An efficient algorith for determining the convex hull of a finite planar set
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A tournament problem
Amer. Math. Monthly
(1959)
Cited by (1442)
On the estimation of the core for TU games
2024, Expert Systems with ApplicationsThe core of a transferable utility (TU) game, if it is not empty, is prescribed by the set of all stable allocations. The exact determination of the core reaches exponential time complexity. Therefore, its exact computation is often avoided as the number of players increases. In this work, we propose an estimator for the core of a TU game based on the statistical theory of set estimation. Concretely, we provide a core reconstruction that is obtained in polynomial time for general dimension. Additionally, convergence rates for the estimation error are derived. Finally, a consistent core-center estimator is established as a geometrical application of this methodology.
Stability constraints in a 3D knapsack problem with non parallelepipedic items
2024, Computers and Industrial EngineeringThis paper concerns stability issues that we encountered while solving an industrial pallet loading problem. The practical problem can be modeled as a three-dimensional knapsack with original constraints related to the stability of the pallet: when the placement of the boxes on the pallet is computed, the weight of the boxes and the placement sequence are not known.
Despite this lack of information, the placement must remain stable throughout the construction of the pallet. Even more important, the major difference with classical placement problems is that the boxes are parallelepipedic rectangle with edge reduction (the upper surface may be smaller than the bottom face).
In this paper, we review stability constraints used in the literature and the assumptions under which these constraints can be used and we detail their adequacy to the problem we consider. We then propose a new stability constraint which takes into account the practical features, which can be integrated into a placement algorithm and which is not too restrictive.
Numerical experiments on benchmarks from the literature show that this constraint, added to a classical placement algorithm, obtains results which are similar to algorithms from the literature dedicated to a specific stability constraint for parallelepipedic boxes. By adjusting the benchmark to take into account the practical problem specificities, we show that this new stability constraint is perfectly suited to the industrial problem and obtains very good results compared to classical constraints. Therefore, it has been integrated in the placement software developed by the company.
Structural and alteration zones controls on Cu mineralisation in the northwest of Nain (northeastern Isfahan, Iran): A remote sensing perspective
2024, Journal of African Earth SciencesRemote sensing data can be utilised for regional mapping of the Earth's surface to enhance structural interpretation and mineral prospecting. To this end, satellite multispectral sensors such as the Advanced Space borne Thermal Emission and Reflectance (ASTER) with six channels in the shortwave infrared and five channels in the thermal area is helpful in detecting alteration and mineralisation zones in areas with good rock exposures. This study has investigated and detected hydrothermal alteration zones and mapped structural elements associated with mafic volcanic rocks-related copper mineralisation in the northwest of the Nain district in Central Iran. In this study, we processed ASTER data (14 bands). We generated maps that depict the distribution of alteration minerals (e.g., sericite, kaolinite, chlorite, and calcite) related to copper mineralisation using various techniques such as different band ratio images, False-colour composition (RGB), Matched Filtering (MF), and Spectral Angle Mapper (SAM). Follow-up ground proofing validated the analysis of results from the ASTER data. The study established the regional distribution of hydrothermal alteration zones (i.e., phyllic, argillic, and propylitic). The regional distribution and extent of these alteration zones are associated with regional structures that served as focusing conduits for the buoyant hypogene mineralizing fluids. The results show that ASTER imagery is useful in mapping the extent of the hydrothermal alteration and lithological units and can thus be used to target hydrothermal ore deposits with large alteration footprints.
An evaluation of GPU filters for accelerating the 2D convex hull
2024, Journal of Parallel and Distributed ComputingThe Convex Hull is one of the most relevant structures in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is often needed to improve the performance to solve more significant problems quickly or in real-time processing. This work presents an experimental evaluation of GPU filters to reduce the cost of computing the 2D convex hull. The techniques first perform a preprocessing of the input set, filtering all points within an eight-vertex polygon to obtain a reduced set of candidate points. We use parallel computation and the use of the Manhattan distance as a metric to find the vertices of the polygon and perform the point filtering. For the filtering stage we study different approaches; from custom CUDA kernels to libraries such as Thrust and Cub. Four types of point distributions are tested: a normal distribution (favorable case), uniform (favorable case), circumference (the worst case), and a case where points are shifted randomly from the circumference (intermediate case). The experimental evaluation shows that the GPU filtering algorithm can be up to 17.5× faster than a sequential CPU implementation, and the whole convex hull computation can be up to 160× faster than the fastest implementation provided by the CGAL library for a uniform distribution and 23× for a normal distribution.
An autonomous coverage path planning algorithm for maritime search and rescue of persons-in-water based on deep reinforcement learning
2024, Ocean EngineeringThe prevalence of maritime transportation and operations is increasing, leading to a gradual increase in drowning accidents at sea. In the context of maritime search and rescue (SAR), it is essential to develop effective search plans to improve the survival probability of persons-in-water (PIWs). However, conventional SAR search plans typically use predetermined patterns to ensure complete coverage of the search area, disregarding the varying probabilities associated with the PIW distribution. To address this issue, this study has proposed a maritime SAR vessel coverage path planning framework (SARCPPF) suitable for multiple PIWs. This framework comprises three modules, namely, drift trajectory prediction, the establishment of a multilevel search area environment model, and coverage search. First, sea area-scale drift trajectory prediction models were employed using the random particle simulation method to forecast drift trajectories. A hierarchical probability environment map model was established to guide the SAR of multiple SAR units. Subsequently, we integrated deep reinforcement learning with a reward function that encompasses multiple variables to guide the navigation behavior of ship agents. We developed a coverage path planning algorithm aimed at maximizing the success rates within a limited timeframe. The experimental results have demonstrated that our model enables vessel agents to prioritize high-probability regions while avoiding repeated coverage.
Twitter user geolocation based on heterogeneous relationship modeling and representation learning
2023, Information SciencesTwitter user geolocation has been garnering considerable attention from academia. Due to the complexity of the Twitter data, the user geolocation performance is limited for some user geolocation methods. Previous works on Twitter user geolocation typically model the user location based on homogeneous relationships, while neglecting the heterogeneous relationships. In this paper, we propose a novel Twitter user geolocation method based on heterogeneous relationship modeling and representation learning. In this method, two heterogeneous graphs are constructed according to the statistical characteristic of the mentioning relationship between users and words, and the mentioning relationship between users in the tweets, respectively. By sampling the nodes in the graph, the complex topological structure of the constructed graph is captured and natural language-like node sequences are generated. The Skip-gram model is used to construct the objective function, and the stochastic gradient descent algorithm is employed to optimize the objective function to learn the representations. Finally, a neural network is used to train the user geolocation model. Experiments conducted on two real-world Twitter datasets demonstrate that the proposed method outperforms the state-of-the-art methods.