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Engineering faster sorters for small sets of items

SOFTWARE-PRACTICE & EXPERIENCE 2021年第5期51卷 965-1004页

作者： Bingmann, Timo Marianczuk, Jasper Sanders, Peter Karlsruhe Inst Technol Inst Theoret Informat Fasanengarten 5 D-76131 Karlsruhe Germany

sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. That is why a lot of effort has been put into finding sorting algorithms that sort large sets as efficiently as possible. But the more sophisticated and complex the algorithms become, the less efficient they are for small sets of items due to large constant factors. A relatively simple sorting algorithm that is often used as a base case sorter is insertion sort, because it has small code size and small constant factors influencing its execution time. We aim to determine if there is a faster way to sort small sets of items to provide an efficient base case sorter. We looked at sorting networks, at how they can improve the speed of sorting few elements, and how to implement them in an efficient manner using conditional moves. Since sorting networks need to be implemented explicitly for each set size, providing networks for larger sizes becomes less efficient due to increased code sizes. To also enable the sorting of slightly larger base cases, we adapted sample sort to Register Sample Sort, to break down those larger sets into sizes that can in turn be sorted by sorting networks. From our experiments we found that when sorting only small sets of integers, the sorting networks outperform insertion sort by a factor of at least 1.76 for any array size between six and 16, and by a factor of 2.72 on average across all machines and array sizes. When integrating sorting networks as a base case sorter into Quicksort, we achieved far less performance improvements over using insertion sort, which is probably due to the networks having a larger code size and cluttering the L1 instruction cache. The same effect occurs when including Register Sample Sort as a base case sorter for IPS4o. But for x86 machines that have a larger L1 instruction cache of 64 KiB or more, we obtained speedups of 12.7% when using sorting networks as a base case sorter in std::sort, and of 5%-6

关键词： base case sorting sample sort sorter sorting sorting algorithm sorting networks

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A framework for Kernel-based multi-category classification

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JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH 2007年第0期30卷 525-564页

作者： Hill, Simon I. Doucet, Arnaud Univ Cambridge Dept Engn Cambridge CB2 1PZ England Univ British Columbia Dept Stat Vancouver BC V6T 1W5 Canada Univ British Columbia Dept Comp Sci Vancouver BC V6T 1W5 Canada

A geometric framework for understanding multi-category classification is introduced, through which many existing 'all-together' algorithms can be understood. The structure enables parsimonious optimisation, through a direct extension of the binary methodology. The focus is on Support Vector Classification, with parallels drawn to related methods. The ability of the framework to compare algorithms is illustrated by a brief discussion of Fisher consistency. Its utility in improving understanding of multi-category analysis is demonstrated through a derivation of improved generalisation bounds. It is also described how this architecture provides insights regarding how to further improve on the speed of existing multi-category classification algorithms. An initial example of how this might be achieved is developed in the formulation of a straightforward multi-category Sequential Minimal Optimisation algorithm. Proof-of-concept experimental results have shown that this, combined with the mapping of pairwise results, is comparable with benchmark optimisation speeds.

关键词： ARCHITECTURE sorting algorithm derivation Building construction Cohort Analysis Frameworks algorithms Optimization algorithms

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A BENCHMARK PARALLEL SORT FOR SHARED MEMORY MULTIPROCESSORS

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IEEE TRANSACTIONS ON COMPUTERS 1988年第12期37卷 1619-1626页

作者： FRANCIS, RS MATHIESON, ID Dept. of Comput. Sci. La Trobe Univ. Bundoora Vic. Australia

The first parallel sort algorithm for shared memory MIMD (multiple-instruction-multiple-data-stream) multiprocessors that has a theoretical and measured speedup near linear is exhibited. It is based on a novel asynchronous parallel merge that evenly partitions data to be merged among any number of processors. A benchmark sorting algorithm is proposed that uses this merge to remove the linear time bottleneck inherent in previous multiprocessors sorts. This sort, when applied to data set on p processors, has a time complexity of O((n log n)/p)+O((n log p)/p) and a space complexity of 2n, where n is the number of keys being sorted. Evaluations of the merge and benchmark sort algorithms on a 12-processor Sequent Balance 21000 System demonstrate near-linear speedup when compared to sequential Quicksort.

关键词： shared memory sorting algorithm Multiprocessor BENCHMARKS Keys complexity classes Parallel Lines space complexities Speeding merger sorting programs

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Development of a semi-implicit solver for detailed chemistry in internal combustion engine simulations

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JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER-TRANSACTIONS OF THE ASME 2007年第1期129卷 271-278页

作者： Liang, Long Kong, Song-Charng Jung, Chulhwa Reitz, Rolf D. Univ Wisconsin Engine Res Ctr Madison WI 53706 USA

An efficient semi-implicit numerical method is developed for solving the detailed chemical kinetic source terms in internal combustion (IC) engine simulations. The detailed chemistry system forms a group of coupled staff ordinary differential equations (ODEs), which presents a very stringent time-step limitation when solved by standard explicit methods, and is computationally expensive when solved by iterative implicit methods. The present numerical solver uses a stiffly stable noniterative semi-implicit method. The formulation of numerical integration exploits the physical requirement that the species density and specific internal energy in the computational cells must be non-negative, so that the Lipschitz time-step constraint is not present and the computation time step can be orders of magnitude larger than that possible in standard explicit methods. The solver exploits the characteristics of the stiffness of the ODEs by using a sequential sort algorithm that ranks an approximation to the dominant eigenvalues of the system to achieve maximum accuracy. Subcycling within the chemistry solver routine is applied for each computational cell in engine simulations, where the subcycle time step is dynamically determined by monitoring the rate of change of concentration of key species, which have short characteristic time scales and are also important to the chemical heat release. The chemistry solver is applied in the KIVA-3V code to diesel engine simulations. Results are compared to those using the CHEMKIN package, which uses the VODE implicit solver Good agreement was achieved for a wide range of engine operating conditions, and 40-70% CPU time savings were achieved by the present solver compared to the standard CHEMKIN.

关键词： Internal energy Solvers sorting algorithm Nonnegative Population density computational time CPU time Ordinary differential equation simulating gasoline engine Chemistry

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GA(M)E-QSAR: A Novel, Fully Automatic Genetic-algorithm-(Meta)-Ensembles Approach for Binary Classification in Ligand-Based Drug Design

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JOURNAL OF CHEMICAL INFORMATION AND MODELING 2012年第9期52卷 2366-2386页

作者： Perez-Castillo, Yunierkis Lazar, Cosmin Taminau, Jonatan Froeyen, Mathy Angel Cabrera-Perez, Miguel Nowe, Ann Vrije Univ Brussel Fac Sci Dept Comp Sci Computat Modeling Lab CoMo B-1050 Brussels Belgium Univ Cent Marta Abreu Villas Ctr Bioact Quim Mol Simulat & Drug Design Grp Santa Clara Cuba Katholieke Univ Leuven Rega Inst Med Res Med Chem Lab B-3000 Louvain Belgium Univ Miguel Hernandez Fac Pharm Dept Engn Pharm & Pharmaceut Technol Area Alicante 03550 Spain

Computer-aided drug design has become an important component of the drug discovery process. Despite the advances in this field, there is not a unique modeling approach that can be successfully applied to solve the whole range of problems faced during QSAR modeling. Feature selection and ensemble modeling are active areas of research in ligand-based drug design. Here we introduce the GA(M)E-QSAR algorithm that combines the search and optimization capabilities of Genetic algorithms with the simplicity of the Adaboost ensemble-based classification algorithm to solve binary classification problems. We also explore the usefulness of Meta-Ensembles trained with Adaboost and Voting schemes to further improve the accuracy, generalization, and robustness of the optimal Adaboost Single Ensemble derived from the Genetic algorithm optimization. We evaluated the performance of our algorithm using five data sets from the literature and found that it is capable of yielding similar or better classification results to what has been reported for these data sets with a higher enrichment of active compounds relative to the whole actives subset when only the most active chemicals are considered. More important, we compared our methodology with state of the art feature selection and classification approaches and found that it can provide highly accurate, robust, and generalizable models. In the case of the Adaboost Ensembles derived from the Genetic algorithm search, the final models are quite simple since they consist of a weighted sum of the output of single feature classifiers. Furthermore, the Adaboost scores can be used as ranking criterion to prioritize chemicals for synthesis and biological evaluation after virtual screening experiments.

关键词： FULL-SCALE sorting algorithm chemical compounds Searches Binary useful area Drug Design weight sums Feature extraction Genetic algorithm (GA) Robustness

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TRANSITIVE ORIENTATIONS OF GRAPHS: 收藏
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引用; SIAM JOURNAL ON COMPUTING 1988年第6期17卷 1119-1133页; 作者： BOLLOBAS, B BRIGHTWELL, G Univ of Cambridge United Kingdom; Suppose that we have a set X of n objects in some unknown total order << . For G a graph on X, we ask, for each edge <span class="mrow" id="MathJax-Span; Suppose that we have a set X of n objects in some unknown total order $<$ . For G a graph on X, we ask, for each edge $x y$; 来源：评论; 学校读者我要写书评

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Exploring Auto-Generation of Network Models With Performance Evaluation Process Algebra

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IEEE ACCESS 2018年 6卷 42971-42983页

作者： Ding, Jie Wang, Rui Chen, Xiao Ge, Ying-En Shanghai Maritime Univ China Inst FTZ Supply Chain Shanghai 201306 Peoples R China Yangzhou Univ Sch Informat Engn Yangzhou 225127 Jiangsu Peoples R China Jiangsu Univ Sch Comp Sci & Commun Engn Zhenjiang 212013 Peoples R China Beihang Univ State Key Lab Software Dev Environm Beijing 100083 Peoples R China Shanghai Maritime Univ Coll Transport & Commun Shanghai 201306 Peoples R China

Formal method plays an important role in modeling large scale concurrent networks through its efficient model construction and analysis. Taking urban road networks and public transportation systems as examples, such models can be defined in a formal method in order to investigate the performance of current bus-line deployment based on a given road network. This paper considers how to efficiently build a formal model based on such an original prototype of the specified road network and transportation system. As the model prototype can be represented by a directed graph that is then transformed into a numerical incidence matrix, we proposed an algorithm, in this paper, to assist the construction of formal models by sorting all potential compositional structures and components based on the previously obtained numerical incidence matrix. Thereafter, a performance evaluation process algebra-based formal model can be automatically generated on the basis of sorted compositional structures, which extends the use of formal method for large-scale and comprehensive network, and system modeling. The findings reveal that the proposed algorithm can efficiently find all potential compositional structures that include all potential components and related activity flows in models.

关键词： Formal method PEPA incidence matrix compositional structures sorting algorithm

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MODELLING AND OPTIMISATION OF VACUUM COLLECTION SYSTEM FOR CRUISE SHIP KITCHEN GARBAGE

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POLISH MARITIME RESEARCH 2020年第1期27卷 152-161页

作者： Du Jun Li Ruonan Wu Xin Zhao Hang Jiangsu Univ Sci & Technol 2 Mengxi Rd Zhenjiang 212003 Jiangsu Peoples R China

Pollution of the marine environment by ship garbage is an urgent problem to be solved at home and abroad. The ship kitchen garbage vacuum collection system is a new environmental protection scheme for garbage disposal. It has many advantages, such as using a pipeline instead of manual operation, creating high-level sanitary conditions, realising completely closed garbage collection and transportation, eliminating cross-pollution, saving space and so on. In this paper, the system is modelled, and the calculation of pipeline pressure loss, the vacuum degree of the vacuum tank and the energy consumption of the system are briefly introduced. In order to reduce the energy consumption, an algorithm for the emptying and discharging port is presented. In order to solve the problem of optimising relevant parameters, the vacuum transport mechanism of garbage is studied based on an optimisation model of the pipe network, and the experimental platform of a simulation device is set up. In engineering, this is of great significance to the design of cruise ship garbage collection and treatment systems and the development of supporting technology.

关键词： Kitchen waste vacuum collection System modeling sorting algorithm Model experiment

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A gas source declaration scheme based on a tetrahedral sensor structure in three-dimensional airflow environments

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REVIEW OF SCIENTIFIC INSTRUMENTS 2019年第2期90卷 024104-1-024104-11页

作者： Hou, Hui-Rang Tong, Yuan Ren, Chao Meng, Qing-Hao Tianjin Univ Tianjin Key Lab Proc Measurement & Control Sch Elect & Informat Engn Inst Robot & Autonomous Syst Tianjin 300072 Peoples R China

A gas source declaration scheme based on a tetrahedral sensor structure in three-dimensional airflow environments is proposed. First, a tetrahedral sensor structure was established. Based on the tetrahedral structure, the gas source declaration problem was converted into a two-class classification issue. Then a classification algorithm combining an extreme learning machine (ELM, a fast neural network classifier) with a gas mass flux criterion is proposed. A novel calculation method for the mass flux through a closed tetrahedral surface is presented, and a mass flux criterion was developed which acts as a training sample filter for the ELM. The source declaration scheme was validated by using both regular and irregular tetrahedron experiments. Published under license by AIP Publishing.

关键词： Mass flux sorting algorithm computational methods Environments valve diameter Sensors Phyla

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Simulation-based SONET ADM optimization approach for dynamic traffic grooming in WDM optical networks

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PHOTONIC NETWORK COMMUNICATIONS 2008年第1期16卷 11-21页

作者： Roy, Kuntal Naskar, Mrinal Kanti Jadavpur Univ Dept Elect & Telecommun Engn Kolkata 700032 India

The article addresses a simulation-based optimization approach for allocation of ADMs in WDM optical networks with stochastic dynamic traffic. Since ADMs are expensive, it is desirable that if each node in WDM optical networks can use a minimum number of ADMs to achieve a near-ideal performance. In this article, first, the utilization statistics of ADMs are gathered by simulation. Then, ADMs are allocated based on the utilization statistics. In this respect, a simple sorting mechanism is used. The distinguished feature of the proposed approach is that it shows the way to allocate ADMs at the nodes of WDM optical networks with stochastic dynamic traffic. The experimental results ensure that the proposed approach can solve the problem of allocating ADMs in practical WDM optical networks considering stochastic dynamic traffic.

关键词： WDM optical networks SONET add-drop multiplexer dynamic traffic grooming sorting algorithm

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