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Feature Papers in Randomized, Online and Approximation Algorithms
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Feature Papers in Randomized, Online and Approximation Algorithms

A topical collection in Algorithms (ISSN 1999-4893). This collection belongs to the section "Randomized, Online, and Approximation Algorithms".

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Editor

Prof. Dr. Frank Werner

E-Mail Website
Collection Editor
Faculty of Mathematics, Otto-von-Guericke-University, P.O. Box 4120, D-39016 Magdeburg, Germany
Interests: scheduling; development of exact and approximate algorithms; stability investigations; discrete optimization; scheduling with interval processing times; complex investigations for scheduling problems; train scheduling; graph theory; logistics; supply chains; packing; simulation; applications
Special Issues, Collections and Topics in MDPI journals

Topical Collection Information

Dear Colleagues,

Many problems in different fields of research and application are so complex that one can find only approximate solutions within reasonable computational time, or they require an algorithm which makes decisions online on the basis of incomplete information. This means that either the search space is too large and complex to efficiently find an optimal solution, or the search space is not completely known. There has been substantial progress in the development of algorithms for such problems over the past decades.

This topical collection is dedicated to the presentation of new and innovative results in the field of the design and analysis of randomized, online, or approximation algorithms. This selection looks both for theoretical results and applications in the real world. Survey papers highlighting the most recent advances and trends in this field are also welcome. There are no restrictions regarding the length of a submission.

Prof. Dr. Frank Werner
Collection Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the collection website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical programming
  • operations research
  • production planning, scheduling, logistics, and transport
  • combinatorial optimization
  • discrete mathematics, graph theory, and networks
  • machine learning
  • multi-criteria decision making
  • design and analysis of algorithms
  • distributed and parallel algorithms
  • approximation algorithms
  • parametrized approximation
  • metaheuristics and matheuristics
  • randomized algorithms
  • online algorithms and competitive analysis
  • new applications in real-world problems

Published Papers (7 papers)

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2024

Jump to: 2023

24 pages, 5669 KiB  
Article
Design of Multichannel Spectrum Intelligence Systems Using Approximate Discrete Fourier Transform Algorithm for Antenna Array-Based Spectrum Perception Applications
by Arjuna Madanayake, Keththura Lawrance, Bopage Umesha Kumarasiri, Sivakumar Sivasankar, Thushara Gunaratne, Chamira U. S. Edussooriya and Renato J. Cintra
Algorithms 2024, 17(8), 338; https://doi.org/10.3390/a17080338 - 1 Aug 2024
Viewed by 1205
Abstract
The radio spectrum is a scarce and extremely valuable resource that demands careful real-time monitoring and dynamic resource allocation. Dynamic spectrum access (DSA) is a new paradigm for managing the radio spectrum, which requires AI/ML-driven algorithms for optimum performance under rapidly changing channel [...] Read more.
The radio spectrum is a scarce and extremely valuable resource that demands careful real-time monitoring and dynamic resource allocation. Dynamic spectrum access (DSA) is a new paradigm for managing the radio spectrum, which requires AI/ML-driven algorithms for optimum performance under rapidly changing channel conditions and possible cyber-attacks in the electromagnetic domain. Fast sensing across multiple directions using array processors, with subsequent AI/ML-based algorithms for the sensing and perception of waveforms that are measured from the environment is critical for providing decision support in DSA. As part of directional and wideband spectrum perception, the ability to finely channelize wideband inputs using efficient Fourier analysis is much needed. However, a fine-grain fast Fourier transform (FFT) across a large number of directions is computationally intensive and leads to a high chip area and power consumption. We address this issue by exploiting the recently proposed approximate discrete Fourier transform (ADFT), which has its own sparse factorization for real-time implementation at a low complexity and power consumption. The ADFT is used to create a wideband multibeam RF digital beamformer and temporal spectrum-based attention unit that monitors 32 discrete directions across 32 sub-bands in real-time using a multiplierless algorithm with low computational complexity. The output of this spectral attention unit is applied as a decision variable to an intelligent receiver that adapts its center frequency and frequency resolution via FFT channelizers that are custom-built for real-time monitoring at high resolution. This two-step process allows the fine-gain FFT to be applied only to directions and bands of interest as determined by the ADFT-based low-complexity 2D spacetime attention unit. The fine-grain FFT provides a spectral signature that can find future use cases in neural network engines for achieving modulation recognition, IoT device identification, and RFI identification. Beamforming and spectral channelization algorithms, a digital computer architecture, and early prototypes using a 32-element fully digital multichannel receiver and field programmable gate array (FPGA)-based high-speed software-defined radio (SDR) are presented. Full article
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20 pages, 2922 KiB  
Article
To Cache or Not to Cache
by Steven Lyons, Jr. and Raju Rangaswami
Algorithms 2024, 17(7), 301; https://doi.org/10.3390/a17070301 - 7 Jul 2024
Viewed by 798
Abstract
Unlike conventional CPU caches, non-datapath caches, such as host-side flash caches which are extensively used as storage caches, have distinct requirements. While every cache miss results in a cache update in a conventional cache, non-datapath caches allow for the flexibility of selective [...] Read more.
Unlike conventional CPU caches, non-datapath caches, such as host-side flash caches which are extensively used as storage caches, have distinct requirements. While every cache miss results in a cache update in a conventional cache, non-datapath caches allow for the flexibility of selective caching, i.e., the option of not having to update the cache on each miss. We propose a new, generalized, bimodal caching algorithm, Fear Of Missing Out (FOMO), for managing non-datapath caches. Being generalized has the benefit of allowing any datapath cache replacement policy, such as LRU, ARC, or LIRS, to be augmented by FOMO to make these datapath caching algorithms better suited for non-datapath caches. Operating in two states, FOMO is selective—it selectively disables cache insertion and replacement depending on the learned behavior of the workload. FOMO is lightweight and tracks inexpensive metrics in order to identify these workload behaviors effectively. FOMO is evaluated using three different cache replacement policies against the current state-of-the-art non-datapath caching algorithms, using five different storage system workload repositories (totaling 176 workloads) for six different cache size configurations, each sized as a percentage of each workload’s footprint. Our extensive experimental analysis reveals that FOMO can improve upon other non-datapath caching algorithms across a range of production storage workloads, while also reducing the write rate. Full article
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14 pages, 341 KiB  
Article
Competitive Analysis of Algorithms for an Online Distribution Problem
by Alessandro Barba, Luca Bertazzi and Bruce L. Golden
Algorithms 2024, 17(6), 237; https://doi.org/10.3390/a17060237 - 3 Jun 2024
Viewed by 663
Abstract
We study an online distribution problem in which a producer has to send a load from an origin to a destination. At each time period before the deadline, they ask for transportation price quotes and have to decide to either accept or not [...] Read more.
We study an online distribution problem in which a producer has to send a load from an origin to a destination. At each time period before the deadline, they ask for transportation price quotes and have to decide to either accept or not accept the minimum offered price. If this price is not accepted, they have to pay a penalty cost, which may be the cost to ask for new quotes, the penalty cost for a late delivery, or the inventory cost to store the load for a certain duration. The aim is to minimize the sum of the transportation and the penalty costs. This problem has interesting real-world applications, given that transportation quotes can be obtained from professional websites nowadays. We show that the classical online algorithm used to solve the well-known Secretary problem is not able to provide, on average, effective solutions to our problem, given the trade-off between the transportation and the penalty costs. Therefore, we design two classes of online algorithms. The first class is based on a given time of acceptance, while the second is based on a given threshold price. We formally prove the competitive ratio of each algorithm, i.e., the worst-case performance of the online algorithm with respect to the optimal solution of the offline problem, in which all transportation prices are known at the beginning, rather than being revealed over time. The computational results show the algorithms’ performance on average and in the worst-case scenario when the transportation prices are generated on the basis of given probability distributions. Full article
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21 pages, 461 KiB  
Article
EPSOM-Hyb: A General Purpose Estimator of Log-Marginal Likelihoods with Applications in Probabilistic Graphical Models
by Eric Chuu, Yabo Niu, Anirban Bhattacharya and Debdeep Pati
Algorithms 2024, 17(5), 213; https://doi.org/10.3390/a17050213 - 15 May 2024
Viewed by 954
Abstract
We consider the estimation of the marginal likelihood in Bayesian statistics, with primary emphasis on Gaussian graphical models, where the intractability of the marginal likelihood in high dimensions is a frequently researched problem. We propose a general algorithm that can be widely applied [...] Read more.
We consider the estimation of the marginal likelihood in Bayesian statistics, with primary emphasis on Gaussian graphical models, where the intractability of the marginal likelihood in high dimensions is a frequently researched problem. We propose a general algorithm that can be widely applied to a variety of problem settings and excels particularly when dealing with near log-concave posteriors. Our method builds upon a previously posited algorithm that uses MCMC samples to partition the parameter space and forms piecewise constant approximations over these partition sets as a means of estimating the normalizing constant. In this paper, we refine the aforementioned local approximations by taking advantage of the shape of the target distribution and leveraging an expectation propagation algorithm to approximate Gaussian integrals over rectangular polytopes. Our numerical experiments show the versatility and accuracy of the proposed estimator, even as the parameter space increases in dimension and becomes more complicated. Full article
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2023

Jump to: 2024

22 pages, 1204 KiB  
Article
An Algorithm for Construction of the Asymptotic Approximation of a Stable Stationary Solution to a Diffusion Equation System with a Discontinuous Source Function
by Nikolay Nefedov, Bogdan Tishchenko and Natalia Levashova
Algorithms 2023, 16(8), 359; https://doi.org/10.3390/a16080359 - 26 Jul 2023
Viewed by 1127
Abstract
An algorithm is presented for the construction of an asymptotic approximation of a stable stationary solution to a diffusion equation system in a two-dimensional domain with a smooth boundary and a source function that is discontinuous along some smooth curve lying entirely inside [...] Read more.
An algorithm is presented for the construction of an asymptotic approximation of a stable stationary solution to a diffusion equation system in a two-dimensional domain with a smooth boundary and a source function that is discontinuous along some smooth curve lying entirely inside the domain. Each of the equations contains a small parameter as a factor in front of the Laplace operator, and as a result, the system is singularly perturbed. In the vicinity of the curve, the solution of the system has a large gradient. Such a problem statement is used in the model of urban development in metropolitan areas. The discontinuity curves in this model are the boundaries of urban biocenoses or large water pools, which prevent the spread of urban development. The small parameter is the ratio of the city’s outskirts linear size to the whole metropolis linear size. The algorithm includes the construction of an asymptotic approximation to a solution with a large gradient at the media interface as well as the steps for obtaining the existence conditions. To prove the existence and stability theorems, we use the upper and lower solutions, which are constructed as modifications of the asymptotic approximation to the solution. The latter is constructed using the Vasil’yeva algorithm as an expansion of a small parameter exponent. Full article
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24 pages, 604 KiB  
Article
ω-Circulant Matrices: A Selection of Modern Applications from Preconditioning of Approximated PDEs to Subdivision Schemes
by Rafael Díaz Fuentes, Stefano Serra-Capizzano and Rosita Luisa Sormani
Algorithms 2023, 16(7), 328; https://doi.org/10.3390/a16070328 - 8 Jul 2023
Cited by 2 | Viewed by 1760
Abstract
It is well known that ω-circulant matrices with ω≠0 can be simultaneously diagonalized by a transform matrix, which can be factored as the product of a diagonal matrix, depending on ω, and of the unitary matrix Fn associated [...] Read more.
It is well known that ω-circulant matrices with ω≠0 can be simultaneously diagonalized by a transform matrix, which can be factored as the product of a diagonal matrix, depending on ω, and of the unitary matrix Fn associated to the Fast Fourier Transform. Hence, all the sets of ω-circulants form algebras whose computational power, in terms of complexity, is the same as the classical circulants with ω=1. However, stability is a delicate issue, since the condition number of the transform is equal to that of the diagonal part, tending to max{|ω|,|ω|−1}. For ω=0, the set of related matrices is still an algebra, which is the algebra of lower triangular matrices, but they do not admit a common transform since most of them (all except the multiples of the identity) are non-diagonalizable. In the present work, we review two modern applications, ranging from parallel computing in preconditioning of PDE approximations to algorithms for subdivision schemes, and we emphasize the role of such algebra. For the two problems, few numerical tests are conducted and critically discussed and the related conclusions are drawn. Full article
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14 pages, 534 KiB  
Communication
Algorithm for Approximate Solving of a Nonlinear Boundary Value Problem for Generalized Proportional Caputo Fractional Differential Equations
by Angel Golev, Snezhana Hristova and Asen Rahnev
Algorithms 2023, 16(6), 272; https://doi.org/10.3390/a16060272 - 29 May 2023
Viewed by 1294
Abstract
In this paper an algorithm for approximate solving of a boundary value problem for a nonlinear differential equation with a special type of fractional derivative is suggested. This derivative is called a generalized proportional Caputo fractional derivative. The new algorithm is based on [...] Read more.
In this paper an algorithm for approximate solving of a boundary value problem for a nonlinear differential equation with a special type of fractional derivative is suggested. This derivative is called a generalized proportional Caputo fractional derivative. The new algorithm is based on the application of the monotone-iterative technique combined with the method of lower and upper solutions. In connection with this, initially, the linear fractional differential equation with a boundary condition is studied, and its explicit solution is obtained. An appropriate integral fractional operator for the nonlinear problem is constructed and it is used to define the mild solutions, upper mild solutions and lower mild solutions of the given problem. Based on this integral operator we suggest a scheme for obtaining two monotone sequences of successive approximations. Both sequences consist of lower mild solutions and lower upper solutions of the studied problem, respectively. The monotonic uniform convergence of both sequences to mild solutions is proved. The algorithm is computerized and applied to a particular example to illustrate the theoretical investigations. Full article
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