Time Complexity Of Algorithm Research Articles

Time Complexity of Knuth Morris Algorithm and Rejang Algorithm in Rejang-Indonesian Translator

Among the pattern-matching algorithms is the Knuth-Morris algorithm. In order to minimize the number of comparisons required and, in the worst scenario, achieve an ideal O(n+m) running time, the Knuth-Morris search algorithm skips unneeded comparisons. Every character in the text and every character in the pattern must be checked at least once by the pattern-matching algorithm. The Knuth-Morris algorithm's primary goal is to preprocess the pattern string P in order to determine the failure function f, which displays P's precise shift, so that earlier comparisons can be reused. In order to extract the fundamental word of the attached sentence, words containing affixes are separated using the Rejang stemming method. The purpose of this research is to determine the time complexity of the Rejang method and the Knuth-Morris algorithm based on affix groups. The Rapid Application Development (RAD) approach, which entails planning, designing, building, and implementing, is used during the research stages. The research results have produced efficient and effective Knuth Morris algorithm and Rejang algorithm, where efficiency is indicated by the algorithm time complexity of O (log n), and effectiveness is indicated by the accuracy results of 99% against testing 6000 affixed words.

Time-Efficient RSA over Large-Scale Multi-Domain EON.

The poor timeliness of routing has always been an urgent problem in practical operator networks, especially in situations with large-scale networks and multiple network domains. In this article, a pruning idea of routing integrated with Dijkstra's shortest path searching is utilized to accelerate the process of routing in large-scale multi-domain elastic optical networks (EONs). The layered-graph approach is adopted in the spectrum allocation stage. To this end, an efficient heuristic algorithm is proposed, called "Branch-and-Bound based Routing and Layered Graph based Spectrum Allocation algorithm (BBR-LGSA)", which is an integrated RSA algorithm. Notably, the significant reduction in algorithm time complexity is not only reflected in the pruning method used in the routing stage but also in the construction of auxiliary graphs during the spectrum allocation stage utilizing the Branch-and-Bound method. Simulation results show that the proposed BBR-LGSA significantly reduces the average running time by nearly 78% with higher spectrum utilization in large-scale multi-domain EONs, compared with benchmark algorithms. In addition, the impact of key parameters on performance comparisons of different algorithms is evaluated.

Robot inverse kinematics solution for center selection battle royale optimization algorithm

In order to solve the problems of high time complexity and insufficient global exploration ability of the battle royale optimization algorithm, this paper proposes an improved battle royale optimization algorithm based on chaos mapping, center selection and elite adaptive strategy. Through benchmark function testing, compared to particle swarm optimization algorithm, whale optimization algorithm, and the battle royale optimization algorithm, the improved algorithm significantly reduces time complexity and notably enhances convergence precision, speed, and stability. The improved algorithm is applied to the inverse kinematics problem of robots. The accuracy and The stability of the improved algorithm is better than those of the traditional battle royale optimization algorithm, it demonstrates superior solving precision and stability, proving its practicality and potential for development in solving robot inverse kinematics problems.

Correction of ‘J. Laderman, V. Pan, X.–H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-588’

In this article, we corrected the trilinear formula for triple disjoint matrix multiplication given in the article ‘J. Laderman, V. Pan, X. H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-588’, which is incorrect for matrix dimensions equal to two or greater. That formula is a base of two algorithms, for disjoint and single matrix multiplication. The necessary correction made the amount of non–scalar products rise, slightly increasing the algorithm time complexity. We also corrected explicit formulas, in the bilinear form, for triple disjoint matrix multiplication. They are explicit, and thus convenient for the practical use of the fast matrix multiplication algorithms in question.

Application of Bubble Sort Optimization in New Student Admission Selection Using Brute Force Algorithm

This study investigates the application of a Brute Force algorithm optimized with Bubble Sort for new student admission selection. The Brute Force algorithm, while guaranteeing accurate results, suffers from exponential time complexity with increasing data size, posing a challenge for large applicant pools. To address this limitation, this research integrates Bubble Sort optimization to reduce the execution time complexity of the Brute Force algorithm. This study goes beyond solving the student admission selection problem; it explores optimizing the Brute Force algorithm by leveraging the simplicity and efficiency of Bubble Sort. This approach aims to determine the extent to which the Brute Force algorithm can be optimized for student selection, particularly regarding execution time complexity. The integration of Bubble Sort is hypothesized to significantly improve the performance of the Brute Force algorithm by reordering data before processing, thereby minimizing unnecessary comparisons. This paper presents a comparative analysis of execution times between the traditional Brute Force approach and the optimized version. Preliminary results indicate a substantial improvement in efficiency, suggesting that this hybrid approach could be a valuable solution for similar combinatorial problems with time complexity constraints. Further research could explore the applicability of this optimized algorithm in other domains where time complexity is a critical factor.

Synesth: Comprehensive Syntenic Reconciliation with Unsampled Lineages

We present Synesth, the most comprehensive and flexible tool for tree reconciliation that allows for events on syntenies (i.e., on sets of multiple genes), including duplications, transfers, fissions, and transient events going through unsampled species. This model allows for building histories that explicate the inconsistencies between a synteny tree and its associated species tree. We examine the combinatorial properties of this extended reconciliation model and study various associated parsimony problems. First, the infinite set of explicatory histories is reduced to a finite but exponential set of Pareto-optimal histories (in terms of counts of each event type), then to a polynomial set of Pareto-optimal event count vectors, and this eventually ends with minimum event cost histories given an event cost function. An inductive characterization of the solution space using different algebras for each granularity leads to efficient dynamic programming algorithms, ultimately ending with an O(mn) time complexity algorithm for computing the cost of a minimum-cost history (m and n: number of nodes in the input synteny and species trees). This time complexity matches that of the fastest known algorithms for classical gene reconciliation with transfers. We show how Synesth can be applied to infer Pareto-optimal evolutionary scenarios for CRISPR-Cas systems in a set of bacterial genomes.

Enhancing Wave Function Collapse Algorithm for Procedural Map Generation Problem

In this study, the Improved Map Generation Algorithm (GHAO) method is presented to improve traditional methods in procedural map creation. Traditional procedural map generation techniques using noise generation exhibit shortcomings in the consistent composition of a real map with its uniformly distributed features. On the other hand, procedural map creation techniques that use wave function collapse require that some map pieces already exist to create a map. The observed disadvantages were eliminated by using a hybrid technique with the designed GHAO method. The developed algorithm is similar to real maps in terms of the distribution of map regions, does not need 3D model parts, and performs map creation operations without increasing the algorithm's time complexity. The evaluation of IMGA was carried out by coding the method into the Unity game engine.

A survey of dynamic programming algorithms

Dynamic programming is an important algorithmic idea with widespread applications in computer science and other disciplines. With the continuous improvement of computing power and the increasing complexity of practical problems, dynamic programming algorithms have also received more and more attention. However, due to the limitations of the dynamic programming algorithm itself, it also brings challenges to the optimization of the algorithm and its application in different fields. This paper uses the methods of literature review and case analysis to systematically summarize and sort out the basic principles, complexity analysis, classic problems, and applications of dynamic programming algorithms. First of all, this paper discusses the basic concepts of splitting and optimal substructure characteristics of related problems in dynamic programming; secondly, it discusses the time complexity and space complexity of dynamic programming algorithms in detail; then, in the classic dynamic programming The case part focuses on the knapsack problem, including the 0-1 knapsack problem and multiple knapsack problems; finally, this paper discusses the wide application and optimization of dynamic programming algorithms in practice, covering natural language processing, bioinformatics and How to optimize the dynamic programming algorithm to improve the efficiency of problem solving and reduce resource consumption. To sum up, this paper fully demonstrates the basic principles and applications of dynamic programming algorithms, as well as optimization methods and development trends, and provides guidance and references for their academic and practical applications.

An effective theoretical and experimental analysis method for the improved slime mould algorithm

Metaheuristic intelligent optimization algorithms are effective methods for solving high-dimensional nonlinear complex optimization problems. The slime mould algorithm is a novel intelligent optimization algorithm proposed in 2020. However, the basic slime mould algorithm still has some shortcomings, such as slow convergence rate, easy to fall into local extremum, and unbalanced exploration and development capability. To further improve and expand the optimization ability and application scope of the slime mould algorithm, and enhance its performance in solving large-scale complex optimization problems, this paper proposes a slime mould algorithm (PPMSMA) based on Gaussian perturbation and phased position update, positive variation, and multi-strategy greedy selection. Firstly, Gaussian perturbation and phased position update mechanism are introduced to avoid the difficulty of the algorithm to jump out of the local extrema and also to speed up the convergence of the algorithm. Then, a positive variation strategy based on the sine cosine mechanism is introduced to move the variation of the population towards a better direction. Finally, a multi-strategy greedy selection mechanism is introduced, which effectively improves the search ability of the algorithm. The analysis and research on the optimization ability and performance of metaheuristic algorithms mainly include two aspects: theoretical analysis and experimental testing. Theoretical analysis has always been a relatively weak link in the research of metaheuristic algorithms, and there is currently no clear and effective method formed. For experimental testing, although there are more methods, they often lack systematization and adequacy. In this paper, a more complete, fine-grained and systematic approach to theoretical and experimental analysis is proposed. In the theoretical analysis part, the time complexity and spatial complexity of the PPMSMA algorithm are analytically proved to be the same as the basic slime mould algorithm, and the probability measure method is used to prove that PPMSMA algorithm can converge to the global optimal solution. In the simulation experiment section, the PPMSMA algorithm is compared with multiple sets of 10 representative comparison algorithms on the CEC2017 complex test function set suite for optimization accuracy analysis, Friedman comprehensive ranking analysis, average optimization rate analysis of PPMSMA relative to other algorithms, convergence curve analysis, and Wilcoxon rank-sum test analysis. To further examine the scalability of the improved algorithm in solving large-scale optimization problems, PPMSMA is compared with the above 10 comparative algorithms under 1000 dimensional conditions in the large-scale global optimization test set CEC2010, and the solution stability of each algorithm is analyzed through violin plots. The results show that the PPMSMA algorithm has significantly improved convergence performance, optimization accuracy, and solution stability in both high-dimensional and large-scale complex problems, and has significant advantages compared to multiple sets of 10 representative comparative algorithms. Finally, PPMSMA and 10 other comparative algorithms are used to solve engineering design optimization problems with different complexities. The experimental results validate the universality, reliability, and superiority of PPMSMA in handling engineering design constraint optimization problems.

New Programmable LFSR Counters with Automatic Encoding and State Extension

An efficient method for detecting the end of a count of a linear feedback shift register (LFSR) is presented. We show how this detector can be used to extend a maximum-length LFSR sequence by a number of states up to one less than the degree of the polynomial. In addition, a new algorithm is proposed to encode binary sequence values into their corresponding LFSR sequence states. Based on this algorithm and an alternative second method, two novel programmable, full-range, high-speed LFSR counter designs are proposed. The time complexity of the conversion algorithms ranges from quadratic to exponential time in the degree of the underlying polynomial. The proposed counter solutions are fully synchronous and can be implemented with standard cells, enabling easy portability across technologies. As the levels of logic are independent of the counter size, high scalability is facilitated. For evaluation, all the designs, including the recreated state-of-the-art solution, have been implemented on an FPGA, and also simulated targeting TSMC’s N3 CMOS process node for a wide range of counter sizes. The results confirm the superiority of the proposed solutions over the state of the art in terms of frequency, area and power efficiency as the counter is scaled up.

An <i>n</i>-dimensional discrete hyperchaotic system and its application in audio encryption

Discrete chaotic system, as a pseudo-random signal source, plays a very important role in realizing secure communication. However, many low-dimensional chaotic systems are prone to chaos degradation. Therefore, many scholars have studied the construction of high-dimensional chaotic systems. However, many existing algorithms for constructing high-dimensional chaotic systems have relatively high time complexity and relatively complex structures. To solve this problem, this paper explores an <i>n</i>-dimensional discrete hyperchaotic system with a simple structure. Firstly, the <i>n</i>-dimensional discrete hyperchaotic system is constructed by using sine function and power function and simple operations. Then, it is theoretically analyzed based on Jacobian matrix method that the system can have the positive Lyapunov exponents. Next, the algorithm time complexity, sample entropy, correlation dimension and other indexes are compared with those of the existing methods. The experimental results show that our system has a simple structure, high complexity and good algorithm time complexity. Therewith, a six-dimensional chaotic system is chosen as an example, and the phase diagram, bifurcation diagram, Lyapunov expnonents, complexity and other characteristics of the system are analyzed. The results show that the proposed system has good chaotic characteristics. Moreover, to show the application of the proposed system, we apply it to audio encryption. According to this system, we combine it with the XOR operation and true random numbers to explore a novel method of one-cipher audio encryption. Through experimental simulation, compared with some existing audio encryption algorithms, this algorithm can satisfy various statistical tests and resist various common attacks. It is also validated that the proposed system can be effectively applied to the field of audio encryption.

Implementation of String Matching Algorithm with Finite Automata in The Indonesian-Korean Dictionary Application

Foreign languages become a connection both in terms of communication, association, culture, and science in the digital era. One of these languages is the Korean language, which has gained significant popularity among Indonesian people. However, learning the Korean language can be challenging due to its distinct alphabet compared to the Indonesian alphabet. Therefore, the user-friendly dictionary is needed for Indonesian people, namely the Indonesian-Korean Dictionary based on Android platform. This dictionary implements Finite Automata for string searching. The system matches the user's input string with the strings in the database. The output of this application includes the matched words and the search time. Based on the results of 10 tests system using Finite Automata, the system's efficiency in processing search patterns showing the average running time is 15.8 ms. Additionally, after conducting an in-depth analysis of the algorithm's time complexity, it was confirmed to have a time complexity of O(n3). This demonstrates that the system successfully matches strings effectively and produces reliable results.

Influence maximization in social networks using community-diversified seed selection

Abstract The community-based influence maximization in social networks refers to the strategy of amplifying the influence by leveraging the underlying connectivity patterns of the online communities. This promotes the widespread dissemination of user-generated content across socially connected entities. In our work, we have combined the simplicity of degree centrality and the bridging strength of betweenness for maximizing the influence performance. We have used community detection for partitioning the whole network into smaller subnetworks for intelligent distribution of seed nodes among these communities for improving the rate of information spreading. The proposed ranking, named as Community Diversified Seed Selection, is compared with degree centrality and betweenness centrality-based ranking in terms of rate of spreading, absolute execution time and algorithmic time complexity. The comparative study was performed on LFRμ= 0.01, LFRμ= 0.02 and LFRμ= 0.03 benchmark networks, and validated using Facebook real-world social network. Our proposed algorithm has better and faster spreading with reasonable time complexity, therefore, making it a suitable choice for larger networks.

Time Complexity of Population-Based Metaheuristics

This paper is a brief guide aimed at evaluating the time complexity of metaheuristic algorithms both mathematically and empirically. Starting with the mathematical foundational principles of time complexity analysis, key notations and fundamental concepts necessary for computing the time efficiency of a metaheuristic are introduced. The paper then applies these principles on three well-known metaheuristics, i.e. differential evolution, harmony search and the firefly algorithm. A procedure for the empirical analysis of metaheuristics' time efficiency is then presented. The procedure is then used to empirically analyze the computational cost of the three aforementioned metaheuristics. The pros and cons of the two approaches, i.e. mathematical and empirical analysis, are discussed.

Data relative currency repair and anomaly detection based on rules

Data currency is a temporal reference of the data, it reflects the degree to which the data is current with the world it models. Currency has a significant impact on the quality and value of the data. Once the time stamp of the data is lost or tampered with, it is difficult to perform an absolute and precise repair. Based on data currency research, the basic currency rules were extended to support the parallelization of rule extraction and incremental updating and theoretically reduce the algorithm time complexity from O(n−1) to O(log(n)). In practical experiments, the repair efficiency of multithreading is improved by up to 75.2% compared with single-threaded operation. According to the problems and requirements encountered in data cleaning, rule-based methods for relative currency repair and anomaly data detection were proposed, a relative currency repair algorithm was implemented, models for evaluating repair results were established, and the method of applying a repair algorithm to detect abnormal currency data was also discussed. The experimental results and analysis show that the extended currency rules that provide more valuable features are feasible and available, and the relative currency repair algorithm can effectively perform data currency repair and anomaly detection.

PLATON: Top-down R-tree Packing with Learned Partition Policy

The exponential growth of spatial data poses new challenges to the performance of spatial databases. Spatial indexes like R-tree greatly accelerate the query performance and can be effectively constructed through packing, i.e., loading all data into the index at once. However, existing R-tree packing methods rely on a set of fixed heuristic rules, which may not be suitable for different data distributions and workload patterns. To address the limitations of existing R-tree packing methods, we propose PLATON, a top-down R-tree packing method with learned partition policy that explicitly optimizes the query performance with regard to the given data and workload instance. We develop a learned partition policy based on Monte Carlo Tree Search and carefully make design choices for the MCTS exploration strategy and simulation strategy to improve algorithm convergence. We propose a divide and conquer strategy and two optimization techniques, early termination and level-wise sampling, to drastically reduce the MCTS algorithm's time complexity and make it a linear-time algorithm. Experiments on both synthetic and real-world datasets demonstrate the superior performance of PLATON over existing R-tree variants and recently proposed learned/workload-aware spatial indexes.

An efficient adaptive Masi entropy multilevel thresholding algorithm based on dynamic programming

Masi entropy multilevel thresholding can utilize additive and non-extensive information in images to effectively segment a complex image. However, the entropy index of Masi entropy cannot be selected automatically, and the time complexity of the multilevel algorithm by exhaustive searching grows exponentially with the increase of the threshold numbers. To address these two problems, an adaptive entropy index selection strategy based on image histogram information is proposed first. To improve the computation efficiency, an efficient solution for the adaptive Masi entropy multilevel thresholding algorithm based on dynamic programming (DP + AMasi) is also proposed. The DP + AMasi algorithm is compared with the Masi entropy multilevel thresholding algorithm by exhaustive search and state-of-the-art metaheuristic algorithms on three benchmark datasets. The effectiveness of the DP + AMasi is verified by fitness function values, Uniformity Measure, Davies Bouldin index, and CPU run time. In addition, the Wilcoxon test is used to analyze the differences between algorithms.

Deterministic constructive vN-NEH[formula omitted] algorithm to solve permutation flow shop scheduling problem with makespan criterion

Scheduling jobs in a permutation flow shop (PFS) environment is one of the most studied problems in scheduling theory and practice. In this paper, we propose a new efficient algorithm to solve the permutation flow shop scheduling problem (PFSP) with the makespan criterion. The proposed algorithm, referred to as vN-NEH+, extends the Nawaz–Enscore–Ham (NEH) heuristic by employing the variable-length list (vN-list) of candidate jobs. Extensive numerical experiments on the standard set of benchmarks show that the proposed vN-NEH+ algorithm is one of the most efficient NEH-based deterministic constructive algorithms in terms of trade-off between solution quality and computing time. Moreover, in contrary to existing scheduling methods, vN-NEH+ produces in a single run a set of good quality solutions that can serve as an initial population in population-based metaheuristics for solving PFSPs. Another advantage of vN-NEH+ is that it can work in parallel mode, which is difficult or even impossible with other NEH-based heuristics. In addition to vN-NEH+, we propose a new ART.NEH (Average Relative Time over NEH) indicator to assess the running time of PFSP algorithms. The main advantage of ART.NEH is its hardware/software and instance size independence, which allows an objective and reliable comparison of computational effort of PFSP algorithms. In addition, the idea behind ART.NEH can be easily adopted to reliably assess time complexity of algorithms for solving various other computational problems.

Analysis and Improvement of the Current Pothole Detection System in Google Maps through Color Segmentation

Abstract: This paper presents algorithms for pothole detection on roads. We have collected a vast dataset from various sources and organized it into a structured format. Data preprocessing techniques were applied to reduce algorithm time and space complexity. The refined dataset was used for training, leading to the development of different models using color segmentation. The results obtained from these models demonstrated an impressive accuracy of 91% using color segmentation. The creation of this pothole detection system can significantly enhance safety for both you and others. Moreover, it has the potential to be widely integrated into Google Maps by extracting coordinates from Geographical Information System (GIS) data and incorporating them into the platform.

Radiant Thermal Test System for Turbine Blades Using a Novel Pattern Search Algorithm

Abstract We established and validated a radiant thermal test system using a miniaturized quartz lamp heating device designed with a novel search algorithm to meet aero-engine blade heating requirements. The device can perform rapid, high-temperature gradient tests on new-material aero-engine blades, which cannot be achieved through electromagnetic induction. The algorithm, derived from the Monte Carlo method (MCM) and pattern search, can solve the problems of the classical iterative search algorithm by searching lamp parameters and reducing the algorithm's time complexity. These searched power parameters enable the system's closed-loop control to achieve temperature gradients easily. The corresponding heating process was also simulated using commercial numerical analysis software, serving as a numerical validation for the algorithm-based system. The device could meet the thermal fatigue test requirements for the blade at six different temperature control points, including a maximum temperature exceeding 1150 K, a maximum temperature difference exceeding 160 K within 20 mm, and a heating rate exceeding 30 K/s. Thus, the device provides a promising technique for rapid, high-temperature heat treatment of complex small components, and the algorithm makes designing miniaturized quartz lamp heating devices more accessible and versatile for small components.