scholarly journals A Heuristic Algorithm for Solving Triangle Packing Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ruimin Wang ◽  
Yuqiang Luo ◽  
Jianqiang Dong ◽  
Shuai Liu ◽  
Xiaozhuo Qi
Keyword(s):  
Approximate Solution ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Packing Problem ◽  
Optimization Method ◽  
Resource Optimization ◽  
Network Resource ◽  
Analogue Experiment ◽  
Processing Network ◽  
Application Prospects

The research on the triangle packing problem has important theoretic significance, which has broad application prospects in material processing, network resource optimization, and so forth. Generally speaking, the orientation of the triangle should be limited in advance, since the triangle packing problem is NP-hard and has continuous properties. For example, the polygon is not allowed to rotate; then, the approximate solution can be obtained by optimization method. This paper studies the triangle packing problem by a new kind of method. Such concepts as angle region, corner-occupying action, corner-occupying strategy, and edge-conjoining strategy are presented in this paper. In addition, an edge-conjoining and corner-occupying algorithm is designed, which is to obtain an approximate solution. It is demonstrated that the proposed algorithm is highly efficient, and by the time complexity analysis and the analogue experiment result is found.

scholarly journals A New Quasi-Human Algorithm for Solving the Packing Problem of Unit Equilateral Triangles

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ruimin Wang ◽  
Xiaozhuo Qi ◽  
Yuqiang Luo ◽  
Jianqiang Dong
Keyword(s):  
Complexity Analysis ◽  
Packing Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Resource Optimization ◽  
Network Resource ◽  
New Concepts ◽  
Theoretical Significance ◽  
Calculation Results ◽  
Equilateral Triangles

The packing problem of unit equilateral triangles not only has the theoretical significance but also offers broad prospects in material processing and network resource optimization. Because this problem is nondeterministic polynomial (NP) hard and has the feature of continuity, it is necessary to limit the placements of unit equilateral triangles before optimizing and obtaining approximate solution (e.g., the unit equilateral triangles are not allowed to be rotated). This paper adopts a new quasi-human strategy to study the packing problem of unit equilateral triangles. Some new concepts are put forward such as side-clinging action, and an approximation algorithm for solving the addressed problem is designed. Time complexity analysis and the calculation results indicate that the proposed method is a polynomial time algorithm, which provides the possibility to solve the packing problem of arbitrary triangles.

Evaluation of Parallel Algorithms of Traffic Volume Statistics per Cell in Cellular Network Based on MapReduce Programming Model

2013 ◽  
Vol 401-403 ◽  
pp. 1859-1863
Author(s):  
Qing Yang ◽  
Jun Liu ◽  
Huan Wang ◽  
Wen Li Zhou ◽  
Hua Yu
Keyword(s):  
Big Data ◽  
Parallel Algorithms ◽  
Network Design ◽  
Time Complexity ◽  
Cellular Network ◽  
Complexity Analysis ◽  
Programming Model ◽  
Resource Optimization ◽  
Network Resource ◽  
Data Network

Understanding traffic per unit time in cell dimension in cellular data network can be of great help for mobile operators to improve the performance of the cellular data network. It is important for network design and resource optimization. In this paper, we describe three methods to count the traffic per unit time per cell. Moreover, we compare the results of the three methods by the deviation distribution of the traffic and time complexity analysis. Our work is distinguished from other related work by using big data which contains around 1.4 billion records and 20 thousands cells. Generally, we expect this paper could deliver important insights into cellar data network resource optimization.

scholarly journals An Optimal Allocation Method of Power Multimodal Network Resources Based on NSGA-II

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ao Xiong ◽  
Yuanzheng Tong ◽  
Shaoyong Guo ◽  
Yanru Wang ◽  
Sujie Shao ◽  
...  
Keyword(s):  
Resource Allocation ◽  
Optimal Allocation ◽  
Optimization Method ◽  
Resource Optimization ◽  
Normal Operation ◽  
Network Resources ◽  
Nsga Ii ◽  
Network Resource ◽  
Allocation Method ◽  
Multimodal Network

Basic services for power business were provided by the power multimodel network providers. However, because the power multimodal network is usually complex and changeable, the service of power business is often unstable. This problem can be solved by a suitable network resource optimization method. Therefore, how to design a network resource optimization method that seeks a compromise between multiple performance indicators that achieve the normal operation of power multimode networks is still extremely challenging. An optimal allocation method of power multimodal network resources based on NSGA-II was proposed by this paper. Firstly, the power multimodal network-resource model is established, and the problems existing in the resource optimization process are analyzed. Secondly, preprocessing technology and indirect coding technology are applied to NSGA-II, which solves the coding problem and convergence problem of the application of genetic algorithm to the optimization of network resource allocation. Finally, the simulation results show that, compared with the control algorithm, this method has further optimized the various indicators of the resource allocation of the power multimodal network, and the performance has been improved by more than 6%.

Real-time engine model development based on time complexity analysis

2021 ◽  
pp. 146808742110397
Author(s):  
Haotian Chen ◽  
Kun Zhang ◽  
Kangyao Deng ◽  
Yi Cui
Keyword(s):  
Real Time ◽  
Time Complexity ◽  
Complexity Analysis ◽  
High Accuracy ◽  
The Real ◽  
Cycle Simulation ◽  
Crank Angle ◽  
Time Requirements ◽  
Improved Model ◽  
Simulation Time

Real-time simulation models play an important role in the development of engine control systems. The mean value model (MVM) meets real-time requirements but has limited accuracy. By contrast, a crank-angle resolved model, such as the filling -and-empty model, can be used to simulate engine performance with high accuracy but cannot meet real-time requirements. Time complexity analysis is used to develop a real-time crank-angle resolved model with high accuracy in this study. A method used in computer science, program static analysis, is used to theoretically determine the computational time for a multicylinder engine filling-and-empty (crank-angle resolved) model. Then, a prediction formula for the engine cycle simulation time is obtained and verified by a program run test. The influence of the time step, program structure, algorithm and hardware on the cycle simulation time are analyzed systematically. The multicylinder phase shift method and a fast calculation method for the turbocharger characteristics are used to improve the crank-angle resolved filling-and-empty model to meet real-time requirements. The improved model meets the real-time requirement, and the real-time factor is improved by 3.04 times. A performance simulation for a high-power medium-speed diesel engine shows that the improved model has a max error of 5.76% and a real-time factor of 3.93, which meets the requirement for a hardware-in-the-loop (HIL) simulation during control system development.

Final Remarks for the Research With Advanced Machine Learning Methods in Colon Cancer Analysis

2021 ◽  
pp. 151-154
Keyword(s):  
Colon Cancer ◽  
Time Complexity ◽  
High Performance ◽  
Complexity Analysis ◽  
Search Algorithm ◽  
Cancer Treatments ◽  
Cancer Dataset ◽  
Performance Accuracy ◽  
Research Questions

Generally, classification accuracy is very important to gene processing and selection and cancer classification. It is needed to achieve better cancer treatments and improve medical drug assignments. However, the time complexity analysis will enhance the application's significance. To answer the research questions in Chapter 1, several case studies have been implemented (see Chapters 4 and 5), each was essential to sustain the methodologies discussed in Chapter 3. The study used a colon-cancer dataset comprising 2000 genes. The best search algorithm, GA, showed high performance with a good efficient time complexity. However, both DTs and SVMs showed the best classification contribution with reference to performance accuracy and time efficiency. However, it is difficult to apply a completely fair comparative study because existing algorithms and methods were tested by different authors to reflect the effectiveness and powerful of their own methods.

scholarly journals Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1914
Author(s):  
Kaizhi Chen ◽  
Jiahao Zhuang ◽  
Shangping Zhong ◽  
Song Zheng
Keyword(s):  
Computational Geometry ◽  
Packing Problem ◽  
Optimization Method ◽  
Raw Material ◽  
Packing Problems ◽  
Permutation Model ◽  
Feasible Solutions ◽  
Packing Method ◽  
Better Than

Research on the rectangle packing problems has mainly focused on rectangular raw material sheets without defects, while natural slate has irregular and defective characteristics, and the existing packing method adopts manual packing, which wastes material and is inefficient. In this work, we propose an effective packing optimization method for nature slate; to the best of our knowledge, this is the first attempt to solve the guillotine packing problem of rectangular items in a single irregular and defective slate. This method is modeled by the permutation model, uses the horizontal level (HL) heuristic proposed in this paper to obtain feasible solutions, and then applies the genetic algorithm to optimize the quality of solutions further. The HL heuristic is constructed on the basis of computational geometry and level packing. This heuristic aims to divide the irregular plate into multiple subplates horizontally, calculates the movable positions of the rectangle in the subplates, determines whether or not the rectangle can be packed in the movable positions through computational geometry, and fills the scraps appropriately. Theoretical analysis confirms that the rectangles obtained through the HL heuristic are inside the plate and do not overlap with the defects. In addition, the packed rectangles do not overlap each other and satisfy the guillotine constraint. Accordingly, the packing problem can be solved. Experiments on irregular slates with defects show that the slate utilization through our method is between 89% and 95%. This result is better than manual packing and can satisfy actual production requirements.

scholarly journals Lexicographic Unranking of Combinations Revisited

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 97
Author(s):  
Antoine Genitrini ◽  
Martin Pépin
Keyword(s):  
Time Complexity ◽  
Complexity Analysis ◽  
Lexicographic Order ◽  
Familiar Word ◽  
Integer Arithmetic ◽  
Combinatorial Objects ◽  
New Strategy ◽  
High Level ◽  
The Cost ◽  
Multinomial Coefficients

In the context of combinatorial sampling, the so-called “unranking method” can be seen as a link between a total order over the objects and an effective way to construct an object of given rank. The most classical order used in this context is the lexicographic order, which corresponds to the familiar word ordering in the dictionary. In this article, we propose a comparative study of four algorithms dedicated to the lexicographic unranking of combinations, including three algorithms that were introduced decades ago. We start the paper with the introduction of our new algorithm using a new strategy of computations based on the classical factorial numeral system (or factoradics). Then, we present, in a high level, the three other algorithms. For each case, we analyze its time complexity on average, within a uniform framework, and describe its strengths and weaknesses. For about 20 years, such algorithms have been implemented using big integer arithmetic rather than bounded integer arithmetic which makes the cost of computing some coefficients higher than previously stated. We propose improvements for all implementations, which take this fact into account, and we give a detailed complexity analysis, which is validated by an experimental analysis. Finally, we show that, even if the algorithms are based on different strategies, all are doing very similar computations. Lastly, we extend our approach to the unranking of other classical combinatorial objects such as families counted by multinomial coefficients and k-permutations.

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