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A deterministic Attitude Estimation Using a Single Vector Information and Rate Gyros

IEEE-ASME TRANSACTIONS ON MECHATRONICS 2015年第5期20卷 2630-2636页

作者： Vinod, Abraham P. Mahindrakar, Arun D. Bandyopadhyay, Sandipan Muralidharan, Vijay Indian Inst Technol Dept Elect Engn Madras 600036 Tamil Nadu India Indian Inst Technol Dept Engn Design Madras 600036 Tamil Nadu India

This paper proposes a deterministic estimator for the estimation of the attitude of a rigid body. A deterministic estimator uses a minimal set of information and does not try to minimize a cost function or fit the measurements into a stochastic process. The proposed estimator obtains the attitude estimation utilizing only the properties of the rotational group SO(3). The information set required by the proposed estimator is a single vector information and rate gyro readings. For systems in which one of the rotational freedom is constrained, the proposed estimator provides an accurate estimate of the reduced attitude. The performance of the algorithm is verified on different experimental testbeds.

关键词： Attitude estimation deterministic algorithm inertial measurement unit special orthogonal group

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Optimal deterministic broadcasting in known topology radio networks

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DISTRIBUTED COMPUTING 2007年第3期19卷 185-195页

作者： Kowalski, Dariusz R. Pelc, Andrzej Univ Liverpool Dept Comp Sci Liverpool L69 7ZF Merseyside England Univ Quebec Dept Informat Gatineau PQ J8X 3X7 Canada

We consider deterministic broadcasting in radio networks whose nodes have full topological information about the network. The aim is to design a polynomial algorithm, which, given a graph G with source s, produces a fast broadcast scheme in the radio network represented by G. The problem of finding a fastest broadcast scheme for a given graph is NP-hard, hence it is only possible to get an approximation algorithm. We give a deterministic polynomial algorithm which produces a broadcast scheme of length O(D + log(2) n), for every n-node graph of diameter D, thus improving a result of Gasieniec et al. (PODC 2005) [ 17] and solving a problem stated there. Unless the inclusion NP subset of BPTIME(n(O(log log n))) holds, the length O(D + log(2) n) of a polynomially constructible deterministic broadcast scheme is optimal.

关键词： broadcast deterministic algorithm radio network graph

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Packet latency of deterministic broadcasting in adversarial multiple access channels

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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2019年 99卷 27-52页

作者： Anantharamu, Lakshmi Chlebus, Bogdan S. Kowalski, Dariusz R. Rokicki, Mariusz A. Univ Colorado Dept Comp Sci & Engn Denver CO 80217 USA Univ Liverpool Dept Comp Sci Liverpool L69 3BX Merseyside England

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.

关键词： Multiple access channel Adversarial queuing Jamming Distributed algorithm deterministic algorithm Packet latency Queues size

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A deterministic gradient-based approach to avoid saddle points

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EUROPEAN JOURNAL OF APPLIED MATHEMATICS 2023年第4期34卷 738-757页

作者： Kreusser, L. M. Osher, S. J. Wang, B. Univ Bath Dept Math Sci Bath Avon England Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA Univ Utah Dept Math Sci Comp & Imaging Inst Salt Lake City UT 84112 USA

Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317], called modified LSGD (mLSGD), and demonstrate its potential to avoid saddle points without sacrificing the convergence rate. Our analysis is based on the attraction region, formed by all starting points for which the considered numerical scheme converges to a saddle point. We investigate the attraction region's dimension both analytically and numerically. For a canonical class of quadratic functions, we show that the dimension of the attraction region for mLSGD is left perpendicular(n-1)/2right perpendicular, and hence it is significantly smaller than that of GD whose dimension is n - 1

关键词： deterministic algorithm gradient-based methods saddle points attraction region Laplacian smoothing

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deterministic non-adaptive contention resolution on a shared channel

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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2023年 133卷 1-22页

作者： De Marco, Gianluca Kowalski, Dariusz R. Stachowiak, Grzegorz Univ Salerno Dipartimento Informat Fisciano Italy Univ Wroclaw Inst Comp Sci Wroclaw Poland Augusta Univ Sch Comp & Cyber Sci Augusta GA USA

In a multiple access channel, autonomous stations are able to transmit and listen to a shared device. A fundamental problem, called contention resolution, is to allow any station to successfully deliver its message by resolving the conflicts that arise when several stations transmit simultaneously. Despite a long history on such a problem, most of the results deal with the static setting when all stations start simultaneously, while many fundamental questions remain open in the realistic scenario when stations can join the channel at arbitrary times. In this paper, we explore the impact that three major channel features (asynchrony among stations, knowledge of the number of contenders and possibility of switching off stations after a successful transmission) can have on the time complexity of non-adaptive deterministic algorithms. We establish upper and lower bounds allowing to understand which parameters permit time-efficient contention resolution and which do not.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Multiple -access channel Contention resolution deterministic algorithm Lower bound

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Superpixel-Guided Two-View deterministic Geometric Model Fitting

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INTERNATIONAL JOURNAL OF COMPUTER VISION 2019年第4期127卷 323-339页

作者： Xiao, Guobao Wang, Hanzi Yan, Yan Suter, David Xiamen Univ Fujian Key Lab Sensing & Comp Smart City Sch Informat Sci & Engn Xiamen Peoples R China Edith Cowan Univ Sch Sci Joondalup Australia

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.

关键词： Model fitting Superpixel deterministic algorithm Multiple-structure data

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Good-case early-stopping latency of synchronous byzantine reliable broadcast: the deterministic case

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DISTRIBUTED COMPUTING 2024年第2期37卷 121-143页

作者： Albouy, Timothe Frey, Davide Raynal, Michel Taiani, Francois Univ Rennes CNRS Inria IRISA F-35042 Rennes France

This paper considers the good-case latency of Byzantine Reliable Broadcast (BRB), i.e., the time taken by correct processes to deliver a message when the initial sender is correct. This time plays a crucial role in the performance of practical distributed systems. Although significant strides have been made in recent years on this question, progress has mainly focused on either asynchronous or randomized algorithms. By contrast, the good-case latency of deterministic synchronous BRB under a majority of Byzantine faults has been little studied. In particular, it was not known whether a good-case latency below the worst-case bound of t+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t+1$$\end{document} rounds could be obtained. This work answers this open question positively and proposes a deterministic synchronous Byzantine reliable broadcast that achieves a good-case latency of max(2,t+3-c)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{max} (2,t+3-c)$$\end{document} rounds (or equivalently max(2,f+t+3-n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{max} (2,f+t+3-n)$$\end{document}), where t is the upper bound on the number of Byzantine processes, f <= t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\le t$$\end{document} the number

关键词： Byzantine fault deterministic algorithm Genericity Good-case latency Reliable broadcast Synchronous system Weighted predicate

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deterministic network exploration by a single agent with Byzantine tokens

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INFORMATION PROCESSING LETTERS 2012年第12期112卷 467-470页

作者： Dieudonne, Yoann Pelc, Andrzej Univ Picardie Jules Verne Amiens MIS Amiens France Univ Quebec Outaouais Dept Informat Gatineau PQ J8X 3X7 Canada

A mobile agent has to explore an unknown network with unlabeled nodes: it must visit all nodes by walking along the links of the network, and eventually stop. If no upper bound on the size of the network is known and nodes of the network cannot be marked, then this exploration task cannot be accomplished for arbitrary networks by a deterministic terminating algorithm. On the other hand, it is feasible, if there is one unmovable token at the starting node of the agent. We investigate the exploration problem ill arbitrary networks in the presence of identical unmovable tokens, some of which are Byzantine. A Byzantine token can be visible or invisible to the agent whenever the latter visits the node where the token is located, and visibility is decided by the adversary at each visit of the agent. If no upper bound on the number of tokens is known to the agent, deterministic exploration of all networks is impossible, even if all tokens are fault free. It is also impossible if all tokens are Byzantine, even if their number is known. Our main result is a deterministic exploration algorithm with cost polynomial in the (unknown) size of the network, which works in arbitrary networks, provided that the agent knows some upper bound on the total number of tokens, and that at least one token is fault free. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Analysis of algorithms deterministic algorithm Exploration Mobile agent Network Graph

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deterministic polynomial approach in the plane

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DISTRIBUTED COMPUTING 2015年第2期28卷 111-129页

作者： Dieudonne, Yoann Pelc, Andrzej Univ Picardie Jules Verne MIS Amiens France Univ Quebec Outaouais Dept Informat Gatineau PQ J8X 3X7 Canada

Two mobile agents with range of vision 1 start at arbitrary points in the plane and have to accomplish the task of approach, which consists in getting at distance at most one from each other, i.e., in getting within each other's range of vision. An adversary chooses the initial positions of the agents, their possibly different starting times, and assigns a different positive integer label and a possibly different speed to each of them. Each agent is equipped with a compass showing the cardinal directions, with a measure of length and a clock. Each agent knows its label and speed but not those of the other agent and it does not know the initial position of the other agent relative to its own. Agents do not have any global system of coordinates and they cannot communicate. Our main result is a deterministic algorithm to accomplish the task of approach, working in time polynomial in the unknown initial distance between the agents, in the length of the smaller label and in the inverse of the larger speed. The distance travelled by each agent until approach is polynomial in the first two parameters and does not depend on the third. The problem of approach in the plane reduces to a network problem: that of rendezvous in an infinite grid.

关键词： Mobile agent Rendezvous Plane Infinite grid deterministic algorithm Polynomial time

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deterministic gathering with crash faults

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NETWORKS 2018年第2期72卷 182-199页

作者： Pelc, Andrzej Univ Quebec Outaouais Dept Informat Gatineau PQ J8X 3X7 Canada

A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, have to meet at the same node and terminate. This problem is known as gathering. We study deterministic gathering algorithms under the assumption that agents are subject to crash faults which can occur at any time. Two fault scenarios are considered. A motion fault immobilizes the agent at a node or inside an edge but leaves intact its memory at the time when the fault occurred. A more severe total fault immobilizes the agent as well, but also erases its entire memory. Of course, we cannot require faulty agents to gather. Thus the gathering problem for fault prone agents calls for all fault-free agents to gather at a single node, and terminate.

关键词： crash fault deterministic algorithm gathering mobile agent network

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