We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space and we compare it with the deterministic a...
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We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space and we compare it with the deterministic algorithm regarding generalized iterated function systems presented by Jaros et al. (Numer. algorithms 73, 477-499, 2016).
Motivated by some algorithmic problems, we give lower bounds on the size of the multiplicative groups containing rational function images of low-dimensional affine subspaces of a finite field F-qn considered as a line...
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Motivated by some algorithmic problems, we give lower bounds on the size of the multiplicative groups containing rational function images of low-dimensional affine subspaces of a finite field F-qn considered as a linear space over a subfield F-q. We apply this to the recently introduced algorithmic problem of identity testing of "hidden" polynomials f and g over a high degree extension of a finite field, given oracle access to f(x)(e) and g(x)(e).
We study broadcasting in multiple access channels with dynamic packet arrivals and jamming. Communication environments are represented by adversarial models that specify constraints on packet arrivals and jamming. We ...
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We study broadcasting in multiple access channels with dynamic packet arrivals and jamming. Communication environments are represented by adversarial models that specify constraints on packet arrivals and jamming. We consider deterministic distributed broadcast algorithms and give upper bounds on the worst-case packet latency and the number of queued packets in relation to the parameters defining adversaries. Packet arrivals are determined by a rate of injections and a number of packets that can be generated in one round. Jamming is constrained by a rate with which an adversary can jam rounds and by a number of consecutive rounds that can be jammed. (C) 2018 Elsevier Inc. All rights reserved.
Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting m...
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Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF), which can obtain reliable and consistent results for real images. Specifically, SDF includes three main parts: a deterministic sampling algorithm, a model hypothesis updating strategy and a novel model selection algorithm. The proposed deterministic sampling algorithm generates a set of initial model hypotheses according to the prior information of superpixels. Then the proposed updating strategy further improves the quality of model hypotheses. After that, by analyzing the properties of the updated model hypotheses, the proposed model selection algorithm extends the conventional fit-and-remove framework to estimate model instances in multiple-structure data. The three parts are tightly coupled to boost the performance of SDF in both speed and accuracy, and SDF has the deterministic nature. Experimental results show that the proposed SDF has significant advantages over several state-of-the-art fitting methods when it is applied to real images with single-structure and multiple-structure data.
The key objects in the group-theoretic approach to matrix multiplication are subsets of a group satisfying the so-called triple product property (TPP). In this paper, we focus on the problem of efficiently finding the...
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The key objects in the group-theoretic approach to matrix multiplication are subsets of a group satisfying the so-called triple product property (TPP). In this paper, we focus on the problem of efficiently finding the triple product property triples. We deduce and present some new characteristics of the triple product property. Using these new characteristics, we firstly propose an efficient deterministic algorithm in which a screening process based on historical information is designed to reduce the search space. In contrast to some of the recent heuristic search methods, the proposed deterministic algorithm can search all kinds of TPP triples in a highly efficient way with the help of a novel representation for subsets and a Moving I principle. In addition, we also propose an efficient randomized algorithm for finding TPP triples, which adopts a greedy randomized strategy to randomly generate possible TPP candidates. Experimental results demonstrate that our proposed deterministic algorithm can achieve a huge speed-up in terms of running time compared with the existing deterministic algorithm, and the proposed randomized algorithm outperforms other existing approaches for finding TPP triples. (C) 2018 Elsevier B.V. All rights reserved.
The Closest Pair problem aims to identify the closest pair (using some similarity measure, e.g., Euclidean distance, Dynamic Time Warping distance, etc.) of points in a metric space. This is one of the fundamental pro...
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The Closest Pair problem aims to identify the closest pair (using some similarity measure, e.g., Euclidean distance, Dynamic Time Warping distance, etc.) of points in a metric space. This is one of the fundamental problems that has a wide range of applications in the data mining area, since most of the data can be represented in a vector form residing in a high dimensional space, and we would like to identify the relationship among those data points. Typical applications include but not limited to, social data analysis, user pattern identification, motif mining in biological data, data clustering, etc. This is a very classical problem and has been studied very well in the past *** this thesis, we study the Closest Pair problem and its variants, and also bring the machine learning perspective to solve some closely related problems. In particular, we have proposed two approximate algorithms to efficiently address the Closest Pair of Points (CPP) problem, and one deterministic approach to solve the Closest Pair of Subsequences (CPS) problem, using Euclidean distance measure. In addition, to identify the closest subsequences in the time series data, we have proposed a learnable feature extractor embedded in an artificial neural network, to learn patterns in the scope of the Dynamic Time Warping metric. In the end, to speed up the inference speed of the proposed algorithm, we have also proposed a neural network pruning technique to obtain a smaller network with similar *** the proposed methods are shown to have achieved the state-of-the-art performance in various standard benchmark datasets.
A team of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node and declare that they have all met. Agents have different labels which are posit...
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ISBN:
(纸本)9781450375825
A team of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node and declare that they have all met. Agents have different labels which are positive integers, and move in synchronous rounds along links of the network. The above task is known as gathering and was traditionally considered under the assumption that when some agents are at the same node then they can talk, i.e., exchange currently available information. In this paper we ask the question of whether this ability of talking is needed for gathering. The answer turns out to be no. Our main contribution are two deterministic algorithms that always accomplish gathering in a much weaker model. We only assume that at any time an agent knows how many agents are at the node that it currently occupies but agents do not see the labels of other co-located agents and cannot exchange any information with them. They also do not see other nodes than the current one. Our first algorithm works under the assumption that agents know a priori some upper bound N on the size of the network, and it works in time polynomial in N and in the length l of the smallest label. Our second algorithm does not assume any a priori knowledge about the network but its complexity is exponential in the size of the network and in the labels of agents. Its purpose is to show feasibility of gathering under this harsher scenario. As a by-product of our techniques we obtain, in the same weak model, the solution of the fundamental problem of leader election among agents: One agent is elected a leader and all agents learn its identity. As an application of our result we also solve, in the same model, the well-known gossiping problem: if each agent has a message at the beginning, we show how to make all messages known to all agents, even without any a priori knowledge about the network. If agents know an upper bound N on the size of the network then our gossiping algorithm works in
We consider arbitrary graphs G with n vertices and minimum degree at least delta n where delta > 0 is constant. (a) If the conductance of G is sufficiently large, then we obtain an asymptotic expression for the cov...
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We consider arbitrary graphs G with n vertices and minimum degree at least delta n where delta > 0 is constant. (a) If the conductance of G is sufficiently large, then we obtain an asymptotic expression for the cover time C-G of G as the solution to an explicit transcendental equation. (b) If the conductance is not large enough to apply (a), but the mixing time of a random walk on G is of a lesser magnitude than the cover time, then we can obtain an asymptotic deterministic estimate via a decomposition into a bounded number of dense subgraphs with high conductance. (c) If G fits neither (a) nor (b), then we give a deterministic asymptotic (2+o(1))-approximation of C-G.
Recently, a class of low-density parity-check (LDPC) codes from affine permutation matrices, called APM-LDPC codes, have attracted because of some advantages rather than QC-LDPC codes in minimum-distance, girth, cycle...
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Recently, a class of low-density parity-check (LDPC) codes from affine permutation matrices, called APM-LDPC codes, have attracted because of some advantages rather than QC-LDPC codes in minimum-distance, girth, cycle distribution and error-rate performance. In this study, a new class of LDPC codes based on Mobius transformations, called MT-LDPC codes, are presented as a generalisation of APM-LDPC codes which have some new achievements rather than QC and APM LDPC codes in the terms of length, cycle distribution and error-rate performance. Moreover, each Mobius transformation is represented by a square matrix which is helpful to pursuing the cycles in the Tanner graph of an MT-LDPC code by the product of some square matrices. In continue, for a given base matrix, the authors propose a deterministic algorithm which efficiently produces MT-LDPC codes with the desired girth. Simulation results show that the binary and non-binary constructed MT-LDPC codes outperform APM, QC, PEG, random-like and some algebraic LDPC codes with the same rates and lengths.
Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high dimensional data. However, classical PCA is ve...
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Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high dimensional data. However, classical PCA is very sensitive to atypical data. Robust methods to estimate the low-dimensional subspace that best approximates the regular data have been proposed. However, for high-dimensional data these algorithms become computationally expensive. Alternative algorithms for the robust subspace estimators are proposed that are better suited to compute the solution for high-dimensional problems. The main ingredients of the new algorithms are twofold. First, the principal directions of the subspace are estimated directly by iterating the first order solutions corresponding to the estimators. Second, to reduce the computation time even further five robust deterministic values are proposed to initialize the algorithms instead of using random starting values. It is shown that the new algorithms yield robust solutions and the computation time is largely reduced, especially for high-dimensional data. (C) 2019 Elsevier B.V. All rights reserved.
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