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On the analysis of stochastic divide and conquer algorithms

algorithmICA 2001年第1-2期29卷 238-261页

作者： Rösler, U Univ Kiel Math Seminar D-24098 Kiel Germany

This paper develops general tools for the analysis of stochastic divide and conquer algorithms. we concentrate on the average performance and the distribution of the running time of the algorithm. As a special example... 详细信息

关键词： recursive equation asymptotics divide and conquer algorithm average analysis renewal process renewal equation cauchy problem dirichlet problem invariant function

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Ensuring High Visibility of Passive Markers at Fixed Camera Gain Using divide and conquer Method

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IEEE ROBOTICS AND AUTOMATION LETTERS 2024年第11期9卷 9741-9748页

作者： Retinger, Marek Michalski, Jacek Kozierski, Piotr Drapikowski, Pawel Poznan Univ Tech Inst Robot & Machine Intelligence PL-60965 Poznan Poland

The letter presents a novel solution to determine exposure and threshold values for cameras in motion capture systems without excessive interaction with the user. The solution is based on the divide and conquer method, which ensures a fast and efficient search of the values. As the results have shown, users without specialist knowledge can significantly improve the tracking capabilities of the motion capture system, especially for smaller passive markers. The tests have proved that for spherical markers with a diameter of 7.9 mm, the full time tracking capabilities can be ensured based on the settings determined with the proposed method, what is difficult to achieve with the default settings. Moreover, the cameras utilisation can be increased, which should have a positive effect on the overall tracking quality. This makes it possible to use smaller and lighter-weight markers, which is desirable for small flying units with payload capacity of a few grams only. The primary tests were performed in the laboratory equipped with 12 OptiTrack Prime(x) 13W cameras. The dedicated programming interfaces (Motive API and Camera SDK) were used. The validation tests included a DJI Tello EDU unit with four markers attached. In addition to analysis and considerations, the document includes pseudocodes that clearly explain the idea behind the algorithms and allow for an easy implementation of the solution.

关键词： Cameras Indexes Robot vision systems Motion capture Tracking Accuracy Software algorithms Visual tracking methods and tools for robot system design motion capture divide and conquer algorithm

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divide and conquer Roadmap for Algebraic Sets

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DISCRETE & COMPUTATIONAL GEOMETRY 2014年第2期52卷 278-343页

作者： Basu, Saugata Roy, Marie-Francoise Purdue Univ Dept Math W Lafayette IN 47907 USA Univ Rennes 1 IRMAR CNRS UMR 6625 F-35042 Rennes France

Let R be a real closed field and D subset of R an ordered domain. We describe an algorithm that given as input a polynomial P is an element of D[X-1, ... , X-k] and a finite set, A = {p(1), ... , p(m)}, of points contained in V = Zer(P, R-k) described by real univariate representations, computes a roadmap of V containing A. The complexity of the algorithm, measured by the number of arithmetic operations in D, is bounded by(Sigma D-m(i-1)i(O(log2(k))) + 1 (k(log(k)) d)(O(log2(k))), where d = deg(P) and D-i is the degree of the real univariate representation describing the point p(i). The best previous algorithm for this problem had complexity card (A)(O(1))d(O(k3/2)) (Basu et al., ArXiv, 2012), where it is assumed that the degrees of the polynomials appearing in the representations of the points in A are bounded by d(O(k)). As an application of our result we prove that for any real algebraic subset V of R-k defined by a polynomial of degree d, any connected component C of V contained in the unit ball, and any two points of C, there exists a semi-algebraic path connecting them in C, of length at most (k(log(k)) d)(O(k log(k))), consisting of at most (k(log(k))d)(O(k log(k))) curve segments of degrees bounded by (k(log(k)) d)(O(k log(k))). While it was known previously, by a result of D'Acunto and Kurdyka (Bull Lond Math Soc 38(6): 951-965, 2006), that there always exists a path of length (O(d))(k-1) connecting two such points, there was no upper bound on the complexity of such a path.

关键词： Real algebraic varieties Roadmaps divide and conquer algorithm

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Least Squares Model Averaging for Distributed Data

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JOURNAL OF MACHINE LEARNING RESEARCH 2023年第1期24卷 1-59页

作者： Zhang, Haili Liu, Zhaobo Zou, Guohua Shenzhen Polytech Univ Inst Appl Math Shenzhen 518055 Peoples R China Shenzhen Univ Inst Adv Study Shenzhen 518060 Peoples R China Capital Normal Univ Sch Math Sci Beijing 100048 Peoples R China

divide and conquer algorithm is a common strategy applied in big data. Model averaging has the natural divide-and-conquer feature, but its theory has not been developed in big data scenarios. The goal of this paper is to fill this gap. We propose two divide-and conquer-type model averaging estimators for linear models with distributed data. Under some regularity conditions, we show that the weights from Mallows model averaging criterion converge in L-2 to the theoretically optimal weights minimizing the risk of the model averaging estimator. We also give the bounds of the in-sample and out-of-sample mean squared errors and prove the asymptotic optimality for the proposed model averaging estimators. Our conclusions hold even when the dimensions and the number of candidate models are divergent. Simulation results and a real airline data analysis illustrate that the proposed model averaging methods perform better than the commonly used model selection and model averaging methods in distributed data cases. Our approaches contribute to model averaging theory in distributed data and parallel computations, and can be applied in big data analysis to save time and reduce the computational burden.

关键词： consistency distributed data divide and conquer algorithm Mallows' criterion model averaging optimality

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Sparse grid distance transforms

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GRAPHICAL MODELS 2010年第4期72卷 35-45页

作者： Michikawa, Takashi Suzuki, Hiromasa Univ Tokyo RCAST Tokyo 1138654 Japan

We present a Sparse Grid Distance Transform (SGDT) an algorithm for computing and storing large distance fields Although SGDT is based on a divide-and conquer algorithm for distance transforms its data structure is quite simplified Our observations revealed that distance fields can be recovered from distance fields of sub block cluster boundaries and the binary information of the cluster through a one-time distance transform This means that it is sufficient to consider only the cluster boundaries and to represent clusters as binary volumes As a result memory usage is less than 0 5% the size of raw files and it works in-core (C) 2010 Elsevier Inc All rights reserved

关键词： Distance fields Volume graphics divide and conquer algorithm

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A parallelizable eigensolver for real diagonalizable matrices with real eigenvalues

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 1997年第3期18卷 869-885页

作者： HussLederman, S Tsao, A Turnbull, T Center for Computing Sciences Bowie MD 20715 17100 Science Drive United States

In this paper, preliminary research results on a new algorithm for finding all the eigenvalues and eigenvectors of a real diagonalizable matrix with real eigenvalues are presented. The basic mathematical theory behind this approach is reviewed and is followed by a discussion of the numerical considerations of the actual implementation. The numerical algorithm has been tested on thousands of matrices on both a Gray-2 and an IBM RS/6000 Model 580 workstation. The results of these tests are presented. Finally, issues concerning the parallel implementation of the algorithm are discussed. The algorithm's heavy reliance on matrix-matrix multiplication, coupled with the divide and conquer nature of this algorithm, should yield a highly parallelizable algorithm.

关键词： eigenvalues divide and conquer algorithm invariant subspaces parallel algorithm

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A design and development of an intelligent jammer and jamming detection methodologies using machine learning approach

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CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS 2019年第1期22卷 93-101页

作者： Sivaprakash, S. Venkatesan, M. KSR Coll Engn Dept Comp Sci & Engn Namakkal 637215 Tamil Nadu India KSR Inst Engn & Technol Dept Comp Sci & Engn Namakkal 637215 Tamil Nadu India

Nowadays, the utilization of mobile phones has increased rapidly. Due to this evolution schools, mosques, prisons, etc., require silence and security. This is achieved by using the mobile phone jammers. An intelligent mobile jammer is designed for allowing only the emergency calls by utilizing the microcontroller. Here, the jammer utilizes the successive approximation for reducing the transmission power. However, it requires few modifications. Therefore in this paper, an improved successive approximation based on divide and conquer algorithm is proposed in order to design the improved intelligent mobile jammer and reduce transmission power. Subsequently, the proposed jammer is analysed based on the different scenarios and frequency bands to illustrate their performance effectiveness. Furthermore, the normal activities are distinguished from jamming by using machine learning-based detection system according to the various parameters. Finally, the proposed algorithm is compared with conventional algorithms to demonstrate its performance efficiency in terms of detection accuracy.

关键词： Mobile phone jammer Successive approximation Binary search algorithm divide and conquer algorithm Machine learning algorithm

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The Quicksort process

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2014年第2期124卷 1036-1054页

作者： Ragab, Mahmoud Roesler, Uwe Al Azhar Univ Fac Sci Dept Math Cairo 11884 Egypt Christian Albrechts Univ Kiel Math Seminar D-24098 Kiel Germany

Quicksort on the fly returns the input of n reals in increasing natural order during the sorting process. Correctly normalized the running time up to returning the l-th smallest out of n seen as a process in 1 converges weakly to a limiting process with path in the space of cadlag functions. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Sorting Quicksort divide and conquer algorithm Random algorithm Running time analysis Stochastic process Cadlag functions Asymptotics Skorodhod metric

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Exponential tail bounds for max-recursive sequences

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ELECTRONIC COMMUNICATIONS IN PROBABILITY 2006年第none期11卷 266-277页

作者： Rueschendorf, Ludger Schopp, Eva-Maria Univ Freiburg Dept Math Stochast D-79104 Freiburg Germany

Exponential tail bounds are derived for solutions of max-recursive equations and for max-recursive random sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise in the worst case analysis of divide and conquer algorithms, in parallel search algorithms or in the height of random tree models. For the proof we determine asymptotic bounds for the moments or for the Laplace transforms and apply a characterization of exponential tail bounds due to Kasahara (1978).

关键词： recursive algorithm exponential bounds divide and conquer algorithm probabilistic analysis of algorithms

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Multisite tumor sampling enhances the detection of intratumor heterogeneity at all different temporal stages of tumor evolution

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VIRCHOWS ARCHIV 2018年第2期472卷 187-194页

作者： Erramuzpe, Asier Cortes, Jesus M. Lopez, Jose I. Biocruces Res Inst Quantitat Biomed Unit Baracaldo 48903 Spain Ikerbasque Basque Fdn Sci Bilbao 48013 Spain Univ Basque Country UPV EHU Dept Cell Biol & Histol Leioa 48940 Spain Cruces Univ Hosp Dept Pathol Plaza Cruces S-N Baracaldo 48903 Bizkaia Spain Biocruces Res Inst Biomarkers Canc Unit Baracaldo 48903 Spain Univ Basque Country UPV EHU Leioa 48940 Spain

Intratumor heterogeneity (ITH) is an inherent process of tumor development that has received much attention in previous years, as it has become a major obstacle for the success of targeted therapies. ITH is also temporally unpredictable across tumor evolution, which makes its precise characterization even more problematic since detection success depends on the precise temporal snapshot at which ITH is analyzed. New and more efficient strategies for tumor sampling are needed to overcome these difficulties which currently rely entirely on the pathologist's interpretation. Recently, we showed that a new strategy, the multisite tumor sampling, works better than the routine sampling protocol for the ITH detection when the tumor time evolution was not taken into consideration. Here, we extend this work and compare the ITH detections of multisite tumor sampling and routine sampling protocols across tumor time evolution, and in particular, we provide in silico analyses of both strategies at early and late temporal stages for four different models of tumor evolution (linear, branched, neutral, and punctuated). Our results indicate that multisite tumor sampling outperforms routine protocols in detecting ITH at all different temporal stages of tumor evolution. We conclude that multisite tumor sampling is more advantageous than routine protocols in detecting intratumor heterogeneity.

关键词： Tumor sampling Personalized Intratumor heterogeneity Tumor evolution In silico analysis divide and conquer algorithm Personalized therapy

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