Recent zbMATH articles in MSC 68Uhttps://www.zbmath.org/atom/cc/68U2021-04-16T16:22:00+00:00WerkzeugBook review of: P. Murrell, R graphics.https://www.zbmath.org/1456.000312021-04-16T16:22:00+00:00"Nielsen, Søren Feodor"https://www.zbmath.org/authors/?q=ai:nielsen.soren-feodorReview of [Zbl 1075.68095].Parallelizable global conformal parameterization of simply-connected surfaces via partial welding.https://www.zbmath.org/1456.650142021-04-16T16:22:00+00:00"Choi, Gary P. T."https://www.zbmath.org/authors/?q=ai:choi.gary-pui-tung"Leung-Liu, Yusan"https://www.zbmath.org/authors/?q=ai:leung-liu.yusan"Gu, Xianfeng"https://www.zbmath.org/authors/?q=ai:gu.xianfeng"Lui, Lok Ming"https://www.zbmath.org/authors/?q=ai:lui.lok-mingImage encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory.https://www.zbmath.org/1456.680342021-04-16T16:22:00+00:00"Wang, Xingyuan"https://www.zbmath.org/authors/?q=ai:wang.xingyuan"Gao, Suo"https://www.zbmath.org/authors/?q=ai:gao.suoSummary: This paper studies chaotic image encryption technology and an application of matrix semi-tensor product theory, and a Boolean network encryption algorithm for a synchronous update process is proposed. A 2D-LASM chaotic system is used to generate a random key stream. First, a Boolean network is coded, and a Boolean matrix is generated. If necessary, the Boolean network matrix is diffused in one round so that the Boolean matrix can be saved in the form of an image. Then, three random position scramblings are used to scramble the plaintext image. Finally, using a matrix semi-tensor product technique to generate an encrypted image in a second round of diffusion, a new Boolean network can be generated by encoding the encrypted image. In secure communications, users can choose to implement an image encryption transmission or a Boolean network encryption transmission according to their own needs. Compared with other algorithms, this algorithm exhibits good security characteristics.Do recommender systems benefit users? A modeling approach.https://www.zbmath.org/1456.911082021-04-16T16:22:00+00:00"Yeung, Chi Ho"https://www.zbmath.org/authors/?q=ai:yeung.chi-hoFunctional dependencies in incomplete databases with limited domains.https://www.zbmath.org/1456.680282021-04-16T16:22:00+00:00"Alattar, Munqath"https://www.zbmath.org/authors/?q=ai:alattar.munqath"Sali, Attila"https://www.zbmath.org/authors/?q=ai:sali.attila|sali.attila-senSummary: Missing data value is an extensive problem in both research and industrial developers. Two general approaches are there to deal with the problem of missing values in databases, they either could be ignored (removed) or imputed (filled in) with new values
[\textit{A. Farhangfar} et al., ``A novel framework for imputation of missing values in databases'', IEEE Trans. Syst., Man, Cybern. A, Syst. Humans 37, No. 5, 692--709 (2007; \url{doi:10.1109/TSMCA.2007.902631})].
In the present paper, we use the second method. Possible worlds were introduced in
[\textit{H. Köhler} et al., ``Possible and certain keys for SQL'', VLDB J. 25, 571--596 (2016; \url{doi:10.1007/s00778-016-0430-9}); \textit{M. Levene} and \textit{G. Loizou}, Theor. Comput. Sci. 206, No. 1--2, 283--300 (1998; Zbl 0912.68025)]
and possible and certain keys, as well as weak and strong functional dependencies were studied. We introduced the intermediate concept of strongly possible worlds that are obtained by imputing values already existing in the table in a preceding paper. This results in strongly possible keys and strongly possible functional dependencies. We give a polynomial algorithm to verify a single spKey, and show that in general, it is NP-complete to verify an arbitrary collection of spKeys. We give a graph theoretical characterization of the validity of a given spFD \(X\rightarrow_{\mathrm{sp}}Y\). We analyze which weak/strong functional dependency axioms remain sound for strongly possible functional dependencies and give appropriate modifications of the not sound ones.
For the entire collection see [Zbl 1435.68031].Book review of: A. Tramontano, Introduction to bioinformatics.https://www.zbmath.org/1456.000372021-04-16T16:22:00+00:00"Ruiz Espejo, Mariano"https://www.zbmath.org/authors/?q=ai:ruiz-espejo.mariano"Delgado Pineda, Miguel"https://www.zbmath.org/authors/?q=ai:delgado-pineda.miguelReview of [Zbl 1115.92022].Sylvester-Gallai type theorems for quadratic polynomials.https://www.zbmath.org/1456.680392021-04-16T16:22:00+00:00"Shpilka, Amir"https://www.zbmath.org/authors/?q=ai:shpilka.amirSummary: We prove Sylvester-Gallai type theorems for quadratic polynomials. Specifically, we prove that if a finite collection \(\mathcal{Q}\), of irreducible polynomials of degree at most 2, satisfy that for every two polynomials \(Q_1,Q_2\in\mathcal{Q}\) there is a third polynomial \(Q_3\in\mathcal{Q}\) so that whenever \(Q_1\) and \(Q_2\) vanish then also \(Q_3\) vanishes, then the linear span of the polynomials in \(\mathcal{Q}\) has dimension \(O(1)\). We also prove a colored version of the theorem: If three finite sets of quadratic polynomials satisfy that for every two polynomials from distinct sets there is a polynomial in the third set satisfying the same vanishing condition then all polynomials are contained in an \(O(1)\)-dimensional space. This answers affirmatively two conjectures of
\textit{A. Gupta} [``Algebraic geometric techniques for depth-4 PIT \& Sylvester-Gallai conjectures for varieties'', Techn. Rep. TR14-130, Electronic Colloquium on Computational Complexity (ECCC). 29 p. (2014)]
that were raised in the context of solving certain depth-4 polynomial identities.
To obtain our main theorems we prove a new result classifying the possible ways that a quadratic polynomial \(Q\) can vanish when two other quadratic polynomials vanish. Our proofs also require robust versions of a theorem of
\textit{M. Edelstein} and \textit{L. M. Kelly} [Can. J. Math. 18, 375--380 (1966; Zbl 0141.30802)]
(that extends the Sylvester-Gallai theorem to colored sets).Robust reversible data hiding scheme based on two-layer embedding strategy.https://www.zbmath.org/1456.682232021-04-16T16:22:00+00:00"Kumar, Rajeev"https://www.zbmath.org/authors/?q=ai:kumar.rajeev"Jung, Ki-Hyun"https://www.zbmath.org/authors/?q=ai:jung.ki-hyunSummary: Robust reversible data hiding (RRDH) prevents the hidden secret information from unintentional modifications. This paper presents a novel RRDH scheme based on two-layer embedding with reduced capacity-distortion trade-off. The proposed scheme first decomposes the image into two planes namely higher significant bit (HSB) and least significant bit (LSB) planes and then employs prediction error expansion (PEE) to embed the secret data into the HSB plane. The high correlation of HSB plane helps in achieving high embedding capacity. Further, non-malicious attacks such as Joint Photographic Experts Group (JPEG) compression which usually changes the LSBs, will not cause any disturbance to the main contents of original image and the hidden secret data. The experimental results show that the proposed scheme has superior performance than the previous works.Quaternion weighted spherical Bessel-Fourier moment and its invariant for color image reconstruction and object recognition.https://www.zbmath.org/1456.682252021-04-16T16:22:00+00:00"Yang, Tengfei"https://www.zbmath.org/authors/?q=ai:yang.tengfei"Ma, Jianfeng"https://www.zbmath.org/authors/?q=ai:ma.jianfeng"Miao, Yinbin"https://www.zbmath.org/authors/?q=ai:miao.yinbin"Wang, Xuan"https://www.zbmath.org/authors/?q=ai:wang.xuan"Xiao, Bin"https://www.zbmath.org/authors/?q=ai:xiao.bin"He, Bing"https://www.zbmath.org/authors/?q=ai:he.bing.1|he.bing|he.bing.2|he.bing.4|he.bing.3"Meng, Qian"https://www.zbmath.org/authors/?q=ai:meng.qianSummary: Moments with capable of representing global features have been widely used in image analysis, pattern recognition and computer vision applications. However, existing image moment theories are still mainly paid close attention to gray-scale images. In this paper, a new quaternion moment termed as Quaternion weighted Spherical Bessel-Fourier Moment (QSBFM) is proposed to address the issue of color image analysis. Moreover, the relationship between QSBFM and the conventional weighted spherical Bessel-Fourier moment has been established so that the computational cost of QSBFM can be efficiently reduced. Furthermore, the natively geometric invariance of QSBFM is presented and discussed in detail. Experimental results show that the proposed QSBFM outperforms frequently-used quaternion moments including quaternion Bessel-Fourier moment, quaternion Radial-Harmonic-Fourier moment, quaternion Chebyshev-Fourier moment and quaternion orthogonal Fourier-Mellin moment in terms of the color image reconstruction capability and invariant recognition accuracy in noise-free, Salt \& Pepper noise and the Gaussian noise conditions.Tomographic reconstruction from a few views: a multi-marginal optimal transport approach.https://www.zbmath.org/1456.490352021-04-16T16:22:00+00:00"Abraham, I."https://www.zbmath.org/authors/?q=ai:abraham.isabelle"Abraham, R."https://www.zbmath.org/authors/?q=ai:abraham.romain"Bergounioux, M."https://www.zbmath.org/authors/?q=ai:bergounioux.maitine"Carlier, G."https://www.zbmath.org/authors/?q=ai:carlier.guillaumeSummary: In this article, we focus on tomographic reconstruction. The problem is to determine the shape of the interior interface using a tomographic approach while very few X-ray radiographs are performed. We use a multi-marginal optimal transport approach. Preliminary numerical results are presented.Marcus-Wyse topological rough sets and their applications.https://www.zbmath.org/1456.682222021-04-16T16:22:00+00:00"Han, Sang-Eon"https://www.zbmath.org/authors/?q=ai:han.sang-eonSummary: The aim of this paper is to establish two new types of rough set structures associated with the Marcus-Wyse (MW, for brevity) topology, such as an M-rough set and an MW-topological rough set. The former focuses on studying the rough set theoretic tools for 2-dimensional Euclidean spaces and the latter contributes to the study of the rough set structures for digital spaces in \(\mathbb{Z}^2\), where \(\mathbb{Z}\) is the set of integers. These two rough set structures are related to each other via an M-digitization. Thus, these can successfully be used in the field of applied science, such as digital geometry, image processing, deep learning for recognizing digital images, and so on. For a locally finite covering approximation (LFC, for short) space \((U, \mathbf{C})\) and a subset \(X\) of \(U\), we firstly introduce a new neighborhood system on \(U\) related to \(X\). Next, we formulate the lower and upper approximations with respect to \(X\), where all of the sets \(U\) and \(X(\subseteq U)\) need not be finite and the covering \( \mathbf{C}\) is locally finite. Actually, the notion of M-digitization of a 2-dimensional Euclidean space plays an important role in developing an M-rough and MW-topological rough set structures. Further, we prove that M-rough set operators have a duality between them. However, each of MW-topological rough set operators need not have the property as an interior or a closure from the viewpoint of MW-topology.Time-aware link prediction based on strengthened projection in bipartite networks.https://www.zbmath.org/1456.622232021-04-16T16:22:00+00:00"Aslan, Serpil"https://www.zbmath.org/authors/?q=ai:aslan.serpil"Kaya, Buket"https://www.zbmath.org/authors/?q=ai:kaya.buketSummary: The traditional projection models in the bipartite networks involve many node pairs that consist of weak relationships. These node pairs lead to poor quality predictions as well as high computation time. In this paper, to cope with these problems, we firstly propose a novel projection model, which is called ``Strengthened Projection Model''. Then, to predict the potential links in the future, we present a new link prediction approach based on the proposed projection model. Thanks to the proposed model, the computation time is shortened, and the high probability predictions are extracted. The majority of the previous works conducted in this area have used the classical proximity measure algorithms that only take into account the current network structure, regardless of when events occur in the network evolution. To overcome these limited methods, in this paper, we also propose a novel proximity measure algorithm that considers the bipartite network evolution. To the best of our knowledge, this is the first attempt that takes into account the time-awareness in bipartite networks. To evaluate the performance of our proposed approach, we conducted experiments on the academic information network. To construct this bipartite network, we collected data from IEEE Xplore. The experimental results show that the success of the proposed method is promising.Reconstruction of convex bodies from moments.https://www.zbmath.org/1456.520052021-04-16T16:22:00+00:00"Kousholt, Astrid"https://www.zbmath.org/authors/?q=ai:kousholt.astrid"Schulte, Julia"https://www.zbmath.org/authors/?q=ai:schulte.juliaSummary: We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which are uniquely determined by a finite number of moments form a dense set. Further, we derive a stability result for convex bodies based on geometric moments. It turns out that the stability result is improved considerably by using another set of moments, namely Legendre moments. We present a reconstruction algorithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stability result for Legendre moments. When only noisy measurements of Legendre moments are available, the consistency of the algorithm is established under certain assumptions on the variance of the noise variables.An efficient exhaustive search algorithm for the Escherization problem.https://www.zbmath.org/1456.520242021-04-16T16:22:00+00:00"Nagata, Yuichi"https://www.zbmath.org/authors/?q=ai:nagata.yuichi"Imahori, Shinji"https://www.zbmath.org/authors/?q=ai:imahori.shinjiSummary: In the Escherization problem, given a closed figure in the plane, the objective is to find a closed figure that is as close as possible to the input figure that tiles the plane. Koizumi and Sugihara's formulation reduces this problem to an eigenvalue problem. In their formulation, only one of the potentially numerous templates is used to parameterize the possible tile shapes for each isohedral type. In this research, we try to search for the best tile shape using all possible templates for the nine most general isohedral types. This extension provides a considerable flexibility in possible tile shapes and improves the quality of the obtained tile shapes. However, the exhaustive search of all possible templates is computationally unrealistic using conventional calculation methods, and we develop an efficient algorithm to perform this in a reasonable computation time.Approximation of intuitionistic fuzzy Bézier curve model.https://www.zbmath.org/1456.650152021-04-16T16:22:00+00:00"Zulkifly, M. I. E."https://www.zbmath.org/authors/?q=ai:zulkifly.m-i-e"Wahab, A. F."https://www.zbmath.org/authors/?q=ai:wahab.abd-fatah|wahab.abdul-fatah"Yusoff, B."https://www.zbmath.org/authors/?q=ai:yusoff.bSummary: In this paper, approximation of Bézier curve by using intuitionistic fuzzy approach is introduced. Firstly, intuitionistic fuzzy point relation is defined based on intuitionistic fuzzy concept to yield intuitionistic fuzzy control point. Some theorems of intuitionistic fuzzy point relation are also introduced. Later, the intuitionistic fuzzy control point is blended with Bernstein blending function and intuitionistic fuzzy Bézier curve model is produced. Next, the approximation curves consists of membership, non-membership and uncertainty curves is visualized. A numerical example is shown and the introduced Bézier curve properties are also discussed. Finally, an algorithm to obtain intuitionistic fuzzy Bézier curve is presented at the end of this paper.Optimization of the algorithm for determining the Hausdorff distance for convex polygons.https://www.zbmath.org/1456.901572021-04-16T16:22:00+00:00"Danilov, Dmitry I."https://www.zbmath.org/authors/?q=ai:danilov.dmitry-i"Lakhtin, Alexey S."https://www.zbmath.org/authors/?q=ai:lakhtin.alexey-sSummary: The paper provides a brief historical analysis of problems that use the Hausdorff distance; provides an analysis of the existing Hausdorff distance optimization elements for convex polygons; and demonstrates an optimization approach. The existing algorithm served as the basis to propose low-level optimization with super-operative memory, ensuring the finding a precise solution by a full search of the corresponding pairs of vertices and sides of polygons with exclusion of certain pairs of vertices and sides of polygons. This approach allows a significant acceleration of the process of solving the set problem.CURE: curvature regularization for missing data recovery.https://www.zbmath.org/1456.621272021-04-16T16:22:00+00:00"Dong, Bin"https://www.zbmath.org/authors/?q=ai:dong.bin|dong.bin.1"Ju, Haocheng"https://www.zbmath.org/authors/?q=ai:ju.haocheng"Lu, Yiping"https://www.zbmath.org/authors/?q=ai:lu.yiping"Shi, Zuoqiang"https://www.zbmath.org/authors/?q=ai:shi.zuoqiangModeling mutual feedback between users and recommender systems.https://www.zbmath.org/1456.682262021-04-16T16:22:00+00:00"Zeng, An"https://www.zbmath.org/authors/?q=ai:zeng.an"Yeung, Chi Ho"https://www.zbmath.org/authors/?q=ai:yeung.chi-ho"Medo, Matúš"https://www.zbmath.org/authors/?q=ai:medo.matus"Zhang, Yi-Cheng"https://www.zbmath.org/authors/?q=ai:zhang.yichengReplication of a binary image on a one-dimensional cellular automaton with linear rules.https://www.zbmath.org/1456.681082021-04-16T16:22:00+00:00"Rao, U. Srinivasa"https://www.zbmath.org/authors/?q=ai:rao.u-srinivasa"Jeganathan, L."https://www.zbmath.org/authors/?q=ai:jeganathan.lSummary: A two-state, one-dimensional cellular automaton (1D CA) with uniform linear rules on an \((r+1)\)-neighborhood replicates any arbitrary binary image given as an initial configuration. By these linear rules, any cell gets updated by an EX-OR operation of the states of extreme (first and last) cells of its \((r+1)\)-neighborhood. These linear rules replicate the binary image in two ways on the 1D CA: one is without changing the position of the original binary image at time step \(t=0\) and the other is by changing the position of the original binary image at time step \(t=0\). Based on the two ways of replication, we have classified the linear rules into three types. In this paper, we have proven that the binary image of size \(m\) gets replicated exactly at time step \(2^k\) of the uniform linear rules on the \((r+1)\)-neighborhood 1D CA, where \(k\) is the least positive integer satisfying the inequality \(m/r\le 2^k\). We have also proved that there are exactly \((r*2^k-m)\) cells between the last cell of the binary image and the first cell of the replicated binary image (or the first cell of the binary image and the last cell of the replicated image).PSO image thresholding on images compressed via fuzzy transforms.https://www.zbmath.org/1456.682242021-04-16T16:22:00+00:00"Martino, Ferdinando Di"https://www.zbmath.org/authors/?q=ai:di-martino.ferdinando"Sessa, Salvatore"https://www.zbmath.org/authors/?q=ai:sessa.salvatoreSummary: We present a new multi-level image thresholding method in which a Chaotic Darwinian Particle Swarm Optimization algorithm is applied on images compressed by using Fuzzy Transforms. The method requires a partition of the pixels of the image under several thresholds which are obtained by maximizing a fuzzy entropy. The usage of compressed images produces benefits in terms of execution CPU times. In a pre-processing phase the best compression rate is found by comparing the grey level histograms of the source and compressed images. Comparisons with the classical Darwinian Particle Swarm Optimization multi-level image thresholding algorithm and other meta-heuristic algorithms are presented in terms of quality of the segmented image via PSNR and SSIM.Exact recovery of multichannel sparse blind deconvolution via gradient descent.https://www.zbmath.org/1456.650432021-04-16T16:22:00+00:00"Qu, Qing"https://www.zbmath.org/authors/?q=ai:qu.qing"Li, Xiao"https://www.zbmath.org/authors/?q=ai:li.xiao"Zhu, Zhihui"https://www.zbmath.org/authors/?q=ai:zhu.zhihuiBidirectional approximate reasoning-based approach for decision support.https://www.zbmath.org/1456.681952021-04-16T16:22:00+00:00"Jin, Shangzhu"https://www.zbmath.org/authors/?q=ai:jin.shangzhu"Peng, Jun"https://www.zbmath.org/authors/?q=ai:peng.jun"Li, Zuojin"https://www.zbmath.org/authors/?q=ai:li.zuojin"Shen, Qiang"https://www.zbmath.org/authors/?q=ai:shen.qiangSummary: Fuzzy rule-based systems are widely applied for real-world decision support, such as policy formation, public health analysis, medical diagnosis, and risk assessment. However, they face significant challenges when the application problem at hand suffers from the ``\textit{curse of dimensionality}'' or ``\textit{sparse knowledge base}''. Combination of hierarchical fuzzy rule models and fuzzy rule interpolation offers a potentially efficient and effective approach to dealing with both of these issues simultaneously. In particular, backward fuzzy rule interpolation (B-FRI) facilitates approximate reasoning to be performed given a sparse rule base where rules do not fully cover all observations or the observations are not complete, missing antecedent values in certain available rules. This paper presents a hierarchical bidirectional fuzzy reasoning mechanism by integrating hierarchical rule structures and forward/backward rule interpolation. A computational method is proposed, building on the resulting hierarchical bidirectional fuzzy interpolation to maintain consistency in sparse fuzzy rule bases. The proposed techniques are utilised to address a range of decision support problems, successfully demonstrating their efficacy.Tight bounds for beacon-based coverage in simple rectilinear polygons.https://www.zbmath.org/1456.682202021-04-16T16:22:00+00:00"Bae, Sang Won"https://www.zbmath.org/authors/?q=ai:bae.sang-won"Shin, Chan-Su"https://www.zbmath.org/authors/?q=ai:shin.chan-su"Vigneron, Antoine"https://www.zbmath.org/authors/?q=ai:vigneron.antoineSummary: We establish tight bounds for beacon-based coverage problems. In particular, we show that \(\lfloor \frac{n}{6} \rfloor\) beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon \(P\) with \(n\) vertices. When \(P\) is monotone and rectilinear, we prove that this bound becomes \(\lfloor \frac{n + 4}{8} \rfloor\). We also present an optimal linear-time algorithm for computing the beacon kernel of \(P\).Faster algorithms for growing prioritized disks and rectangles.https://www.zbmath.org/1456.682192021-04-16T16:22:00+00:00"Ahn, Hee-Kap"https://www.zbmath.org/authors/?q=ai:ahn.hee-kap"Bae, Sang Won"https://www.zbmath.org/authors/?q=ai:bae.sang-won"Choi, Jongmin"https://www.zbmath.org/authors/?q=ai:choi.jongmin"Korman, Matias"https://www.zbmath.org/authors/?q=ai:korman.matias"Mulzer, Wolfgang"https://www.zbmath.org/authors/?q=ai:mulzer.wolfgang-johann-heinrich"Oh, Eunjin"https://www.zbmath.org/authors/?q=ai:oh.eunjin"Park, Ji-won"https://www.zbmath.org/authors/?q=ai:park.jiwon"van Renssen, André"https://www.zbmath.org/authors/?q=ai:van-renssen.andre"Vigneron, Antoine"https://www.zbmath.org/authors/?q=ai:vigneron.antoineSummary: Motivated by map labeling,
\textit{S. Funke} et al. [Lect. Notes Comput. Sci. 9843, 43--54 (2016; Zbl 1457.68289)]
introduced the following problem: we are given a sequence of \(n\) disks in the plane. Initially, all disks have radius 0, and they grow at constant, but possibly different, speeds. Whenever two disks touch, the one with the higher index disappears. The goal is to determine the elimination order, i.e., the order in which the disks disappear. We provide the first general subquadratic algorithm for this problem. Our solution extends to other shapes (e.g., rectangles), and it works in any fixed dimension.
We also describe an alternative algorithm that is based on quadtrees. Its running time is \(O(n(\log n + \min \{\log \Delta, \log \Phi \}))\), where \(\Delta\) is the ratio of the fastest and the slowest growth rate and \(\Phi\) is the ratio of the largest and the smallest distance between two disk centers. This improves the running times of previous algorithms by
Funke et al. [loc. cit.],
\textit{D. Bahrdt} et al. [in: Proceedings of the 19th workshop on algorithm engineering and experiments, ALENEX'17. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). 247--258 (2017; Zbl 1429.68316)],
and \textit{S. Funke} and \textit{S. Storandt} [Lect. Notes Comput. Sci. 11949, 181--196 (2019; Zbl 1435.68345)].
Finally, we give an \(\Omega(n \log n)\) lower bound, showing that our quadtree algorithms are almost tight.Minimizing the sum of distances to a server in a constraint network.https://www.zbmath.org/1456.682212021-04-16T16:22:00+00:00"Carmi, Paz"https://www.zbmath.org/authors/?q=ai:carmi.paz"Chaitman-Yerushalmi, Lilach"https://www.zbmath.org/authors/?q=ai:chaitman-yerushalmi.lilach"Ozeri, Bat-Chen"https://www.zbmath.org/authors/?q=ai:ozeri.bat-chenSummary: This paper deals with constructing centralized geometric network that represents a set of clients that need to be connected to a server. We consider the problem of minimizing the sum of the shortest paths from the clients to the server in the network, subject to some constraints. We refer to this summation as the network \textit{cost}. The motivation for this work was derived from the combination of centralized communication network and geometric sink spanner.
Formally, given a set \(V\) of points (representing clients) in the plane, a special point \(q \in V\) (representing a server), a real number \(w > 0\) (the network weight bound), and an integer \(h \geq 1\) (the hop bound), the goal is to construct a directed network \(G = (V, E)\) of minimum cost, such that there is a directed path from every point in \(V\) to \(q\) with at most \(h\) hops, and \(\sum_{(v, u) \in E} | v u | \leq w\), where \(| v u |\) denotes the Euclidean distance between \(v\) and \(u\).
In this paper we start by establishing a connection between the considered problem and geometric sink spanner network. Then, we present our main result, a bi-criteria approximation algorithm, that approximates both the weight and the \textit{cost} of the network with respect to an optimal network, in \((| V | / \varepsilon)^{O(h / \varepsilon)}\). More precisely, we construct a network such that its \textit{cost} (i.e., sum of the shortest paths from every \(v \in V\) to \(q)\) is at most \((1 + h \varepsilon)\) times the \textit{cost} of an optimal network and its weight (i.e., \(\sum_{(v, u) \in E} | v u |)\) is at most \((1 + \varepsilon) \cdot w\), for any \(\varepsilon > 0\).Quantum vision representations and multi-dimensional quantum transforms.https://www.zbmath.org/1456.811462021-04-16T16:22:00+00:00"Li, Hai-Sheng"https://www.zbmath.org/authors/?q=ai:li.haisheng.1|li.haisheng"Song, Shuxiang"https://www.zbmath.org/authors/?q=ai:song.shuxiang"Fan, Ping"https://www.zbmath.org/authors/?q=ai:fan.ping"Peng, Huiling"https://www.zbmath.org/authors/?q=ai:peng.huiling"Xia, Hai-ying"https://www.zbmath.org/authors/?q=ai:xia.haiying"Liang, Yan"https://www.zbmath.org/authors/?q=ai:liang.yanSummary: Quantum vision representation (QVR) is the foundation of quantum vision information processing, which is a possible solution to store and process massive visual data efficiently. In this paper, firstly, quantum image representations are divided into three categories based on different methods of color information storage. Secondly, in order to systematize quantum image representation, we propose five new methods. Thirdly, we develop models of QVR by extending three categories of quantum image representations into corresponding QVRs. Next, we design and implement 1D, 2D, and 3D quantum transforms based on QVR for the first time. Simulation experiments demonstrate that proposed multi-dimensional quantum transforms are effective. In conclusion, this paper develops a model of QVR and provides a feasible scheme for multi-dimensional quantum transforms to be applied in quantum vision information processing.