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作者： Li, Yuanbing Wu, Xian Jin, Yifei Li, Jian Li, Guoliang Feng, Jianhua Department of Computer Science and Technology Tsinghua University Beijing China Tsinghua University Beijing China

We study the problem of utilizing human intelligence to categorize a large number of objects. In this problem, given a category hierarchy and a set of objects, we can ask humans to check whether an object belongs to a category, and our goal is to find the most cost-effective strategy to locate the appropriate category in the hierarchy for each object, such that the cost (i.e., the number of questions to ask humans) is minimized. There are many important applications of this problem, including image classification and product categorization. We develop an online framework, in which category distribution is gradually learned and thus an effective order of questions are adaptively determined. We prove that even if the true category distribution is known in advance, the problem is computationally intractable. We develop an approximation algorithm, and prove that it achieves an approximation factor of 2. We also show that there is a fully polynomial time approximation scheme for the problem. Furthermore, we propose an online strategy which achieves nearly the same performance guarantee as the offline optimal strategy, even if there is no knowledge about category distribution beforehand. We develop effective techniques to tolerate crowd errors. Experiments on a real crowdsourcing platform demonstrate the effectiveness of our method. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： approximation algorithms

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Near-Field Localization for Non-circular Sources in the Presence of Sensor Phase Uncertainties

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IEEE WIRELESS COMMUNICATIONS LETTERS 2021年第3期10卷 562-566页

作者： Shu, Ting Li, Linna He, Jin Shanghai Jiao Tong Univ Shanghai Key Lab Intelligent Sensing & Recognit Sch Elect Informat & Elect Engn Shanghai 200240 Peoples R China Shanghai Aerosp Elect Commun Equipment Res Inst Dept Radar Res Ctr Shanghai 201109 Peoples R China

We address the problem of locating multiple near-field non-circular sources in the presence of sensor phase errors. Such phase error may arise in MIMO applications where perfect phase synchronization is not achieved. Using source non-circularity and based on the virtual ESPRIT idea, we define three cumulant matrices to form two matrix pencils, whose generalized eigenvalues are dependent only on the amplitude but not on the phase of the near-field propagation geometry. We introduce a linear operator to estimate the generalized eigenvalues of the defined matrix pencils, and then apply our recently proposed SPatial Amplitude Ratio based Estimator (SPARE) approach to estimate angle and range parameters of the sources. We define the presented algorithm as Rotational SPARE (R-SPARE) since it obtains the spatial amplitudes from the rotational structures embedded in the defined matrices. R-SPARE shares all advantages offered by the SPARE. We finally examine the performance of R-SPARE via numerical simulations.

关键词： Signal processing algorithms Eigenvalues and eigenfunctions Sensor arrays Geometry approximation algorithms Phased arrays Manifolds Array signal processing near-field source localization phase error spatial amplitude ratio

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Faster Approximate Covering of Subcurves under the Fréchet Distance 30

Faster Approximate Covering of Subcurves under the Fréchet ...

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30th Annual European Symposium on algorithms, ESA 2022

作者： Brüning, Frederik Conradi, Jacobus Driemel, Anne Department of Computer Science Universität Bonn Germany Hausdorff Center for Mathematics Universität Bonn Germany

ISBN: (纸本)9783959772471

Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of a set cover problem for a given polygonal curve: Find the smallest number k of representative curves such that any point on the input curve is contained in a subcurve that has Fréchet distance at most a given Δ to a representative curve. We focus on the case where the representative curves are line segments and approach this NP-hard problem with classical techniques from the area of geometric set cover: we use a variant of the multiplicative weights update method which was first suggested by Brönniman and Goodrich for set cover instances with small VC-dimension. We obtain a bicriteria-approximation algorithm that computes a set of O(k log(k)) line segments that cover a given polygonal curve of n vertices under Fréchet distance at most O(Δ). We show that the algorithm runs in eO(k2n + kn3) time in expectation and uses eO(kn + n3) space. For input curves that are c-packed and lie in the plane, we bound the expected running time by eO(k2c2n) and the space by eO(kn + c2n). In addition, we present a variant of the algorithm that uses implicit weight updates on the candidate set and thereby achieves near-linear running time in n without any assumptions on the input curve, while keeping the same approximation bounds. This comes at the expense of a small (polylogarithmic) dependency on the relative arclength. © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： approximation algorithms

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Spanner approximations in Practice 30

Spanner Approximations in Practice

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30th Annual European Symposium on algorithms, ESA 2022

作者： Chimani, Markus Stutzenstein, Finn Theoretical Computer Science Universität Osnabrück Germany

ISBN: (纸本)9783959772471

A multiplicative α-spanner H is a subgraph of G = (V,E) with the same vertices and fewer edges that preserves distances up to the factor α, i.e., dH(u, v) ≤ α dG(u, v) for all vertices u, v. While many algorithms have been developed to find good spanners in terms of approximation guarantees, no experimental studies comparing different approaches exist. We implemented a rich selection of those algorithms and evaluate them on a variety of instances regarding, e.g., their running time, sparseness, lightness, and effective stretch. © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： approximation algorithms

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Mechanisms for Resource Allocation and Pricing in Mobile Edge Computing Systems

Mechanisms for Resource Allocation and Pricing in Mobile Edg...

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作者： Bahreini, Tayebeh Badri, Hossein Grosu, Daniel Department of Computer Science Wayne State University DetroitMI United States

In this article, we address the resource allocation and monetization challenges in Mobile Edge Computing (MEC) systems, where users have heterogeneous demands and compete for high quality services. We formulate the Edge Resource Allocation Problem ({{\sf ERAP}}ERAP) as a Mixed-Integer Linear Program ({{\sf MILP}}MILP) and prove that {{\sf ERAP}}ERAP is {{\sf NP}}NP-hard. To solve the problem efficiently, we propose two resource allocation mechanisms. First, we develop an auction-based mechanism and prove that the proposed mechanism is individually-rational and produces envy-free allocations. We also propose an {{\sf LP}}LP-based approximation mechanism that does not guarantee envy-freeness, but it provides solutions that are guaranteed to be within a given distance from the optimal solution. We evaluate the performance of the proposed mechanisms by conducting an extensive experimental analysis on {{\sf ERAP}}ERAP instances of various sizes. We use the optimal solutions obtained by solving the {{\sf MILP}}MILP model using a commercial solver as benchmarks to evaluate the quality of solutions. Our analysis shows that the proposed mechanisms obtain near optimal solutions for fairly large size instances of the problem in a reasonable amount of time. © 1990-2012 IEEE.

关键词： approximation algorithms

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Scheduling with Machine Conflicts 1

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20th International Workshop on approximation and Online algorithms, WAOA 2022

作者： Buchem, Moritz Kleist, Linda Schmidt genannt Waldschmidt, Daniel School of Business and Economics Maastricht University Maastricht Netherlands Department of Computer Science TU Braunschweig Braunschweig Germany Institute for Mathematics TU Berlin Berlin Germany

ISBN: (数字)9783031183676

ISBN: (纸本)9783031183669

We study the scheduling problem of makespan minimization with machine conflicts that arise in various settings, e.g., shared resources for pre- and post-processing of tasks or spatial restrictions. In this context, each job has a blocking time before and after its processing time, i.e., three parameters. Given a set of jobs, a set of machines, and a graph representing machine conflicts, the problem SchedulingWithMachineConflicts (smc), asks for a conflict-free schedule of minimum makespan in which the blocking times of no two jobs intersect on conflicting machines. We show that, unless P = NP, smc on m machines does not allow for a O(m1-Ε) -approximation algorithm for any Ε> 0, even in the case of identical jobs and every choice of fixed positive parameters, including the unit case. Complementary, we provide approximation algorithms when a suitable collection of independent sets is given. Finally, we present polynomial time algorithms to solve the problem for the case of unit jobs smc-Unit on special graph classes. As our main result, we solve smc-Unit for bipartite graphs by using structural insights for conflict graphs of star forests. As the set of active machines at each point in time induces a bipartite graph, the insights yield a local optimality criterion. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： approximation algorithms

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Half-Guarding Weakly-Visible Polygons and Terrains 42

Half-Guarding Weakly-Visible Polygons and Terrains

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42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2022

作者： Duraisamy, Nandhana Hillberg, Hannah Miller Jallu, Ramesh K. Krohn, Erik Maheshwari, Anil Nandy, Subhas C. Pahlow, Alex PSG College of Technology Coimbatore India University of Wisconsin OshkoshWI United States Indian Institute of Information Technology Raichur India Carleton University Ottawa Canada Indian Statistical Institute Kolkata India

ISBN: (纸本)9783959772617

We consider a variant of the art gallery problem where all guards are limited to seeing 180°. Guards that can only see in one direction are called half-guards. We give a polynomial time approximation scheme for vertex guarding the vertices of a weakly-visible polygon with half-guards. We extend this to vertex guarding the boundary of a weakly-visible polygon with half-guards. We also show NP-hardness for vertex guarding a weakly-visible polygon with half-guards. Lastly, we show that the orientation of half-guards is critical in terrain guarding. Depending on the orientation of the half-guards, the problem is either very easy (polynomial time solvable) or very hard (NP-hard). © Nandhana Duraisamy, Hannah Miller Hillberg, Ramesh K. Jallu, Erik Krohn, Anil Maheshwari, Subhas C. Nandy, and Alex Pahlow

关键词： approximation algorithms

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Analytic Sensor Rules for Optimal Distributed Decision Given K-Out-of-L Fusion Rule Under Monte Carlo approximation

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第12期65卷 5488-5495页

作者： Liao, Yiwei Shen, Xiaojing Rao, Hang Sichuan Univ Sch Math Chengdu 610017 Peoples R China

With the development of large-scale sensor networks, there is an increasing interest for high dimensional distributed decision fusion problem in statistical decision, machine learning, control theory, etc. In this article, we investigate the optimal sensor quantized rules of the distributed decision under a given fusion rule for conditionally dependent and high dimensional sensor observations. We provide a Monte Carlo importance sampling method to reduce the computational complexity of the distributed decision fusion. For the K-out-of-L rule, we derive a group of analytic sensor rules based on the necessary and sufficient condition of the optimal sensor rules. In term of efficiency, it is significantly better than the traditional iterative search algorithms, such as the Riemann sum approximation iteration algorithm. The analytic solution is also a general result since it does not rely on the specific K value of the K-out-of-L rule, the specific conditional probability density function and the dimension of sensor observations. Thus, it can be applied to multisensor decision fusion problems with high dimensional dependent sensor observations. For the general fusion rules rather than the K-out-of-L rule, the Monte Carlo Gauss-Seidel algorithm is also provided. The numerical examples demonstrate the effectiveness of the analytic solution and the Monte Carlo Gauss-Seidel algorithm.

关键词： Monte Carlo methods Bayes methods Cost function approximation algorithms Computational complexity approximation methods Probability density function Decision fusion dependent observation fusion rule high dimensional observation Monte Carlo approximation

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Average Sensitivity of the Knapsack Problem 30

Average Sensitivity of the Knapsack Problem

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30th Annual European Symposium on algorithms, ESA 2022

作者： Kumabe, Soh Yoshida, Yuichi The University of Tokyo Japan National Institute of Informatics Tokyo Japan

ISBN: (纸本)9783959772471

In resource allocation, we often require that the output allocation of an algorithm is stable against input perturbation because frequent reallocation is costly and untrustworthy. Varma and Yoshida (SODA'21) formalized this requirement for algorithms as the notion of average sensitivity. Here, the average sensitivity of an algorithm on an input instance is, roughly speaking, the average size of the symmetric difference of the output for the instance and that for the instance with one item deleted, where the average is taken over the deleted item. In this work, we consider the average sensitivity of the knapsack problem, a representative example of a resource allocation problem. We first show a (1 - ϵ)-approximation algorithm for the knapsack problem with average sensitivity O(ϵ-1 log ϵ-1). Then, we complement this result by showing that any (1 - ϵ)-approximation algorithm has average sensitivity Ω(ϵ-1). As an application of our algorithm, we consider the incremental knapsack problem in the random-order setting, where the goal is to maintain a good solution while items arrive one by one in a random order. Specifically, we show that for any ϵ > 0, there exists a (1 - ϵ)-approximation algorithm with amortized recourse O(ϵ-1 log ϵ-1) and amortized update time O(log n + fϵ), where n is the total number of items and fϵ > 0 is a value depending on ϵ. © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： approximation algorithms

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Secure Beamforming for Multiple Intelligent Reflecting Surfaces Aided mmWave Systems

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IEEE COMMUNICATIONS LETTERS 2021年第2期25卷 417-421页

作者： Xiu, Yue Zhao, Jun Yuen, Chau Zhang, Zhongpei Gui, Guan Univ Elect Sci & Technol China Natl Key Lab Sci & Technol Commun Chengdu 611731 Peoples R China Nanyang Technol Univ Script Lab Singapore 639798 Singapore Singapore Univ Technol & Design Inst Engn Singapore 487372 Singapore Nanjing Univ Posts & Telecommun Focus Lab Nanjing 210003 Peoples R China

In this letter, secure beamforming in a multiple intelligent reflecting surfaces (IRSs)-aided millimeter-wave (mmWave) system is investigated. In this system, the secrecy rate is maximized by controlling the on-off status of each IRS as well as optimizing the phase shift matrix of the IRSs. This problem is posed as a joint optimization problem of transmit beamforming and IRS control, whose goal is to maximize the secrecy rate under the total transmission power and unit-modulus constraints. The problem is difficult to solve optimally due to the nonconvexity of constraint conditions and coupled variables. To deal with this problem, we propose an alternating optimization (AO)-based algorithm based on successive convex approximation (SCA) and manifold optimization (MO) technologies. Numerical simulations show that the proposed AO-based algorithm can effectively improve the secrecy rate and outperforms traditional single IRS-aided scheme.

关键词： Optimization Array signal processing approximation algorithms Linear programming Electronic mail Propagation losses Millimeter wave communication Multiple intelligent reflecting surfaces millimeter-wave secrecy rate alternating optimization

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