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Criticality and Covered Area Fraction in Confetti and Voronoi Percolation

JOURNAL OF STATISTICAL PHYSICS 2022年第1期186卷 1-1页

作者： Ghosh, Partha Pratim Roy, Rahul Indian Stat Inst New Delhi India

Using the randomized algorithm method developed by Duminil-Copin et al. (Probab Theory Relat Fields 173(1-2):479-90, 2019), we exhibit sharp phase transition for the confetti percolation model. This provides an alternate proof, than that of Ahlberg et al. (Probab Theory Relat Fields 172(1-2):525-581, 2018), for the critical parameter for percolation in this model to be 1/2 when the radius of the underlying shapes for the distinct colours arise from the same distribution. In addition, we study the covered area fraction for this model, which is akin to the covered volume fraction in continuum percolation. Modulo a certain 'transitivity condition', this study allows us to calculate exact critical parameter for percolation when the underlying shapes for different colours may be of different sizes. Similar results are also obtained for the Poisson Voronoi percolation model when different coloured points have different growth speeds.

关键词： Confetti percolation Voronoi percolation randomized algorithm Boolean model Covered area fraction

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Approximating Edit Distance Within Constant Factor in Truly Sub-quadratic Time

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JOURNAL OF THE ACM 2020年第6期67卷 1–22页

作者： Chakraborty, Diptarka Das, Debarati Goldenberg, Elazar Koucky, Michal Saks, Michael Natl Univ Singapore Sch Comp 13 Comp Dr Singapore 117417 Singapore Univ Copenhagen Univ Pk 1 DK-2100 Copenhagen Denmark Acad Coll Tel Aviv Yaffo Rabenu Yeruham St IL-61083 Yaffo Israel Charles Univ Prague Malostranske Nam 25 Prague 11800 Czech Republic Rutgers State Univ Dept Math 110 Frelinghuysen Rd Piscataway NJ USA

Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a dynamic programming algorithm that runs in quadratic time. Andoni, Krauthgamer, and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within approximation factor poly(log n). In this article, we provide an algorithm with running time (O) over tildeO(n(2-2/7)) that approximates the edit distance within a constant factor.

关键词： Edit distance approximation algorithm sub-quadratic time algorithm randomized algorithm

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Voltage Control for Distribution Networks via Coordinated Regulation of Active and Reactive Power of DGs

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IEEE TRANSACTIONS ON SMART GRID 2020年第5期11卷 4017-4031页

作者： Hu, Xiong Liu, Zhi-Wei Wen, Guanghui Yu, Xinghuo Liu, Chen Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Key Lab Image Proc & Intelligent Control Minist Educ Wuhan 430074 Peoples R China Southeast Univ Sch Math Dept Syst Sci Nanjing 210096 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3001 Australia

Fast-acting reactive power support from distributed generations (DGs) is a promising approach for tackling rapid voltage fluctuations in distribution networks. However, the voltage regulation range via reactive power of DGs alone is narrow especially in distribution networks with high resistance-reactance ratio. In this paper, a randomized algorithm is proposed to improve the voltage profile in distribution networks via coordinated regulation of the active and reactive power of DGs. To this end, first the variables of the proposed quadratically constrained quadratic programming problem on voltage control are partitioned into disjoint subsets, each of which corresponds to a unique low-dimensional subproblem. Second, these subsets are updated serially in a randomized manner via solving their corresponding subproblems, which overcomes the requirement for system-wide coordination among participating agents and guarantees an optimal solution. Compared with the existing algorithms, the proposed algorithm is resilient to network reconfigurations and achieves a wider voltage regulation range. The effectiveness and convergence performance of the proposed algorithm is validated by the case studies.

关键词： Reactive power Voltage control Distribution networks Regulation Partitioning algorithms Quadratic programming Convergence Voltage control distribution network coordinated regulation quadratically constrained quadratic programming randomized algorithm

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Targeted Protection Maximization in Social Networks

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2020年第3期7卷 1645-1655页

作者： Guo, Jianxiong Li, Yi Wu, Weili Univ Texas Dallas Dept Comp Sci Erik Jonsson Sch Engn & Comp Sci Richardson TX 75080 USA Univ Texas Tyler Dept Comp Sci Soules Coll Business Tyler TX 75799 USA

Even though the widespread use of social platforms provides convenience to our daily life, it causes some bad results at the same time. For example, misinformation and personal attack can be spread easily on social networks, which drives us to study how to block the spread of misinformation effectively. Unlike the classical rumor blocking problem, we study how to protect the targeted users from being influenced by rumor, called targeted protection maximization (TPM). It aims to block the least edges such that the expected ratio of nodes in targeted set influenced by rumor is at most beta. Under the IC-model, the objective function of TPM is monotone non-decreasing, but not submodular and not supermodular, which makes it difficult for us to solve it by existing algorithms. In this paper, we propose two efficient techniques to solve TPM problem, called Greedy and General-TIM. The Greedy uses simple Hill-Climbing strategy, and get a theoretical bound, but the time complexity is hard to accept. The second algorithm, General-TIM, is formed by means of randomized sampling by Reverse Shortest Path (Random-RS-Path), which reduces the time consuming significantly. A precise approximation ratio cannot be promised in General-TIM, but in fact, it can get good results in reality. Considering the community structure in networks, both Greedy and General-TIM can be improved after removing unrelated communities. Finally, the effectiveness and efficiency of our algorithms is evaluated on several real datasets.

关键词： Targeted Protection Maximization rumor blocking social network randomized algorithm

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Exact simulation of first exit times for one-dimensional diffusion processes

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ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 2020年第3期54卷 811-844页

作者： Herrmann, Samuel Zucca, Cristina Univ Bourgogne Franche Comte CNRS UMR 5584 Inst Math Bourgogne F-21000 Dijon France Univ Turin Dept Math G Peano Via Carlo Alberto 10 I-10123 Turin Italy

The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study are the Girsanov transformation, the convergent series method for the simulation of random variables and the classical rejection sampling. The efficiency of the method is described through theoretical results and numerical examples.

关键词： Exit time Brownian motion diffusion processes Girsanov's transformation rejection sampling exact simulation randomized algorithm conditioned Brownian motion

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randomized algorithm for UAVs Group Flight Optimization

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IFAC Proceedings Volumes 2013年第11期46卷 205-208页

作者： Konstantin Amelin Natalia Amelina Oleg Granichin Olga Granichina Boris Andrievsky St. Petersburg State University St. Petersburg Russia Norwegian University of Science and Technology Department of Telematics Trondheim Norway Institute for Problems of Mechanical Engineering of RAS Russia Saint Petersburg National Research University of Information Technologies Mechanics and Optics St. Petersburg Russia

The problem of small UAVs flight optimization is considered. To solve this problem thermal updrafts are used. For the precise detection of the thermal updrafts center the simultaneous perturbation stochastic approximation (SPSA) type algorithm is proposed. If UAVs use thermal updrafts so they can save the energy during the flight. Therefore the flight time will be vary for different UAVs. In order to optimize the area monitoring, the consensus approach has been proposed.

关键词： Unmanned aerial vehicle (UAV) UAVs network UAVs group simultaneous perturbation stochastic approximation randomized algorithm consensus

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A randomized algorithm for Roadside Units Placement in Vehicular Ad Hoc Network

A Randomized Algorithm for Roadside Units Placement in Vehic...

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IEEE 9th International Conference on Mobile Ad-hoc and Sensor Networks (MSN)

作者： Xu Liya Huang Chuanhe Li Peng Zhu Junyu Wuhan Univ Sch Comp Wuhan 430072 Peoples R China

ISBN: (纸本)9780769551593

In this paper, we investigate the problem of optimal road side units (RSUs) placement in Vehicular Ad Hoc Network (VANET) on a highway, which enables the VANET maintain a good connectivity. Our goal is to find out minimal number of road side units, such that the vehicles could communicate with RSUs. These road side units are connected by wire. We develop a randomized algorithm to deploy road side units in the VANET. It gives an approximation to the optimal distance to guarantee the information can be passed to RSUs from the accident site via the VANET. Simulations are conducted to show the performance of our proposed method.

关键词： VANET RSU Placement randomized algorithm

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Improved randomized algorithm for Square Root Extraction

Improved Randomized Algorithm for Square Root Extraction

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4th International Conference on Information Computing and Applications (ICICA)

作者： Liu, Lihua Cao, Zhengjun Sha, Qian Shanghai Maritime Univ Dept Math Shanghai Peoples R China

ISBN: (纸本)9783642537035;9783642537028

Square root extraction plays a key role in cryptosystems based on elliptic curves. Motwani and Raghavan had proposed an algorithm for square root extraction over finite field F-p, where p is an odd prime. It is a randomized algorithm with expected running time O(len(p)(4)). Its complexity relies mainly on the loops calling Euclid's algorithm for polynomials over F-p. In this paper, we propose an improvement of it. The new algorithm calls a subroutine for computing a Legendre symbol. Since the running time of computing a Legendre symbol is much less than that of Euclid's algorithm for polynomials over F-p, the new algorithm is more efficient. It only takes time O(len(p)(3)). We also compare the new algorithm with those algorithms for square root extraction over finite fields.

关键词： Quadratic Residue Legendre Symbol randomized algorithm

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Opinion Dynamics With Topological Gossiping: Asynchronous Updates Under Limited Attention

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IEEE CONTROL SYSTEMS LETTERS 2020年第3期4卷 566-571页

作者： Rossi, Wilbert Samuel Frasca, Paolo Univ Twente Dept Appl Math NL-7500 AE Enschede Netherlands Univ Groningen Univ Coll Groningen NL-9701 BA Groningen Netherlands Univ Grenoble Alpes Inria CNRS Grenoble INPGIPSA Lab F-38000 Grenoble France

This letter introduces a general model of opinion dynamics with opinion-dependent connectivity. Agents update their opinions asynchronously: for the updating agent, the new opinion is the average of the k closest opinions within a subset of m agents that are sampled from the population of size n. Depending on k and m with respect to n, the dynamics can have a variety of equilibria, which include consensus and clustered configurations. The model covers as special cases a classical gossip update (if m = n) and a deterministic update defined by the k nearest neighbors (if m = k). We prove that the dynamics converges to consensus if n > 2(m - k). Before convergence, however, the dynamics can remain for long time in the vicinity of metastable clustered configurations.

关键词： Convergence Sociology Mathematical model Nickel Statistics Indexes Social network services Agent-based systems large-scale systems network analysis and control randomized algorithm

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A randomized adaptive neighbor discovery for wireless networks with multi-packet reception capability

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2019年第0期131卷 235-244页

作者： Chae, Sung-Yoon Kang, Kyungran Cho, Young-Jong Korea Railrd Res Inst Control & Commun Res Team Uiwang South Korea Ajou Univ Coll Informat & Technol Suwon South Korea

Neighbor discovery is a first step in the initialization of wireless networks in large-scale ad hoc networks. In this paper, we propose a randomized neighbor discovery scheme for wireless networks with a multi packet reception (MPR) capability. We let the nodes to have different advertisement probabilities. The node gradually adjusts its probability according to its operation phases: greedy or slow-start. In the greedy phase, the node advertises aggressively while it does moderately in the slow-start phase. Initial phase and advertisement probability are determined randomly. Then, the nodes change the probability adaptively according to advertisements the reception state from the other nodes. In order to decide the reception state precisely, the exact number of nodes in the network is necessary. To make our proposed scheme work in case of no prior knowledge of the population, we propose a population estimation method based on a maximum likelihood estimation. We evaluate our proposed scheme through numerical analysis and simulation. Through the numerical analysis, we show that the discovery completion time is lower bounded in Theta(N/k) and upper bounded in Theta(NlnN/k) when there exists N nodes with MPR-k capability. The bounds are the same as those of previous studies that propose static optimal advertisement probability. Through the simulation, we evaluate that our adaptive scheme outperforms in terms of discovery completion time, advertisement efficiency, and wasted time slot ratio than a scheme with static advertisement probability when the population of the network is unknown. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Neighbor discovery Wireless network randomized algorithm Multi-packet reception Maximum likelihood estimation Adaptive advertisement

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