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Decision Trees of algorithms and a Semivaluation to Measure Their Distance

ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 2006年第1期161卷 175-183页

作者： Keeffe, M. O' Pajoohesh, H. Schellekens, M. Univ Coll Cork Ctr Efficiency Oriented Languages CEOL Dept Comp Sci Cork Ireland

We use the set T-n of binary trees with n leaves to study decision trees of algorithms. The set T-n. of binary trees with n leaves can be ordered by the so called "imbalance" order, where two trees are related in the order iff the second is less "balanced" than the first. This order forms a lattice. We show that this lattice is nonmodular and extend the imbalance lattice with an algebraic operation. The operation corresponds to the extension of a binary tree with new binary trees at the leafs, which reflects the effect of recursive calls in an algorithm on the decision tree and we will characterize as an illustration the decision tree of the insertion sort algorithm. We investigate the semivaluations on the binary trees which is related to the running time of the algorithm.

关键词： Decision trees sorting algorithms level of balance time complexity semivaluations

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Improved Design of Classification Algorithm in Cloud Computing and Big Data Environment 1

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3rd European-Alliance-for-Innovation (EAI) International Conference on Advanced Hybrid Information Processing (ADHIP)

作者： Jiang, Yihuo Fuzhou Univ Int Studies & Trade Fuzhou Peoples R China

ISBN: (数字)9783030364021

ISBN: (纸本)9783030364021;9783030364014

With the rapid improvement of China's economic level, science and technology are also progresses, and the scope of the application of science and technology in daily life is becoming more and more extensive, and the large data of cloud computing is also applied to all aspects of our daily life. The classification algorithm is the key to reflect the large data computing ability of the cloud computing. It can further improve the analysis ability of the related data, make the operation of the related data more convenient, more close to the needs of the searcher for information, and avoid a large number of invalid information, because this is very demanding for the classification algorithm. On this basis, we analyzed the operation of the classification algorithm in the cloud computing environment, and used the clustering algorithm to improve the design, improve the efficiency of the related data and improve the accuracy of the data collection.

关键词： Cloud computing Big data sorting algorithms Improved design

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Efficient computation of multivariate empirical distribution functions at the observed values

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COMPUTATIONAL STATISTICS 2018年第3期33卷 1413-1428页

作者： Lee, David Joe, Harry Univ British Columbia Dept Stat Vancouver BC V6T 1Z4 Canada

Consider the evaluation of model-based functions of cumulative distribution functions that are integrals. When the cumulative distribution function does not have a tractable form but simulation of the multivariate distribution is easily feasible, we can evaluate the integral via a Monte Carlo sample, replacing the model-based distribution function by the empirical distribution function. Given a simulation sample of size N, the naive method uses comparisons to compute the empirical distribution function at all N sample vectors. To obtain faster computational speed when N needs to be large to achieve a desired accuracy, we propose methods modified from the popular merge sort and quicksort algorithms that preserve their average complexity in the bivariate case. The modified merge sort algorithm can be extended to the computation of a d-dimensional empirical distribution function at the observed values with complexity. Simulation studies suggest that the proposed algorithms provide substantial time savings when N is large.

关键词： Integral evaluation Joint probabilities Monte Carlo simulation sorting algorithms

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Use of Randomized algorithms for Enhancing Learning Ability in algorithms Course

Use of Randomized Algorithms for Enhancing Learning Ability ...

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IEEE International Conference on MOOCs, Innovation and Technology in Education (IEEE MITE)

作者： Goyal, Puneet Dwivedi, Monika Awais, Mohd Graph Era Univ Dept Comp Sci & Engn Dehra Dun India

ISBN: (纸本)9781479968763

In the field of Computer Science and Engineering, the algorithms course is considered very important for not only it forms the basis for several concepts but also, its in-depth understanding can help one solve many new and challenging problems in an efficient manner. Whether a student pursues his career in academia or industry, depth of his understanding in algorithms is certainly tested during competitive exams directly or indirectly. In this paper, we discuss a case study of using an innovative approach based on randomized algorithms and some statistics in teaching algorithms to engineering students, with aim to provide students a better individual learning experience. The approach has wider applicability but here it is practiced in relation to sorting algorithms. In this paper, we also discuss the student's feedback that we collected after completion of the course. It was observed that students were very appreciative of this novel approach used, and the majority of students found that it helped them in getting more clarity and deeper understanding of sorting algorithms.

关键词： Enhanced learning survey randomized algorithms statistics sorting algorithms

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Exploring the Solution Space of sorting by Translocations

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Procedia Computer Science 2012年 11卷 160-168页

作者： Amritanjali Shivani Anand G. Sahoo Department of Computer Science and Engineering Birla Institute of Technology Mesra Ranchi-835215 India Department of Information Technology Birla Institute of Technology Mesra Ranchi-835215 India

Genome sorting is a way to trace back the genomes of two species to their common ancestor. The study of genome rearrangements allows to better understand the process of evolution and is an important tool in comparative genomics. Given two genomes A and B, the goal is to find a shortest sequence of exchanges of non-empty chromosome ends that transform A into B. The length of such a shortest sequence is called the translocation distance between A and B, and the problem of finding the optimal sequence of translocations is called the sorting by translocations problem. For most problem instances, however, several minimum length sequences or optimal sequences of translocation exist, and in the absence of any additional information, no one is of greater value than the others. The problem of finding all optimal solutions for sorting by translocations is thus a natural generalization of sorting by translocations. In this paper, an algorithm is presented to find all solutions for sorting by translocations.

关键词： Genome rearrangements sorting algorithms Translocations

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Improved Divide/Sort/Merge sorting Networks

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SIAM Journal on Computing 1975年第3期4卷 264-270页

作者： R. L. (Scot) Drysdale, III Frank H. Young

This paper develops sorting networks using the divide/sort/merge strategy. These networks require \[ (0.25)N( \log _2 N )^2 - (0.386)N( \log _2 N ) + O(N) \] comparison-interchanges to sort a list of length N. This is an improvement of order $N(\log _2 N)$ over the best networks previously reported. (Using different methods, Van Voorhis [8] has improved upon these results.)

关键词： networks sorting networks sorting algorithms divide/sort/merge strategy

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Split Trees - A Unifying Model for Many Important Random Trees of Logarithmic Height: A Brief Survey 1st

Split Trees - A Unifying Model for Many Important Random Tre...

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1st IAPR International Joint Conference on Discrete Geometry and Mathematical Morphology (DGMM)

作者： Holmgren, Cecilia Uppsala Univ Dept Math Uppsala Sweden

ISBN: (纸本)9783030766566;9783030766573

Split trees were introduced by Devroye [28] as a novel approach for unifying many important random trees of logarithmic height. They are interesting not least because of their usefulness as models of sorting algorithms in computer science;for instance the well-known Quicksort algorithm (introduced by Hoare [35,36]) can be depicted as a binary search tree (which is one example of a split tree). A split tree of cardinality n is constructed by distributing n balls (which often represent data items) to a subset of nodes of an infinite tree. In [39], renewal theory was introduced by the author as a novel approach for studying split trees. This approach has proved to be highly useful for investigating such trees and has lead (often in combination with other methods) to several general results valid for all split trees. In this brief survey, we will present split trees, give an introduction to renewal theory in relation to split trees and describe some of the characteristics of split trees including results on the depths for the balls and nodes in the tree, the height (maximal depth) of the tree and the size of the tree in terms of the number of nodes;see [11,17,18,28,39]. Furthermore, we will briefly describe some of our later results for this large class of random trees, e.g. on the total path length [19], number of cuttings [12,21,38] and number of inversions (and more general permutations) [2,20] as well as on the size of the giant and other components after bond percolation [11,13].

关键词： Random trees Split trees sorting algorithms Quicksort Binary search tree Renewal theory Contraction method Limit laws Size Depths Height Total path length Inversions Cuttings Bond percolation

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Teaching Parallel Programming to Freshmen in an Undergraduate Computer Science Program 49

Teaching Parallel Programming to Freshmen in an Undergraduat...

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49th IEEE Frontiers in Education Conference (FIE)

作者： Vasconcelos, Leonardo B. A. Soares, Felipe A. L. Penna, Pedro Henrique M. M. Machado, Max V. Goes, Luis Fabricio W. Martins, Carlos Augusto P. S. Freitas, Henrique C. Pontificia Univ Catolica Minas Gerais Dept Comp Sci Belo Horizonte MG Brazil

ISBN: (纸本)9781728117461

This Research to Practice Full Paper proposes a teaching approach that introduces parallel programming early in the undergraduate Computer Science curriculum. Experiments were conducted to freshmen in the second course of algorithms and data structures. The strategy for the evaluation of the early education of parallel programming includes the use of OpenMP Application Programming Interface and sorting algorithms. The results indicate that students improved their skills by participating in parallel programing activities introduced at early stages or even at the very beginning of the undergraduate program. Freshmen could hit about 92%, 63% and 44% of easy, medium and hard questions after theoretical and practice activities. This represents an improvement about 19%, 14% and 39% 14 each respective difficulty level in comparison to the beginning of the study when all freshmen had no knowledge relative to parallel programming. These results aid to demystify parallel programming and to show that freshmen can learn it.

关键词： Teaching parallel programming freshmen sorting algorithms OpenMP undergraduate curriculum

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Travel Kinematics in Virtual Reality Increases Learning Efficiency

Travel Kinematics in Virtual Reality Increases Learning Effi...

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IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)

作者： Nersesian, Eric Vinnikov, Margarita Lee, Michael J. New Jersey Inst Technol Dept Informat Newark NJ 07102 USA

ISBN: (纸本)9781665445924

Virtual reality (VR) computer interfaces show promise for improving societal communication and representation of information due to their unique ability to be placed spatially around the user in three-dimensional (3D) space. This opens new possibilities for presentation and user interaction with the target information, and may be especially impactful for the education of science, technology, engineering, and mathematics (STEM) professionals. Simulations and visualizations have been shown in research studies to improve the efficiency of STEM learners compared to the less sensorimotor rich learning mediums of live instruction and textbook reading. Yet, learning science research into immersive computer simulation environments for educational applications remains limited. To address this research gap, we analyzed a fundamental VR interface capability, virtual environmental traversal, and its impact on participants' learning. We altered the traversal ability between two groups of STEM learners within the same virtual environment and compared their performance. Findings point that VR computer interfaces, regardless of environmental traversal, are suitable STEM learning environments, but that environmental traversal can increase learning efficiency.

关键词： virtual reality educational technology computer science education STEM education sorting algorithms

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Neurons Can Sort Data Efficiently 16th

Neurons Can Sort Data Efficiently

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16th International Conference on Artificial Intelligence and Soft Computing (ICAISC)

作者： Horzyk, Adrian AGH Univ Sci & Technol Dept Automat & Biomed Engn Mickiewicza Ave 30 PL-30059 Krakow Poland

ISBN: (纸本)9783319590639;9783319590622

This paper introduces an efficient sorting algorithm that uses new models of receptors and neurons which apply the time-conditional approach characteristic for nervous systems. These models have been successfully applied to automatically construct neural graphs that consolidate representation of all sorted objects and relations between them. The introduced parallely working algorithm sorts objects simultaneously for all attributes constructing an active associative neural graph representing all sorted objects in linear time. The sequential version works in linear or sub-linearithmic time. The paper argues that neurons can be used for efficient sorting of objects and the constructed network can be further used to explore relationships between these objects.

关键词： Brain-inspired computations Neuron models sorting algorithms ASSORT Associative representation Computational complexity

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