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Randomized and optimal algorithms for k-Lifetime Dominating Set in Wireless Sensor Networks

IEEE ACCESS 2022年 10卷 23774-23784页

作者： Luo, Weizhong Liang, Junbin Wang, Tianshu Huizhou Univ Sch Comp Sci & Engn Huizhou 516007 Guangdong Peoples R China Guangxi Univ Sch Comp & Elect Informat Guangxi Key Lab Multimedia Commun & Network Techn Nanning 530004 Peoples R China Neusoft Grp Co Ltd Nanning 530004 Peoples R China

In wireless sensor networks, rotating dominating set is an efficient method for balancing the energy consumption of nodes, and thereby extending the network operational time. This method can be abstracted as k-Lifetime Dominating Set in bipartite graph, that partitions the set of graph vertices representing sensors into k disjoint dominating sets. However, the considered problem has been proven to be NP-hard, and there is no hope of solving it in polynomial time unless P = NP. Existing studies mainly focus on developing approximation or heuristic algorithms, which usually cannot guarantee a solution for a given problem yes instance. In this study, we first propose a randomized algorithm that can generate a solution with guaranteed probability 1-epsilon (0 < epsilon < 1). Using the color coding method, we show that the randomized algorithm can be improved to guarantee the generation of a solution for a given problem yes instance in exponential time. Based on the idea of randomized partition, we further present a more practical centralized greedy algorithm, and then a distributed implementation. Simulation results indicate that the centralized algorithm can efficiently generate optimal solutions for almost all the given problem instances if the partition redundancy is above a certain limit. Compared with existing algorithm, the centralized algorithm increases the number of dominating sets by factors between 0% and 21%.

关键词： Dominating set NP-hard color coding random partition optimal algorithms

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Efficient and optimal algorithms for Contextual Dueling Bandits under Realizability 33

Efficient and Optimal Algorithms for Contextual Dueling Band...

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33rd International Conference on Algorithmic Learning Theory (ALT)

作者： Saha, Aadirupa Krishnamurthy, Akshay Microsoft Res New York NY 10012 USA

We study the K-armed contextual dueling bandit problem, a sequential decision making setting in which the learner uses contextual information to make two decisions, but only observes preference-based feedback suggesting that one decision was better than the other. We focus on the regret minimization problem under realizability, where the feedback is generated by a pairwise preference matrix that is well-specified by a given function class F. We provide a new algorithm that achieves the optimal regret rate for a new notion of best response regret, which is a strictly stronger performance measure than those considered in prior works. The algorithm is also computationally efficient, running in polynomial time assuming access to an online oracle for square loss regression over F. This resolves an open problem of Dudik et al. (2015) on oracle efficient, regret-optimal algorithms for contextual dueling bandits.

关键词： Contextual Dueling Bandits Preference-based learning Realizability Function approximation Regret analysis Best-Response Policy regret Regression oracles Efficient optimal algorithms Markov games Linear realizability Agnostic

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optimal algorithms for doubly weighted approximation of univariate functions

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JOURNAL OF APPROXIMATION THEORY 2016年 201卷 30-47页

作者： Kuo, F. Y. Plaskota, L. Wasilkowski, G. W. Univ New S Wales Sch Math & Stat Sydney NSW 2052 Australia Univ Warsaw Fac Math Informat & Mech PL-02097 Warsaw Poland Univ Kentucky Dept Comp Sci Lexington KY 40506 USA

We consider a rho-weighted L-q approximation in the space of univariate functions f : R+ -> R with finite parallel to f((r)) psi parallel to L-p. Let alpha = r - 1/p + 1/q and omega = rho/psi. Assuming that psi and omega are non-increasing and the quasi-norm parallel to omega parallel to L-1/alpha is finite, we construct algorithms using function/derivatives evaluations at n points with the worst case errors proportional to parallel to omega parallel to L-1/alpha n(-r+(1/p-1/q)+). In addition we show that this bound is sharp;in particular, if parallel to omega parallel to L-1/alpha = infinity then the rate n(-r+(1/p-1/q)+) cannot be achieved. Our results generalize known results for bounded domains such as [0, 1] and rho = psi equivalent to 1. We also provide a numerical illustration. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Function approximation Unbounded domains optimal algorithms

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optimal algorithms for Universal Random Number Generation From Finite Memory Sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第3期61卷 1277-1297页

作者： Seroussi, Gadiel Weinberger, Marcelo J. Univ Republica Montevideo 11100 Uruguay Stanford Univ Ctr Sci Informat Stanford CA 94305 USA

We study random number generators (RNGs), both in the fixed to variable-length (FVR) and the variable to fixed-length (VFR) regimes, in a universal setting in which the input is a finite memory source of arbitrary order and unknown parameters, with arbitrary input and output (finite) alphabet sizes. Applying the method of types, we characterize essentially unique optimal universal RNGs that maximize the expected output (respectively, minimize the expected input) length in the FVR (respectively, VFR) case. For the FVR case, the RNG studied is a generalization of Elias's scheme, while in the VFR case the general scheme is new. We precisely characterize, up to an additive constant, the corresponding expected lengths, which include second-order terms similar to those encountered in universal data compression and universal simulation. Furthermore, in the FVR case, we consider also a twice-universal setting, in which the Markov order k of the input source is also unknown.

关键词： Random number generation fixed to variable-length variable to fixed-length method of types type classes Markov sources finite memory processes universal generators optimal algorithms

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optimal algorithms in a Krylov subspace for solving linear inverse problems by MFS

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2014年 44卷 64-75页

作者： Liu, Chein-Shan Natl Taiwan Univ Dept Civil Engn Taipei 10617 Taiwan

The method of fundamental solutions (MFS) is used to solve backward heat conduction problem, inverse heat source problem, inverse Cauchy problem and inverse Robin problem. In order to overcome the ill-posedness of resulting linear equations, two optimal algorithms with optimal descent vectors that consist of m vectors in a Krylov subspace are developed, of which the m weighting parameters are determined by minimizing a properly defined merit function in terms of a quadratic quotient. The optimal algorithms OA1 and OA2 are convergent fast, accurate and robust against large noise, which are confirmed through numerical tests. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Inverse problem Method of fundamental solutions Inverse Cauchy problem Inverse Robin problem Krylov subspace optimal algorithms Orthogonal projection

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Move-optimal arbitrary pattern formation by mobile robots on rectangular grid using near-optimal spatial area

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THEORETICAL COMPUTER SCIENCE 2025年 1038卷

作者： Sharma, Avisek Ghosh, Satakshi Goswami, Pritam Sau, Buddhadeb Jadavpur Univ Dept Math Kolkata 700032 West Bengal India Int Inst Informat Technol IIIT Bhubaneswar Dept Basic Sci & Humanities Bhubaneswar 751003 Odisha India Sister Nivedita Univ Dept Comp Sci & Engn Kolkata 700156 West Bengal India

Arbitrary pattern formation (APF) is a well-studied problem in swarm robotics. To the best of our knowledge, the problem has been considered in two different settings: one in a euclidean plane and another in an infinite grid. This work deals with the problem in an infinite rectangular grid setting. The previous works in literature dealing with the APF problem in an infinite grid had a fundamental issue. These deterministic algorithms use a lot of spatial area in the grid to solve the problem, mainly to maintain the asymmetry of the configuration and avoid any collision. These solution techniques cannot be useful if there is a spatial constraint in the application field. In this work, we consider luminous robots (each robot equipped with a light that can take three colors) to avoid symmetry, but we carefully designed a deterministic algorithm that solves the APF problem using the minimal required spatial area in the grid if the initial pattern is asymmetric. The robots are autonomous, identical, and anonymous, and they operate in Look-Compute-Move cycles under a fully-asynchronous scheduler. The APF algorithm proposed in [1] by Bose et al. can be modified using luminous robots so that it uses minimal spatial area, but that algorithm is not move-optimal. The algorithm proposed in this paper not only uses minimal spatial area but is also asymptotically move-optimal.

关键词： Distributed algorithms Arbitrary pattern formation Rectangular grid Robot with lights optimal algorithms

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Finding optimal solutions to several gray pattern instances

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OPTIMIZATION LETTERS 2022年第2期16卷 713-722页

作者： Drezner, Zvi Kalczynski, Pawel Misevicius, Alfonsas Palubeckis, Gintaras Calif State Univ Fullerton Coll Business & Econ Fullerton CA 92834 USA Kaunas Univ Technol Dept Multimedia Engn Kaunas Lithuania

In this paper we compare two new binary linear formulations to a standard quadratic binary program for the gray pattern problem and solved all three by the Gurobi solver. One formulation performed significantly better and obtained seven optimal solutions that were not proven optimal before. It is interesting that the formulation that performed best is based on significantly more variables and constraints.

关键词： optimal algorithms Quadratic assignment problem Gray pattern

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Minimum consistent subset of simple graph classes

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DISCRETE APPLIED MATHEMATICS 2023年第1期338卷 255-277页

作者： Dey, Sanjana Maheshwari, Anil Nandy, Subhas C. Indian Stat Inst ACM Unit Kolkata India Carleton Univ Sch Comp Sci Ottawa ON Canada

In the minimum consistent subset (MCS) problem, a connected simple undirected graph G = (V, E) is given whose each vertex is colored by one of the colors {c1, c2, ... , ck}, and the objective is to compute a minimum size subset C & SUBE;V such that for each vertex v & ISIN;V, its set of nearest neighbors in C (with respect to the hop-distance) contains at least one vertex of the same color as v. The decision version of the MCS problem is NP complete for general graphs. Even for planar graphs, the problem remains NP-complete. We will consider some simple graph classes like path, spider, caterpillar and comb;and present polynomial-time algorithms.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： Minimum consistent subset Graphs optimal algorithms

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Obnoxious facility location in multiple dimensional space

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TOP 2023年第2期31卷 331-354页

作者： Kalczynski, Pawel Suzuki, Atsuo Drezner, Zvi Calif State Univ Fullerton Coll Business & Econ Fullerton CA 92834 USA Nanzan Univ Dept Data Sci Nagoya Aichi 4668673 Japan

The obnoxious facility location problem in three dimensions is optimally solved by an exact method based on Apollonius spheres, and in three or more dimensions by a modification of the Big-Cube-Small-Cube (BCSC, Schobel and Scholz in Comput Oper Res 37:115-122, 2010) global optimization method to within a pre-specified accuracy. In our implementation, no specifically designed bounds are required. The general purpose bounds proposed in this paper do not employ derivatives of the functions. Such an approach can be used, for example, for locating multiple obnoxious facilities in two dimensional space, locating obnoxious facilities on the plane with demand points in three-dimensional space, or applying different distance norms. We concentrated mainly on three-dimensional problems which have the most practical applications. A four dimensional practical application is presented. We solved problems in a cube, part of a cube, a non-convex building, and locating a facility on the plane when demand points are in a three-dimensional space. We also solved problems in 4-6 dimensions to illustrate the effectiveness of the BCSC method.

关键词： Multi-dimensional space Obnoxious facility optimal algorithms

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An excellent derivative-free multiple-zero finding numerical technique of optimal eighth order convergence

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Annali dell'Universita di Ferrara 2022年第1期68卷 161-186页

作者： Sharma, Janak Raj Kumar, Sunil Department of Mathematics Sant Longowal Institute of Engineering and Technology Sangrur Longowal 148106 India Department of Mathematics Amrita School of Engineering Amrita Vishwa Vidyapeetham Channai 601103 India

A number of higher order Newton-like methods (i.e. the methods requiring both function and derivative evaluations) are available in literature for multiple zeros of a nonlinear function. However, higher order Traub-Steffensen-like methods (i.e. the methods requiring only function evaluations) for computing multiple zeros are rare in literature. Traub-Steffensen-like iterations are important in the circumstances when derivatives are complicated to evaluate or expensive to compute. Motivated by this fact, here we present an efficient and rapid-converging Traub-Steffensen-like algorithm to locate multiple zeros. The method achieves eighth order convergence by using only four function evaluations per iteration, therefore, this convergence rate is optimal. Performance is demonstrated by applying the method on different problems including some real life models. The computed results are compared with that of existing optimal eighth-order Newton-like techniques to reveal the computational efficiency of the new approach. © 2022, The Author(s) under exclusive license to Università degli Studi di Ferrara.

关键词： Iteration function Multiple roots Nonlinear equations optimal algorithms Traub-Steffensen method

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