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19th International Conference on Computational Statistics (COMPSTAT'2010)

作者： Verdonck, Tim Hubert, Mia Rousseeuw, Peter J. Univ Antwerp Dept Math & Comp Sci Middelheimlaan 1 Antwerp Belgium Katholieke Univ Leuven Dept Math Leuven Belgium

ISBN: (数字)9783790826043

ISBN: (纸本)9783790826036

The minimum covariance determinant (MCD) method is a robust estimator of multivariate location and scatter (Rousseeuw (1984)). Computing the exact MCD is very hard, so in practice one resorts to approximate algorithms. Most often the FASTMCD algorithm of Rousseeuw and Van Driessen (1999) is used. The FASTMCD algorithm is affine equivariant but not permutation invariant. Recently a deterministic algorithm, denoted as DetMCD, is developed which does not use random subsets and which is much faster (Hubert et al. (2010)). In this paper DetMCD is illustrated in a calibration framework. We focus on robust principal component regression and partial least squares regression, two very popular regression techniques for collinear data. We also apply DetMCD on data with missing elements after plugging it into the M-RPCR technique of Serneels and Verdonck (2009).

关键词： deterministic algorithm outliers robustness RPCR RSIMPLS

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Pairwise Test Set Calculation using k-partite Graphs

Pairwise Test Set Calculation using k-partite Graphs

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International Conference on Software Maintenance

作者： Salecker, Elke Glesner, Sabine Berlin Inst Technol TU Berlin Berlin Germany

ISBN: (纸本)9781424486298

of input values and can be detected using pairwise test sets that cover each pair of input values. The generation of pairwise test sets with a minimal size is an NP-complete problem which implies that many algorithms are either expensive or based on a random process. In this paper we present a deterministic algorithm that exploits our observation that the pairwise testing problem can be modeled as a k-partite graph problem. We calculate the test set using well investigated graph algorithms that take advantage of properties of k-partite graphs. We present evaluation results that prove the applicability of our algorithm and discuss possible improvement of our approach.

关键词： NP-complete problem computational complexity deterministic algorithm deterministic algorithms fault diagnosis graph theory k-partite graph problem k-partite graphs pairwise test set calculation pairwise testing problem program testing random process software fault tolerance software faults

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Distance-2-Dispersion with Termination by a Strong Team 10th

Distance-2-Dispersion with Termination by a Strong Team

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10th International Conference on algorithms and Discrete Applied Mathematics (CALDAM)

作者： Gorain, Barun Kaur, Tanvir Mondal, Kaushik Indian Inst Technol Bhilai Bhilai India Indian Inst Technol Ropar Rupnagar India

ISBN: (纸本)9783031522123;9783031522130

Distance-2-Dispersion (D-2-D) problem aims to disperse k mobile robots starting from an arbitrary initial configuration on an anonymous port-labeled graph G with n nodes such that no two robots occupy adjacent nodes in the final configuration, though multiple robots may occupy a single node if there is no other empty node whose all adjacent nodes are also empty. In the existing literature, this problem is solved starting from a rooted configuration for k(>= 1) robots using O(m Delta) synchronous rounds with a total of O(log n) memory per robot, where m is the number of edges and Delta is the maximum degree of the graph. In this work, we start with k > n mobile robots and improve the run time to O(m) starting from a rooted configuration using the same amount of memory per robot. Further, we achieve D-2-D for an arbitrary initial configuration in O(pm) rounds using O(log n) memory per robot, where p is the number of nodes containing robots in the initial configuration. Both the algorithms terminate without any global knowledge of m, n, Delta, k, p. As we start with k > n robots, the nodes occupied by robots in the final configuration form a maximal independent set of the graph.

关键词： Mobile robots Dispersion Distance-2-Dispersion deterministic algorithm Distributed algorithm

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WANT TO GATHER? NO NEED TO CHATTER!

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SIAM JOURNAL ON COMPUTING 2023年第2期52卷 358-411页

作者： Boucharddagger, Sebastien Dieudonne, Yoann Pelcdagger, Andrzej Univ Quebec Outaouais Dept Informat Gatineau PQ J8X 3X7 Canada Univ Picardie Jules Verne MIS Lab F-80039 Amiens France

A team of mobile agents with different labels, starting from different nodes of an unknown anonymous network, must meet at the same node and declare that they all met. This task of gathering was traditionally considered assuming that agents at the same node can exchange information. We ask if this ability of talking is needed. The answer turns out to be no. We design two deterministic algorithms that accomplish gathering in a much weaker model. We only assume that each agent knows how many agents are at the node that it currently occupies. Our first algorithm assumes that agents know some upper bound N on the size of the network, and works in time polynomial in N and in the length l of the smallest label. Our second algorithm does not assume any knowledge about the network, but its complexity is at least 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 we solve, in the same weak model, the fundamental problem of leader election among agents. As an application we solve the gossiping problem in this model: if each agent has a message, all agents can learn all messages. This is perhaps our most surprising finding: agents without any transmitting devices can solve the most general information exchange problem if they can count the number of agents present at visited nodes.

关键词： gathering leader election gossiping deterministic algorithm mobile agent

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Testing primality deterministically

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INTERNATIONAL JOURNAL OF QUANTUM INFORMATION 2005年第1期3卷 269-273页

作者： Toffalori, C Univ Camerino Dept Math & Comp Sci I-62032 Camerino Italy

We introduce and discuss the recent Agrawal-Kayal-Saxena deterministic algorithm solving primality in polynomial time.

关键词： deterministic algorithm probabilistic algorithm primality

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Collaborative Dispersion by Silent Robots 24th

Collaborative Dispersion by Silent Robots

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24th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)

作者： Gorain, Barun Mandal, Partha Sarathi Mondal, Kaushik Pandit, Supantha Indian Inst Technol Bhilai Sejbahar India Indian Inst Technol Guwahati Gauhati India Indian Inst Technol Ropar Rupnagar Punjab India Dhirubhai Ambani Inst Informat & Commun Technol Gandhinagar Gujarat India

ISBN: (纸本)9783031210167;9783031210174

In the dispersion problem, a set of k co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph G = (V, E), where the graph's nodes are not labeled. The edges incident to a node v with degree d are labeled with port numbers in the range {0, 1,..., d - 1} at v. The robots have unique IDs in the range [0, L], where L >= k, and are initially placed at a source node s. Each robot knows only its ID, however, it does not know the IDs of the other robots or the values of L or k. The task of the dispersion was traditionally achieved based on the assumption of two types of communication abilities: (a) when some robots are at the same node, they can communicate by exchanging messages between them, and (b) any two robots in the network can exchange messages between them. This paper investigates whether this communication ability among co-located robots is absolutely necessary to achieve the dispersion. We established that even in the absence of the ability of communication, the task of the dispersion by a set of mobile robots can be achieved in a much weaker model, where a robot at a node v has the access of following very restricted information at the beginning of any round: (1) am I alone at v? (2) did the number of robots at v increase or decrease compared to the previous round? We propose a deterministic distributed algorithm that achieves the dispersion on any given graph G = (V, E) in time O (k log L + k(2) log Delta), where. is the maximum degree of a node in G. Further, each robot uses O(log L + log Delta) additional memory. We also prove that the task of the dispersion cannot be achieved by a set of mobile robots with o(log L + log Delta) additional memory.

关键词： Autonomous mobile robots Anonymous graphs Dispersion deterministic algorithm Time and memory complexity

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CUDA-Assisted Energy-Efficient Primality Test

CUDA-Assisted Energy-Efficient Primality Test

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IEEE SOUTHEASTCON

作者： Abu Asaduzzaman Yip, Chok M. Maiti, Anindya Wichita State Univ Dept Elect Engn & Comp Sci Wichita KS 67260 USA

ISBN: (纸本)9781479965854

It has been known that the primes are infinite in number but the exact sequence of primes is not predictable. Prime numbers and computers have been linked since the 1950s. Computer security authorities use extremely large prime numbers when they devise cryptographs, like RSA (short for Rivest, Shamir, and Adleman) algorithm, for protecting vital information that is transmitted between computers. There are many primality testing algorithms including mathematical models and computer programs. However, they are very time and energy consuming when the given number n is very large. In this paper, we propose a Compute Unified Device Architecture (CUDA)-accelerated deterministic algorithm to determine whether an input number is prime or composite much faster to save energy. We develop and implement the proposed algorithm using a system with an 8-core CPU and a 448-core GPu. Experimental results indicate that up to 45x speedup and 88% energy saving can be achieved for 20-digit decimal numbers.

关键词： CUDA architecture deterministic algorithm GPU computing parallel computing primality test

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Indirect investigation of heat transfer of electronic system 19

Indirect investigation of heat transfer of electronic system

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19th International Conference on Applied Electronics (AE)

作者： Frivaldsky, M. Spanik, P. Drgona, P. Koscelnik, J. Univ Zilina Fac Elect Engn Dept Mechatron & Elect Zilina Slovakia

ISBN: (纸本)9788026102762

This paper deals with the development of methodology suited for design of computation algorithm which is able to determine power losses of electronic systems based on measured temperature distribution. Second part of paper is given to development of methodology for optimal selection of mentioned active components for thermal simulation model of given electronic system. Finally experimental verification of proposed methodology is presented.

关键词： deterministic algorithm thermal model optimization

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Distance-2-Dispersion: Dispersion with Further Constraints 11th

Distance-2-Dispersion: Dispersion with Further Constraints

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11th International Conference on Networked Systems (NETYS)

作者： Kaur, Tanvir Mondal, Kaushik Indian Inst Technol Ropar Rupnagar Punjab India

The aim of the dispersion problem is to place a set of k (= n, it is guaranteed that the nodes with robots form a maximal independent set of the underlying network. The graph G = (V, E) is a port-labelled graph having... 详细信息

ISBN: (纸本)9783031377648;9783031377655

The aim of the dispersion problem is to place a set of k (<= n) mobile robots in the nodes of an unknown graph consisting of n nodes such that in the final configuration each node contains at most one robot, starting from any arbitrary initial configuration of the robots on the graph. In this work, we propose a variant of the dispersion problem, namely Distance-2-Dispersion, in short, D-2-D, where we start with any number of robots, and put an additional constraint that no two adjacent nodes contain robots in the final configuration. However, if a maximal independent set is already formed by the nodes which contain a robot each, then any other unsettled robot, if exists, will not find a node to settle. Hence we allow multiple robots to sit on some nodes only if there is no place to sit. If k >= n, it is guaranteed that the nodes with robots form a maximal independent set of the underlying network. The graph G = (V, E) is a port-labelled graph having n nodes and m edges, where nodes are anonymous. The robots have unique ids in the range [1, L], where L >= k. Co-located robots can communicate among themselves. We provide an algorithm that solves D-2-D starting from a rooted configuration (i.e., initially all the robots are co-located) and terminates after 2 Delta(8m - 3n + 3) synchronous rounds using O(log Delta) memory per robot without using any global knowledge of the graph parameters m, n and Delta, the maximum degree of the graph. We also provide Omega(m Delta) lower bound on the number of rounds for the D-2-D problem.

关键词： Mobile robots Collaborative dispersion deterministic algorithm

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Fractal fitting research on stock prices

Fractal fitting research on stock prices

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1st International Congress on Image and Signal Processing

作者： Lin, Yong Tong, Xin Renmin Univ China Informat Sch Dept Math Beijing 100872 Peoples R China

ISBN: (纸本)9780769531199

In this paper, we mainly study the law of stock price changes and the fitting method of it. After introducing the key point of fractal and Genetic algorithm, we focus on explaining the inverse problems of piecewise fractal interpolation theoretically first. Then, based on the theory, we analyze a large amount of stock price data, calculate all the values of parameters in the model, and finally get an image of the attractor. The result is comparatively satisfying, so that this algorithm is very effective.

关键词： piecewise fractal interpolation function deterministic algorithm Genetic algorithm

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