Discrete Algorithm Research Articles

A discrete artificial bee colony algorithm and its application in flexible flow shop scheduling with assembly and machine deterioration effect

In real production, assembly and machine deterioration are extremely common phenomenon and flexible flow shop scheduling problem (FFSP) is also extensively investigated. However, assembly FFSP with machine deterioration effect (AFFSP-DE) is neglected. This paper addresses an AFFSP-DE with makespan criterion and proposes a discrete artificial bee colony (DABC) algorithm. In DABC, the number of employed (onlooker) bees is dynamically changeable according to evolutionary quality to adaptively allocate computing resources for two kinds of bees, and a new scout bee phase is designed to improve convergence speed. Finally, the relationships between makespan and different deterioration rates are analyzed systematically by extensive experiments, and the results demonstrate that DABC outperforms the existing algorithms over 82% test instances in solving the AFFSP-DE.

DISCRETE OPTIMIZATION OF THE IMPLEMENTATION STAGES OF PHARMACEUTICAL DEVELOPMENT FOR A SPRAY TREATMENT FOR ORAL DISEASES

Introduction. All over the world more than 3.5 billion people suffer from oral diseases, which can lead to endogenous infectious diseases and create conditions for external infections. The growing antimicrobial resistance of bacterial strains is a global health threat. Oligoalkyleneguanidine polymers may be promising compounds to solve this problem. The spray form for the application of these substances is the most optimal. The aim of the study is to apply discrete optimization to implement the stages of pharmaceutical development of a spray based on branched oli-gohexamethyleneguanidine for the treatment of oral diseases. Material and methods. Experiments are carried out using various equipment and samples with different compositions have been developed. The implementation of the pharmaceutical development stages was carried out using a discrete optimization algorithm. Results. When implementing discrete optimization in pharmaceutical development, it is necessary to prioritize criteria and limitations using the target quality profile of the drug being developed. As a result of the optimization cycles carried out, the optimal composition was selected, which corresponds to the target quality profile, including such parameters as pH, dynamic viscosity, sterilizing filtration, adhesion of the formulations to the oral mucosa and the spray torch. A discrete optimization was carried out, taking into account the wetting edge angle and particle size distribution. The optimal com-position was sample No. 8, which has pseudoplastic properties, provides unhindered spraying and prevents the composition from draining from the mucous membrane of the oral cavity. Conclusion. During the study, the optimal ratio of components was determined and the development of a spray based on oligohexamethyleneguani-dine with the implementation of stages of pharmaceutical development for discrete optimization was proposed.

Scheduling optimization of flexible flow shop with buffer capacity limitation based on an improved discrete particle swarm optimization algorithm

To address the challenge of production scheduling in flexible flow shops with buffer capacity limitations, a mathematical model is established to minimize the maximum completion time and maximize equipment utilization. To efficiently solve the problem, an improved discrete particle swarm optimization algorithm with multi-population reduction (MPREDPSO) is developed. It integrates an elite retention strategy, which significantly contributes to its efficiency and robustness. The algorithm stands out for its ability to effectively navigate through potential local optima, a common pitfall in optimization problems, through a Euclid algorithm coupled with a sophisticated gene backtracking mechanism. The performance of MPREDPSO is rigorously tested and proven through comparative analyses. Its effectiveness is proven through comparisons with other algorithms, namely the discrete particle swarm algorithm, genetic algorithm, whale algorithm, grey wolf optimizer and whale swarm algorithm. In addition, MPREDPSO’s practical utility is demonstrated in a high-temperature ham sausage production workshop, showcasing its industrial application capabilities.

A reliable spacecraft power supply subsystem based on discrete water cycle multi-objective optimization

The successful execution of spacecraft missions relies heavily on the performance and reliability of their power supply subsystems. Achieving optimal component size and configuration is crucial for efficient power generation, distribution, and storage. Designing an efficient power supply subsystem for spacecraft missions is a complex and multi-objective optimization problem. Traditional optimization techniques, such as genetic algorithm and particle swarm optimization, have been employed, but their limitations in handling discrete variables and achieving global optima necessitate the exploration of alternative methods. In this context, this research paper explores the application of discrete water cycle algorithm (DWCA) optimization as a novel approach for optimizing the component size and configuration of spacecraft power supply subsystems. By emulating the dynamic flow and distribution of water, DWCA seeks to efficiently explore the design space and identify optimal solutions.Through comprehensive experimentation and comparative analysis, this research demonstrates that the proposed DWCA outperforms/surpasses other traditional optimization techniques in optimizing component size and configuration for spacecraft power supply subsystems. It consistently determines designs that are more efficient in power generation and storage. Moreover, DWCA enhances the efficiency and reliability of spacecraft power supply systems, especially in mission-critical scenarios. The successful optimization of spacecraft power supply subsystems is paramount to the overall success of space missions. Therefore, this advancement contributes significantly to the ongoing efforts to ensure the success of future space missions.

Loading pattern optimization of VVER-1000 reactor core based on the discrete golden eagle optimization algorithm

The main features of the loading pattern optimization (LPO) problem, such as high-dimensionality, multi-modality, and non-linearity, make it difficult to achieve a truly optimal configuration. In recent years, metaheuristic methods have been successfully used to solve this problem. In this research, a discrete golden eagle optimization (DGEO) algorithm has been developed to solve the LPO problem in the first cycle of VVER-1000 reactor core. To evaluate the proposed algorithm, a linear multi-purpose fitness function has been used to improve the safety parameters of the reactor core by obtaining a flatter power distribution during the first cycle, and also to enhance the economic parameters by increasing the cycle length and reducing the cost of fuel recycling. For this purpose, a FORTRAN program has been written to map the DGEO algorithm for the LPO problem using the PMAX and PARCS core calculation code to compute the fitness function in each iteration. To speed up the calculations, parallel computing has been applied in the written program. The results demonstrated that the loading pattern, which is suggested by the DGEO algorithm, enhances all the safety and economic parameters in the fitness function. Thus, the DGEO algorithm is highly reliable for the LPO problems in the VVER 1000 reactor core.

Real-Time Detection Method for Saturation Speed of Air-Core Coil Current Transformer

Traditional methods generally rely on a fixed threshold to determine whether the current transformer is saturated. However, this threshold based judgment method is difficult to adapt to different working conditions and changes in current waveforms. In view of the different characteristics of current transformer and the diversity of working environment, it may not be accurate to judge its saturation state only by relying on a fixed threshold. In order to improve the efficiency of current transformer speed saturation detection and reduce the error, a new type of air core coil current transformer speed saturation real-time detection method is proposed. Based on the working and current characteristics of the fast saturation current transformer, the discrete Fourier algorithm is used to suppress power frequency interference signals, with the fundamental frequencies set to 45 Hz and 55 Hz respectively, in order to separate the signal from power frequency interference and reduce the interference intensity of the power frequency interference signal; Identify all faults and saturation points, and extract effective data segments. The wavelet transform characteristics of the secondary current waveform of current transformer in saturated and unsaturated states are deeply studied. By analyzing the changes of different operating conditions and current waveforms, more discriminant features are extracted by using the characteristics of wavelet transform, so as to realize the real-time and accurate detection of saturation state. The results indicate that after adopting the proposed method, the highest accuracy of data segment extraction reached 97%; The maximum detection error is only 4%. The detection time is only 1.31 s. This indicates that the proposed method improves the detection performance and is practical.

Numerical modeling of edge inhomogeneity in a macro cantilever beam

This study explores the inhomogeneity problem near the edge of a cantilever beam. Common in gears and turbine blades, inhomogeneities under local edge contact, coupled with macroscale bending effects, result in extreme and complex stress concentration. This model employs the Conjugate Gradient Method to combines the macroscopic beam theory and microscopic elasticity. The Eshelby inclusion method for simulating inhomogeneities. The Hetényi image method is used for address edge contacts in the beam. Enhanced by the Discrete Convolution fast Fourier Transform algorithm, the model’s accuracy and efficiency are validated with the Finite element method. Parametric analysis highlights the influence of distance between indenter and edge, stress components distribution and potential failure in cross-scale challenges.

Optimal scheduling and demand response implementation for home energy management

The optimal scheduling of the loads based on dynamic tariffs and implementation of a direct load control (DLC) based demand response program for the domestic consumer is proposed in this work. The load scheduling is carried out using binary particle swarm optimization and a newly prefaced nature-inspired discrete elephant herd optimization technique, and their effectiveness in minimization of cost and the peak-to-average ratio is analyzed. The discrete elephant herd optimization algorithm has acceptable characteristics compared to the conventional algorithms and has determined better exploring properties for multi-objective problems. A prototype hardware model for a home energy management system is developed to demonstrate and analyze the optimal load scheduling and DLC-based demand response program. The controller effectively schedules and implements DLC on consumer devices. The load scheduling optimization helps to improve PAR by a value of 2.504 and results in energy cost savings of ₹ 12.05 on the scheduled day. Implementation of DLC by 15% results in monthly savings of ₹ 204.18. The novelty of the work is the implementation of discrete elephant herd optimization for load scheduling and the development of the prototype hardware model to show effects of both optimal load scheduling and the DLC-based demand response program implementation.

Constraint tightening-based control for small-satellite formations using differential aerodynamic forces

Aerodynamic forces hold significant promise for controlling small-satellite formations in low Earth orbit. However, significant challenges still exist regarding complex input constraints and their application to multi-satellite formations. This paper proposes a constraint tightening-based control scheme for small-satellite formations, utilizing differential drag and lift as actuating forces. Two attitude adjustment strategies, namely the reorientation strategy and the single-radial rotation strategy, are compared in terms of their control effectiveness and applicability. Relative aerodynamic coefficients are employed as control inputs in view of their solid reachable region, followed by the development of a decoupling algorithm for determining pointing angles. Through a method that tightens the reachable region using liner models, the input constraints are linearized and can be explicitly expressed. Subsequently, an observer-based Model Predictive Control (MPC) algorithm is formulated to meet these linearized input constraints and provide feedforward compensation for system disturbances. This discrete algorithm enables practical onboard implementations owing to its low computational complexity. Additionally, a concept of overall computation for all satellites’ attitudes is proposed to adapt the control scheme for multi-satellite formations. Hardware-in-the-loop simulations are conducted to evaluate the control scheme's performance in along-track and circular formations, accounting for uncertainties in aerodynamic forces and attitude dynamics.

Decomposition-based multi-objective approach for a green hybrid flowshop rescheduling problem with consistent sublots

Rescheduling in a hybrid flowshop holds significant importance in modern industries that face uncertain events. Moreover, real-world manufacturing scenarios often utilise lot streaming to enhance market competitiveness. In light of escalating energy demands and their consequential environmental impacts, contemporary manufacturing companies are placing a heightened emphasis on energy efficiency. This study addressed a green hybrid flowshop rescheduling problem with consistent sublots (GHFRP_CS) in the context of urgent lot insertion. Initially, we establish an optimisation model aimed at minimising the makespan, total energy consumption, and system stability. To tackle this NP-hard multi-objective optimization problem, we develop a constructive heuristic generating promising solutions based on lot split, sequence, and local search rules. Further improvement is achieved through a multi-objective discrete artificial bee colony algorithm (MDABC). MDABC decomposes the problem into sub-problems, initiating solutions with the constructive heuristic and refining them through employed bee, onlooker bee, and scout bee phases. Computational experiments compare MDABC with other multi-objective evolutionary algorithms (MOEAs) on small- and large-scale problems. Results demonstrate MDABC's superiority, achieving fourfold accuracy and efficiency enhancement for small-scale instances and sixfold improvement for large-scale problems at low cost compared to other MOEAs.

Manipulation order optimization in industrial pick-and-place operations: application to textile and leather industry

This work addresses the problem of the development of a robotic system for the picking of parts cut by a CNC machine and the optimization of the sequencing of this picking process. An automated parts collection system is optimized to reduce the time required to perform the task of both picking and the subsequent classification by the type of part. The automated picking system, which is located at the end of a cutting machine, uses a robot equipped with an additional axis to expand its working space. Therefore, in this proposal, the industrial equipment necessary to automate this process is designed and the process to be optimized is computationally modeled. In particular, three discrete optimization algorithms are analyzed, with different evolution strategies and operators, but all of them are free of specific configuration parameters. The whole process is shown in this research, from the design of the procedure to the design of the tool, the algorithm selection, and elements validation. Finally, the first steps towards its industrial implementation are presented, and the hypothesis behind this project is validated.

Optimization for cost-effective design of water distribution networks: a comprehensive learning approach

The Comprehensive Learning Gravitational Search Algorithm (CLGSA) has demonstrated its effectiveness in solving continuous optimization problems. In this research, we extended the CLGSA to tackle NP-hard combinatorial problems and introduced the Discrete Comprehensive Learning Gravitational Search Algorithm (D-CLGSA). The D-CLGSA framework incorporated a refined position and velocity update scheme tailored for discrete problems. To evaluate the algorithm's efficiency, we conducted two sets of experiments. Firstly, we assessed its performance on a diverse range of 24 benchmarks encompassing unimodal, multimodal, composite, and special discrete functions. Secondly, we applied the D-CLGSA to a practical optimization problem involving water distribution network planning and management. The D-CLGSA model was coupled with the hydraulic simulation solver EPANET to identify the optimal design for the water distribution network, aiming for cost-effectiveness. We evaluated the model's performance on six distribution networks, namely Two-loop network, Hanoi network, New-York City network, GoYang network, BakRyun network, and Balerma network. The results of our study were promising, surpassing previous studies in the field. Consequently, the D-CLGSA model holds great potential as an optimizer for economically and reliably planning and managing water networks.

Research on Flexible Job Shop Scheduling Problem with Handling and Setup Time Based on Improved Discrete Particle Swarm Algorithm

With the gradual emergence of customized manufacturing, intelligent manufacturing systems have experienced widespread adoption, leading to a surge in research interests in the associated problem of intelligent scheduling. In this paper, we study the flexible job shop scheduling problem (FJSP) with setup time, handling time, and processing time in a multi-equipment work center production environment oriented toward smart manufacturing and make-to-order requirements. A mathematical model with the optimization objectives of minimizing the maximum completion time, the total number of machine adjustments, the total number of workpieces handled and the total load of the machine is constructed, and an improved discrete particle swarm algorithm based on Pareto optimization and a nonlinear adaptive inertia weighting strategy is proposed to solve the model. By integrating the model characteristics and algorithm features, a hybrid initialization method is designed to generate a higher-quality initialized population. Next, three cross-variance operators are used to implement particle position updates to maintain information sharing among particles. Then, the performance effectiveness of this algorithm is verified by testing and analyzing 15 FJSP test instances. Finally, the feasibility and effectiveness of the designed algorithm for solving multi-objective FJSPs are verified by designing an FJSP test example that includes processing time, setup time and handling time.

Symbol detection based on a novel discrete harmony search algorithm in MIMO-FBMC/OQAM system

Due to its high spectral efficiency and various other advantages, filter bank multicarrier/offset quadrate amplitude modulation (FBMC/OQAM) has long been considered as a candidate waveform for the fifth generation (5G) and beyond telecommunication technologies. On the other hand, it is possible to both increase the data rate and alleviate the channel fading effects by using the multiple-input multiple-output (MIMO) antenna structure in the FBMC/OQAM transceiver. However, since the symbol detection is an indispensable task to be fulfilled in wireless communication, it is crucial to employ an efficient symbol detector at the MIMO-FBMC/OQAM receiver. Maximum likelihood (ML) detector, which always finds the optimal symbols by trying all of the possible symbol combinations likely to be transmitted, is known for its extremely high computational complexity making it impractical to be used in any system. On the other hand, it is possible to both considerably reduce the ML complexity and achieve the near-ML performance by optimizing the symbol vectors instead of implementing an exhaustive search. Since searching for the optimal symbol combination in discrete space is a combinatorial optimization problem, we developed a novel discrete harmony search (disHS) algorithm to perform this operation. According to the simulation results, the newly developed disHS algorithm not only achieves near-ML performance with lower computational complexity, but also clearly leaves behind the other symbol detectors considered in this paper.

Iterated Crank–Nicolson Method for Peridynamic Models

In this paper, we explore the iterated Crank–Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method was originally developed for hyperbolic advection equations. In peridynamics, we apply the ICN algorithm for temporal discretization and the midpoint quadrature method for spatial integration. Several numerical tests are carried out to evaluate the performance of the ICN method. In general, the ICN method demonstrates second-order accuracy, consistent with the Störmer–Verlet (SV) method. When the weight is 1/3, the ICN method behaves as a third-order Runge–Kutta method and maintains strong stability-preserving (SSP) properties for linear problems. Regarding energy conservation, the ICN algorithm maintains at least second-order accuracy, making it superior to the SV method, which converges linearly. Furthermore, selecting a weight of 0.25 results in fourth-order superconvergent energy variation for the ICN method. In this case, the ICN method exhibits energy variation similar to that of the fourth-order Runge–Kutta method but operates approximately 20% faster. Higher-order convergence for energy can also be achieved by increasing the number of iterations in the ICN method.

A Discrete Adaptive Lion Optimization Algorithm for QoS-Driven IoT Service Composition with Global Constraints

A Discrete Adaptive Lion Optimization Algorithm for QoS-Driven IoT Service Composition with Global Constraints

Advanced vehicle routing in cement distribution: a discrete Salp Swarm Algorithm approach

ABSTRACT In this research, the focus is on addressing the capacitated vehicle routing problem (CVRP), a prominent logistical challenge within transportation management. The discrete salp swarm algorithm (DSSA) has been introduced as an innovative adaptation of the traditional salp swarm algorithm (SSA), specifically redesigned to cater to discrete characteristics inherent in problems like the CVRP. This algorithm integrates the core principles of SSA with mutation and crossover techniques, enhancing its applicability for discrete problems. The paper contributes in two main areas: firstly, the development of DSSA, tailored to address the unique requirements of VRP scenarios and ensuring a balanced approach between exploration and exploitation in discrete optimization. Secondly, the effectiveness of DSSA is demonstrated through practical applications, including an 8-customer routing task and a real-world case study involving cement delivery in Vietnam. In these scenarios, DSSA consistently demonstrates superior performance over other meta-heuristic strategies, marking a noteworthy advancement in the domain of optimization and providing a potential tool for complex routing challenges in logistics and distribution systems.

Pattern Masking for Dictionary Matching: Theory and Practice

Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application areas, such as in record linkage of personal data. This work formalizes the Pattern Masking for Dictionary Matching (PMDM) problem: given a dictionary D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {D}$$\\end{document} of d strings, each of length ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document}, a query string q of length ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document}, and a positive integer z, we are asked to compute a smallest set K⊆{1,…,ℓ}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K\\subseteq \\{1,\\ldots ,\\ell \\}$$\\end{document}, so that if q[i] is replaced by a wildcard for all i∈K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i\\in K$$\\end{document}, then q matches at least z strings from D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {D}$$\\end{document}. Solving PMDM allows providing data utility guarantees as opposed to existing approaches. We first show, through a reduction from the well-known k-Clique problem, that a decision version of the PMDM problem is NP-complete, even for binary strings. We thus approach the problem from a more practical perspective. We show a combinatorial O((dℓ)|K|/3+dℓ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {O}((d\\ell )^{|K|/3}+d\\ell )$$\\end{document}-time and O(dℓ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {O}(d\\ell )$$\\end{document}-space algorithm for PMDM for |K|=O(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|K|=\\mathscr {O}(1)$$\\end{document}. In fact, we show that we cannot hope for a faster combinatorial algorithm, unless the combinatorial k-Clique hypothesis fails (Abboud et al. in SIAM J Comput 47:2527–2555, 2018; Lincoln et al., in: 29th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2018). Our combinatorial algorithm, executed with small |K|, is the backbone of a greedy heuristic that we propose. Our experiments on real-world and synthetic datasets show that our heuristic finds nearly-optimal solutions in practice and is also very efficient. We also generalize this algorithm for the problem of masking multiple query strings simultaneously so that every string has at least z matches in D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {D}$$\\end{document}. PMDM can be viewed as a generalization of the decision version of the dictionary matching with mismatches problem: by querying a PMDM data structure with string q and z=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=1$$\\end{document}, one obtains the minimal number of mismatches of q with any string from D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {D}$$\\end{document}. The query time or space of all known data structures for the more restricted problem of dictionary matching with at most k mismatches incurs some exponential factor with respect to k. A simple exact algorithm for PMDM runs in time O(2ℓd)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {O}(2^\\ell d)$$\\end{document}. We present a data structure for PMDM that answers queries over D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {D}$$\\end{document} in time O(2ℓ/2(2ℓ/2+τ)ℓ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {O}(2^{\\ell /2}(2^{\\ell /2}+\ au )\\ell )$$\\end{document} and requires space O(2ℓd2/τ2+2ℓ/2d)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {O}(2^{\\ell }d^2/\ au ^2+2^{\\ell /2}d)$$\\end{document}, for any parameter τ∈[1,d]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au \\in [1,d]$$\\end{document}. We complement our results by showing a two-way polynomial-time reduction between PMDM and the Minimum Union problem [Chlamtáč et al., ACM-SIAM Symposium on Discrete Algorithms (SODA) 2017]. This gives a polynomial-time O(d1/4+ϵ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {O}(d^{1/4+\\epsilon })$$\\end{document}-approximation algorithm for PMDM, which is tight under a plausible complexity conjecture. This is an extended version of a paper that was presented at International Symposium on Algorithms and Computation (ISAAC) 2021.

Multi-distribution bi-deniable inner product encryption based on Decision-LWE

Bi-deniable Encryption scheme means that when the sender and the receiver are coerced, the coercer can obtain fake plaintext, random numbers, and secret keys. It’s a solution strategy in the case of information leakage. Compared with traditional encryption, deniable encryption can provide secret communications in situations of coercion in the Post-Quantum era. Compared with sender-deniable encryption and receiver-deniable encryption, bi-deniable encryption can achieve secret communications in the situation that both sender and receiver are coerced by the coercer. So, we propose to design a bi-deniable encryption scheme under the multi-distribution model. In our bi-deniable encryption scheme, we construct a bi-deniable encryption scheme based on the assumption of Decision-Learning With Errors (DLWE) under the multi-distribution model. Firstly, the principle of Inner Product Predicate Encryption (IPPE) is applied in our scheme. Secondly, we apply the framework of Bi-Translucent Set (BTS), combined with inner product predicate encryption. Thirdly, we construct a series of probabilistic polynomial time algorithms, which apply linear transformation between different lattice structures, and Regev dual encryption. Fourthly, the statistical indistinguishability between the sampling algorithm with discrete Gaussian sampling algorithm, and the computational indistinguishability between LWE’s ciphertext samples with uniform samples, the property of indistinguishability is applied in theorem proving, which obtain Indistinguishability under Chosen Plaintext Attacks (IND-CPA) security and the property of bi-deniability. Given the value range of the Gaussian parameter and security parameter in our scheme, the correctness of the bi-deniable encryption scheme is guaranteed. We also give the security proof of IND-CPA and bi-deniability’s property by a series of games. The ‘Inner-Product Bi-Translucent Set’ Bi-Deniable Encryption scheme under the multi-distribution model is based on Decision-LWE assumption, and can avoid quantum-resistant attacks. The bi-deniable encryption scheme is firstly constructed by the inner product with the Decision-LWE assumption, which can provide better properties of security and deniability.

A study on the application of discrete curvature feature extraction and optimization algorithms to battery health estimation

A study on the application of discrete curvature feature extraction and optimization algorithms to battery health estimation