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30th Annual European Symposium on algorithms, ESA 2022

作者： Xi, Zoe Kuszmaul, William Massachusetts Institute of Technology CambridgeMA United States

ISBN: (纸本)9783959772471

Dynamic Time Warping (DTW) is a widely used similarity measure for comparing strings that encode time series data, with applications to areas including bioinformatics, signature verification, and speech recognition. The standard dynamic-programming algorithm for DTW takes O(n2) time, and there are conditional lower bounds showing that no algorithm can do substantially better. In many applications, however, the strings x and y may contain long runs of repeated letters, meaning that they can be compressed using run-length encoding. A natural question is whether the DTW-distance between these compressed strings can be computed efficiently in terms of the lengths k and of the compressed strings. Recent work has shown how to achieve O(k2 +k2) time, leaving open the question of whether a near-quadratic O(k)-time algorithm might exist. We show that, if a small approximation loss is permitted, then a near-quadratic time algorithm is indeed possible: our algorithm computes a (1+ϵ)-approximation for DTW(x, y) in O(k/ϵ3) time, where k and are the number of runs in x and y. Our algorithm allows for DTW to be computed over any metric space (Σ, δ) in which distances are O(log n)-bit integers. Surprisingly, the algorithm also works even if δ does not induce a metric space on Σ (e.g., δ need not satisfy the triangle inequality). © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： approximation algorithms

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Pricing Problems with Buyer Preselection

Pricing Problems with Buyer Preselection

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作者： Bilò, Vittorio Flammini, Michele Monaco, Gianpiero Moscardelli, Luca University of Salento Italy GSSI L’Aquila Italy University of L’Aquila Italy University of Chieti-Pescara Italy

We investigate the problem of preselecting a subset of buyers (also called agents) participating in a market so as to optimize the performance of stable outcomes. We consider four scenarios arising from the combination of two stability notions, namely market envy-freeness and agent envy-freeness, with the two state-of-the-art objective functions of social welfare and seller’s revenue. When insisting on market envy-freeness, we prove that the problem cannot be approximated within n1−Ε (with n being the number of buyers) for any Ε > 0, under both objective functions;we also provide approximation algorithms with an approximation ratio tight up to subpolynomial multiplicative factors for social welfare and the seller’s revenue. The negative result, in particular, holds even for markets with single-minded buyers. We also prove that maximizing the seller’s revenue is NP-hard even for a single buyer, thus closing a previous open question. Under agent envy-freeness and for both objective functions, instead, we design a polynomial time algorithm transforming any stable outcome for a market involving any subset of buyers into a stable outcome for the whole market without worsening its performance. This result creates an interesting middle-ground situation where, if on the one hand buyer preselection cannot improve the performance of agent envy-free outcomes, on the other one it can be used as a tool for simplifying the combinatorial structure of the buyers’ valuation functions in a given market. Finally, we consider the restricted case of multi-unit markets, where all items are of the same type and are assigned the same price. For these markets, we show that preselection may improve the performance of stable outcomes in all of the four considered scenarios, and design corresponding approximation algorithms. © 2022 AI Access Foundation. All rights reserved.

关键词： approximation algorithms

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Fairness-Aware algorithms for Seed Allocation in Social Advertising 24

Fairness-Aware Algorithms for Seed Allocation in Social Adve...

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24th IEEE International Conference on High Performance Computing and Communications, 8th IEEE International Conference on Data Science and Systems, 20th IEEE International Conference on Smart City and 8th IEEE International Conference on Dependability in Sensor, Cloud and Big Data Systems and Application, HPCC/DSS/SmartCity/DependSys 2022

作者： Wang, Pengzi Zhu, Yiming Han, Kai Yin, Zhizhuo Xiu, Qing Hui, Pan University of Science and Technology of China China Hong Kong University of Science and Technology Hong Kong Hong Kong School of Computer Science and Technology Soochow University China

ISBN: (纸本)9798350319934

As a crucial and widely researched application in social networks, social advertising refers to selecting seed users for several advertisers to propagate their advertisements in the network via a information cascade effect. Prior studies on this topic have presented approximation algorithms merely for maximizing the expected revenue. However, regarding to the fairness issue, no existing works have provided effective solution. Such a issue would cause polarized revenues among different advertisers and the draining of them. In this paper, we investigate the fairness issue in social advertising. That is, how the social network platform owner distributes seeds users fairly to different advertisers. We define the fairness metric according to the maximin share, a concept about fair distribution in computation economics, and develop a novel approximation algorithm. Our approach achieves an approximation factor of (1-1/e)2/3 1/h2, where h is the number of different advertisers. Our result recovers the best-known proposed (1-1/e)2/2. -approximation ratio when h=1 and extends settings to a more general case. The evaluation on real datasets indicates that our solution is effective and outperforms the existing algorithms in terms of fairness. © 2022 IEEE.

关键词： approximation algorithms

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Opposing Half Guards* 34

Opposing Half Guards*

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34th Canadian Conference on Computational Geometry, CCCG 2022

作者： Krohn, Erik Nilsson, Bengt J. Schmidt, Christiane Department of Computer Science University of Wisconsin - Oshkosh OshkoshWI United States Department of Computer Science and Media Technology Malmö University Sweden Department of Science and Technology Linköping University Sweden

We study the art gallery problem for opposing half guards: guards that can either see to their left or to their right only. We present art gallery theorems, show that the problem is NP-hard in monotone polygons, present approximation algorithms for spiral and staircase polygons, and show that the location of half guards in 2- guardable polygons is not restricted to extensions. © 2022 Yeganeh Bahoo and Konstantinos Georgiou.

关键词： approximation algorithms

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Maximizing Sums of Non-Monotone Submodular and Linear Functions: Understanding the Unconstrained Case 30

Maximizing Sums of Non-Monotone Submodular and Linear Functi...

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30th Annual European Symposium on algorithms, ESA 2022

作者： Bodek, Kobi Feldman, Moran Department of Mathematics and Computer Science Open University of Israel Ra'anana Israel Computer Science Department University of Haifa Israel

ISBN: (纸本)9783959772471

Motivated by practical applications, recent works have considered maximization of sums of a submodular function g and a linear function . Almost all such works, to date, studied only the special case of this problem in which g is also guaranteed to be monotone. Therefore, in this paper we systematically study the simplest version of this problem in which g is allowed to be non-monotone, namely the unconstrained variant, which we term Regularized Unconstrained Submodular Maximization (RegularizedUSM). Our main algorithmic result is the first non-trivial guarantee for general RegularizedUSM. For the special case of RegularizedUSM in which the linear function is non-positive, we prove two inapproximability results, showing that the algorithmic result implied for this case by previous works is not far from optimal. Finally, we reanalyze the known Double Greedy algorithm to obtain improved guarantees for the special case of RegularizedUSM in which the linear function is non-negative;and we complement these guarantees by showing that it is not possible to obtain (1/2, 1)-approximation for this case (despite intuitive arguments suggesting that this approximation guarantee is natural). © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： approximation algorithms

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Multiscale Quantum Gradual approximation Algorithm: An Optimization Algorithm With a Step-by-Step approximation Strategy

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IEEE ACCESS 2020年 8卷 71548-71557页

作者： Cheng, Kun Wang, Peng Li, Zhendong Univ Chinese Acad Sci Beijing 1UUU49 Peoples R China Chinese Acad Sci Chengdu Inst Comp Applicat Beijing 100864 Peoples R China Southwest Minzu Univ Sch Comp Sci & Technol Chengdu 610041 Peoples R China Ningxia Univ Sch Informat Engn Yinchuan 750021 Ningxia Peoples R China Ningxia Municipal & Minist Educ Collaborat Innovat Ctr Ningxia Big Data & Artific Yinchuan 750021 Ningxia Peoples R China

In quantum swarm intelligence algorithms, the tunneling effect of the particles is determined by the potential energy acting on the particles. The tunneling effect of the particles affects the global search ability and convergence speed of the algorithm. Quantum algorithms with a single potential energy are prone to premature convergence under certain complex test functions. In this paper, we propose a multiscale quantum gradual approximation algorithm (MQGAA), which simply uses different approximation strategies to obtain different potential energy functions, to solve the premature problem of the optimization algorithm. In the MQGAA, particles undergo a transition from an unconstrained state to a constrained state at each scale. To demonstrate the effectiveness of the proposed algorithm, experiments are carried out with several common and effective stochastic algorithms on N-dimensional double-well potential functions and classical benchmark functions. We also use the Wilcoxon rank test to detect the performance of MQGAA. The experimental results show that the algorithm using a step-by-step approximation strategy achieves a better optimization performance on some complex test functions.

关键词： approximation algorithms Optimization Potential energy Linear programming Particle swarm optimization Tunneling Taylor approximation unconstrained state constrained state multiscale multiscale quantum harmonic oscillator algorithm

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Improved approximation for Fractionally Subadditive Network Design

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INFORMATION PROCESSING LETTERS 2020年 154卷 105861-000页

作者： Mucha, Marcin Smulewicz, Marcin Univ Warsaw Inst Informat Warsaw Poland

Recently, Guruganesh et al. [1] proposed the Fractionally Subadditive Network Design (f-SAND) problem. In this problem, we are given a weighted graph G with a special root vertex r together with k subsets of its vertices called scenarios. We need to assign capacities to the edges of G so that for every scenario, the assigned capacities support a unit flow from the root to all vertices in the scenario, simultaneously. The goal is to minimize the total cost of the solution. f-SAND is a fairly natural problem and it generalizes several well -studied problems, such as the Steiner Tree problem. The added interest to this problem stems from the fact that standard tools used for approximating network design problems do not seem to apply to f-SAND. Despite this, Guruganesh et al. conjecture the existence of an algorithm with an approximation ratio bounded by a constant, i.e. independent of k. They make a step towards this goal by giving a 3 -approximation algorithm for k = 2. In this paper, we present an algorithm similar to that of [1], together with an analysis that not only yields an improved approximation ratio of 4, but is also significantly simpler. We also generalize it to arbitrary k, giving a 4k-approximation. On the negative side, we argue that without additional insights, the techniques used are not likely to produce a constant factor approximation algorithm. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Flow approximation algorithms Network design

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Assortment Optimization under a Single Transition Choice Model

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PRODUCTION AND OPERATIONS MANAGEMENT 2021年第7期30卷 2122-2142页

作者： Nip, Kameng Wang, Zhenbo Wang, Zizhuo Xiamen Univ Sch Math Sci Xiamen 361005 Fujian Peoples R China Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China Chinese Univ Hong Kong Sch Data Sci Shenzhen 518172 Guangdong Peoples R China

In this study, we consider a new customer choice model which we call the single transition choice model. In this model, there is a universe of products and customers arrive at each product with a certain probability. If the arrived product is unavailable, then the seller can recommend a subset of available products and the customer will purchase one of the recommended products or choose not to purchase with certain transition probabilities. The distinguishing features of the model are that the seller can control which products to recommend depending on the arrived product, and each customer either purchases a product or leaves the market after one transition. We study the assortment optimization problem under this model. Particularly, we show that it is NP-Hard even if the customer can transition from each product to at most two products. Despite the computational complexity, we provide polynomial time algorithms or approximation algorithms for several special cases, such as when the customer can only transition from each product to at most a given number of products and the size of each recommended set is bounded. Our approximation algorithms are developed by invoking the submodularity arguments, or connecting the problem with maximum constraint satisfaction problem and applying randomized rounding techniques to its semidefinite programming relaxation. We also provide a tight worst-case performance bound for revenue-ordered assortments. In addition, we propose a compact mixed-integer program formulation, which is efficient for moderate size problems. Finally, we conduct numerical experiments to demonstrate the effectiveness of the proposed algorithms.

关键词： assortment optimization choice model approximation algorithms revenue‐ ordered assortment

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Robust Beamforming for Enhancing Security in Multibeam Satellite Systems

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IEEE COMMUNICATIONS LETTERS 2021年第7期25卷 2161-2165页

作者： Zhang, Jian Lin, Min Ouyang, Jian Zhu, Wei-Ping De Cola, Tomaso Nanjing Univ Posts & Telecommun Coll Telecommun & Informat Engn Nanjing 210003 Peoples R China Concordia Univ Dept Elect & Comp Engn Montreal PQ H3G 1M8 Canada German Aerosp Ctr DLR Inst Commun & Nav D-82234 Oberpfaffenhofen Germany

This letter proposes a robust beamforming (BF) scheme to enhance physical layer security (PLS) of the downlink of a multibeam satellite system in the presence of either uncoordinated or coordinated eavesdroppers (Eves). Specifically, with knowing only the approximate locations of the Eves, we aim at maximizing the worst-case achievable secrecy rate (ASR) of the legitimate user (LU), subject to the constraints of per-antenna transmit power and quality of service (QoS) requirement of the LU. Since the optimization problem is non-convex, we first adopt the discretization method to deal with the unknown regions of the Eves and then exploit the log-sum-exp function to approximate the objective function. Afterwards, a BF method joint alternating direction method of multipliers (ADMM) with Dinkelbach iteration is presented to solve this non-convex problem. Finally, simulation results verify that our robust BF algorithm can effectively improve the security of multibeam satellite systems.

关键词： Manganese Satellites Security Quality of service Optimization Array signal processing approximation algorithms Multibeam satellite communications robust beamforming physical layer security alternating direction method of multipliers

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Image Distortion Characterization due to Equivalent Monostatic approximation in Near-Field Bistatic SAR Imaging

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2020年第7期69卷 4898-4907页

作者： Manzoor, Zahra Al Qaseer, Mohammad Tayeb Donnell, Kristen M. Missouri Univ Sci & Technol Elect Engn Dept Rolla MO 65409 USA Iowa State Univ Elect Engn Dept Ames IA 50011 USA

The omega-k synthetic aperture radar (SAR) algorithm is a computationally efficient algorithm for near-field 3-D monostatic SAR imaging in nondestructive testing (NDT) applications. However, bistatic measurements are preferred in order to obtain high dynamic range, in particular when real-time imaging arrays are used. This article investigates the image distortion caused by using an equivalent monostatic imaging algorithm for bistatic measurements. Simulations and measurements at millimeter-wave frequencies in the Ka-band (26.5-40 GHz) are used to investigate the resultant image distortion. Furthermore, the image distortion is quantified through the root-mean-square (rms) error, which is calculated as a function of the bistatic transmitterreceiver separation distance, range, and noise power. Simulations and measurements are conducted for imaging using the raster scanning of a pair of antennas and for nonuniform imaging arrays. In addition, an approximate method for phase compensation is introduced to improve the image error from the monostatic approximation of bistatic measurement.

关键词： Distortion Imaging Receivers Transmitters Distortion measurement approximation algorithms Biomedical measurement Bistatic imaging configuration equivalent monostatic model image error phase-compensation method synthetic aperture radar (SAR) imaging

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