, and commercial solvers were inadequate for the task. The data’s characteristics werecritical to the algorithms’ performance, and the lack of specifications for instruments andexchange posed a challenge. The algorithms were tested on a broad range of datasets with different characteristics, as well as real trades of stocks from the Stockholm Stock Exchange. Evaluating the best-performing algorithm became a trade-off between time and accuracy, where the quickest algorithm did not have the highest solution accuracy. Therefore, the importance of these factors should be considered before deciding which algorithm to implement. Eight algorithms were evaluated: four greedy algorithms and four clusteralgorithms capable of identifying 2-1 and 3-1 matches. If execution time is the single most crucial factor, the Unsorted Greedy Algorithm should be considered. However, if accuracyi s a priority, the Cluster 3-1 &amp; 1-3 Algorithm should be considered, even though it takes longer to find a solution. Ultimately, the report concluded that while no single algorithm can be definitively la-beled as the best, the Cluster 2-1 Algorithm strikes the most effective balance between execution time and solution accuracy, while also remaining relatively stable in perfor-mance for all test cases. The recommendation was based on the fact that the Cluster 2-1 Algorithm proved to be the quickest of the developed cluster algorithms, and that cluster algorithms were able to find the best solutions for all tested data sets. This study successfully addressed its purpose by developing eight algorithms that solved the given problem and suggested an appropriate algorithm that strikes a balance between execution time and solution quality.