Interpolation Search Research Articles

Interpolation Once Binary Search over a Sorted List

Searching over a sorted list is a classical problem in computer science. Binary Search takes at most log2⁡n+1 tries to find an item in a sorted list of size n. Interpolation Search achieves an average time complexity of O(log⁡log⁡n) for uniformly distributed data. Hybrids of Binary Search and Interpolation Search are also available to handle data with unknown distributions. This paper analyzes the computation cost of these methods and shows that interpolation can significantly affect their performance—accordingly, a new method, Interpolation Once Binary Search (IOBS), is proposed. The experimental results show that IOBS outperforms the hybrids of Binary Search and Interpolation Search for nonuniformly distributed data.

Mechanical Fault Sound Source Localization Estimation in a Multisource Strong Reverberation Environment

Aiming at the sound source localization of mechanical faults in a strong reverberation scenario with multiple sound sources, this paper investigates a mechanical fault source localization method using the U-net deep convolutional neural network. The method utilizes the SRP-PHAT algorithm to calculate the response power spectra of the collected multichannel fault signals. Through the utilization of the U-net neural network, the response power spectra containing spurious peaks are transformed into “clean” estimated source distribution maps. By employing interpolation search, the estimated source distribution maps are processed to obtain location estimations for multiple fault sources. To validate the effectiveness of the proposed method, this paper constructs an experimental dataset using mechanical fault data from electromechanical equipment relays and conducts sound source localization experiments. The experimental results show that the U-net network under 0.2 s/0.5 s/0.7 s reverberation time can effectively eliminate spurious peak interference in the response power spectrum. As the signal-to-noise ratio decreases, it can still distinguish the sound sources with a distance of 0.2 m. In the context of multifault source localization, the method is capable of simultaneously locating the positions of four fault sources, with an average localization error of less than 0.02 m. The method in this paper effectively eliminates spurious peaks in the response power spectra under conditions of multisource strong reverberation. It accurately locates multiple mechanical fault sources, thereby significantly enhancing the efficiency of mechanical fault detection.

A progressive damage model for carbon fiber-reinforced polymer laminates subjected to fastener pull-through failure

Most studies on composite joints focus on in-plane bearing mode, while little attention to fastener pull-through failure mode from out-of-plane loads. This paper presents a 3D continuum damage mechanics (CDM) model to investigate and assess the mechanical behaviors of carbon fiber-reinforced polymer (CFRP) laminates subjected to pull-through failure. The proposed model based on the use of intralaminar and interlaminar damage models is established and implemented by means of a user-defined subroutine VUMAT for Abaqus/Explicit. The novelty lies in the material model integrating the thresholds preset by the semianalytical approximation approach, which largely eliminates unnecessary fracture angle enumerations in Puck’s IFF theory, coupled with the simple parabolic interpolation search (SPIS) technique for optimal fracture angle search, considerably reducing the computational burden. Moreover, the numerical results compare well with experiments, effectively replicating the load–displacement response, damage modes, failure behaviors and damaged areas. This study provides an accurate and efficient computational methodology to analyze pull-through failures, enhancing the damage modeling and predictive capabilities for composite joints under out-of-plane loads.

Псевдоспектральный метод поиска оптимального управления пучками траекторий на базе мультиагентных алгоритмов оптимизации

<p>A class of problems of optimal control of nonlinear continuous deterministic systems under conditions of uncertainty is considered. To solve the problem, a numerical algorithm for finding the optimal control is formed, in which the parameterization of the control law is used, which depends on time and a set of coordinates of the state vector available for measurement. This approach is based on the approximation of the control law by a series using a system of basis functions with unknown coefficients. The search for unknown coefficients in the expansion of the control law is implemented using multi-agent optimization methods: a hybrid multi-agent interpolation search algorithm and a multi-agent algorithm based on the use of linear controllers for controlling the movement of agents. A software has been developed and two model examples and an applied problem of stabilizing a satellite with the help of engines installed on it have been solved.</p>

Speed Analysis of Binary Search and Interpolation Search for Searching Identification Numbers on National Identity Cards

Aims: The purpose of the work is to make comparisons and find the best search algorithm between binary search and interpolation search algorithms for searching identity number on Indonesian identity cards.
 Study Design: This study was designed by implementing binary and interpolation algorithms into C language, with a dataset of 5000.
 Place and Duration of Study: Department of Informatic Universitas Multimedia Nusantara, between November 2022 until March 2023.
 Methodology: Binary algorithms and interpolation search will be tested by searching for identity number on identity card data, totaling 5000 data. To measure the level of speed and effectiveness of the two algorithms, this will be done by trying to search for data in various amounts, namely 1000, 2000 and 5000 data, with the data sought between the two algorithms having the same value. Testing is carried out by implementing the two algorithms into C language to get the number of loops and execution time, and testing of the algorithms on each sample dataset is carried out five times to get the average value of the test results.
 Results: The results of the tests that have been carried out between the binary search and interpolation search algorithms from the existing dataset, found that the number of loops in the interpolation loop is 36.57% better than the binary search algorithm, while for execution time, binary search has a faster execution speed of 12.43% than interpolation search.
 Conclusion: It can be concluded that if the dataset is large enough, such as identity card data on Indonesian citizens, and if the computer specifications are adequate, binary search, which has a faster execution time, should be used; however, if the computer specifications are inadequate, interpolation search, which has a smaller number of loop processes, should be used.

Paw Search – A Searching Approach for Unsorted Data Combining with Binary Search and Merge Sort Algorithm

Searching is one of the oldest core mechanism of nature. Nature is changing gradually along with searching approaches too. Data Mining is one of the most important industrials topic now-a-days. Under this area all social networks, governmental or non-governmental institutions and ecommerce industries produce a huge number of unsorted data and they are to utilize it. For utilizing this huge number of unsorted data there needs some specific features based unsorted data structure tools like searching algorithm. At present there are several sorted data based searching algorithms like Binary Search, Linear Search, Jump Search and Interpolation Search and so on. In this paper of Paw Search Algorithm, it is fully focused to develop a new approach of searching that can work on unsorted data merging several searching techniques and sorting techniques. This algorithm starts its operation by breaking down the given unsorted array into several blocks by making the square root of the length of the given array. Then these blocks will be searched within its specific formula till the target data is found or not, and in the inner side of each block there will be performed Merge Sort and Binary Search approach gradually. Time and Space Complexity of this Paw Search algorithm is comparatively optimal.

An efficient enhanced prefix hash tree model for optimizing the storage and image deduplication in cloud

SummaryThe popularity of the cloud storage space mainly attracted organizations to store their data in them. Therefore, the avoidance of duplicate data contents is unavoidable and several users share the cloud storage space for data storage, and sometimes this makes higher storage space utilization. Because of the extremely high duplicate copy, memory wastage arises in the case of multimedia data. Identifying the final duplicate copies in the cloud takes more time. To overcome this problem, we employ a significant storage optimization model for deduplication. The digital data hash value is stored by requiring an additional memory space. This study proposed an enhanced prefix hash tree (EPHT) method to optimize the image and text deduplication system to reduce the overhead caused by this procedure. The efficiency of the proposed approach is compared with the interpolation search technique using different levels of tree height (2, 4, 2, 8, 16) in terms of space and time complexity. The proposed EPHT technique shows improvements in terms of speed and space complexity when the number of levels in the EPHT increases.

General Data Search Algorithms for Earth Simulation Systems with Cyclic Boundaries

Grid remapping is one of the most fundamental functions in Earth simulation systems, and is essentially a kind of data interpolation. The key to an efficient interpolation method is how to quickly find the relevant grid points required for interpolation. With the rise of unstructured grid models, the demand for general and efficient interpolation search algorithms is becoming stronger and stronger. KD (K-dimensional) tree has proven to be effective in dealing with unstructured grids. However, it is unable to tackle the cyclic boundary conditions in Earth simulation systems, which restricts the application of KD tree. Taking the nearest neighbor search as an example, this paper introduces two new KD tree-based multi-dimensional data search methods, which break through the limitations of the original method with regards to the cyclic boundary. One method is based on target points duplication, and the other method is based on source points duplication. Their time complexity and space complexity are analyzed and verified by carefully designed experiments. The results show that the method based on target points duplication generally performs better than that based on source points duplication when the data are basically evenly distributed.

APLIKASI GAME EDUKASI BELAJAR MENGHAFAL AYAT-AYAT PENDEK BERBASIS ANDROID MENGGUNAKAN METODE INTERPOLATION SEARCH (STUDI KASUS : TK SULAMUL ULUM)

This research produces output in the form of android-based educational games that can be used in early childhood learning. The results of testing on students illustrate that games can motivate students in learning, especially the introduction of short verses. The interpolation search method helps users search for short verses to be learned.

Aplikasi Kamus Bahasa Indonesia – Palembang Menggunakan Algoritma Interpolation Search Berbasis Android

A dictionary is a book that has been arranged in alphabetical order, the dictionary that we usually find is complete and good, but lately the use of book dictionaries has become a bit behind because people prefer an easy way to interpret a word, namely using an electronic dictionary. Nowadays, there are many Palembang language dictionary applications based on android, but this application has not changed too much from other similar applications. The author took the initiative to develop this electronic dictionary application so that it looks more attractive and user friendly, this application can later facilitate the communication process between tourists and the people of Palembang City, and can be a place to preserve the Palembang language. In the process of making this mobile application, the author uses an interpolation search algorithm to make it easier to search for sorted data tables or files that have a scalar key. Data collection techniques that will be used by conducting observations, interviews and using the Mobile-D development method. The result of this research is an android-based Indonesian-Palembang and Palembang-Indonesian translator dictionary application.

Vector analysis of inverse objective function for electrochemical impedance spectroscopy of big capacity lead-acid battery

The important emergency power supply needs a large capacity battery. The batteries are long-term float charging. Electrochemical impedance spectroscopy (EIS) is important for remaining useful capacity warnings. This paper establishes the EIS inverse calculation technique that is centered in the vector objective function and linear interpolation search algorithm. This technique simplifies the initial value preparation and the gradient descent direction search for the inverse calculation of EIS. The root-mean-square errors of online embedded programming are smaller than the offline results of numerical software for EIS. The vector objective function targets the rotation angle of the initial polarization impedance vector to be zero during the EIS inverse calculation. This equivalently replaces the regular minimization of root-mean-square error. The linear interpolation algorithm simplifies the gradient descent direction search to a one-dimensional search for the double-layer capacitance of the initial polarization impedance. This algorithm replaces the conventional graphic method and evolutionary algorithm. The proposed algorithm is verified by the microcontroller at Valve-regulated lead-acid (VRLA) batteries (4200 Ah). The result of the algorithm is close to special numerical software for EIS. This algorithm improves the performance of an embedded management board.

Searching String in Big-Data: A Better Approach by Applied Machine Learning

There are hot patterns of huge data sets in numerous regions in the course of the most recent 5 years. Looking through string or pattern from a gigantic record is intense generally in the event of randomized situation. These require the advancement of new algorithmic strategies to investigate such enormous data sets and solve optimization errands utilizing sorting on indexing levels and Applied Machine Learning Models. One of the essential strides in text processing is string searching and pattern matching. A word search algorithm works by finding the first or all the occurrences of a word in a textual data or ASCII files. The pre-processing phase is used to determine the formula for number of positions by which the pattern needs to be shifted in case of a mismatch in the matching phase. The fundamental objective of string search or pattern matching algorithms is to increase efficiency by reducing the number of comparisons and increase the length of shifts in event of a mismatch. The issue of efficiency of string search algorithms has probably never been considered so seriously and genuinely until the virtual content explosion caused by the web and the task of mining valuable data and information from it. In this paper, a better search algorithm “Tara–Paras String Search” is introduced that is faster than conventional Binary Search and Interpolation Search. Indexing levels are introduced by length of the word, sequence total of alphabets and starting letter of the word to reduce the size of input. For analysis, 2 data sets are considered. The dictionary of English words having more than 109,000 words and a list of more than 2.5 Lac sorted numbers and uniformly distributed (multiples of 7) are taken for data sets. Analysis and Implementations Models have been implemented, compared and executed in Python with time complexity and obviously Applied Machine Learning will select the faster one.

Interpolated binary search: An efficient hybrid search algorithm on ordered datasets

The exponential increase in the rate of data size is much higher than the increase in the speed of the computer, which has given much focus to search algorithms in the research literature. Finding an item in an ordered dataset is an efficient method in the data processing. However, binary and interpolation algorithms are commonly used to search ordered datasets in many applications. In this paper, we propose a hybrid algorithm for searching ordered datasets based on the idea of interpolation and binary search. The proposed algorithm is called Interpolated Binary Search (IBS). It is well known that the performance of traditional interpolation search depends specifically on key distribution, and its performance degrades significantly in non-uniform distributed datasets. Therefore, our proposed algorithm works efficiently on various distribution datasets. In particular, IBS aims to search datasets of unknown distribution or datasets that change dynamically and produce a dynamic distribution. Experimental results show that IBS performs better compared to other algorithms that use a similar approach.

A Novel Fast Searching Algorithm Based on Least Square Regression

Currently, the machine learning group is well-understood and commonly used for predictive modelling and feature generation through linear methodologies such as reversals, principal analysis and canonical correlation analyses. All these approaches are typically intended to capture fascinating subspaces in the original space of high dimensions. These methods have all a closed-form approach because of its simple linear structures, which makes estimation and theoretical analysis for small datasets very straightforward. However, it is very common for a data set to have millions or trillions of samples and features in modern machine learning problems. We deal with the problem of fast estimation from large volumes of data for ordinary squares. The search operation is a very important operation and it is useful in many applications. Some applications when the data set size is large, the linear search takes the time which is proportional to the size of the data set. Binary search and interpolation search performs good for the search of elements in the data set in O(logn) and ⋅O(log(⋅logn)) respectively in the worst case. Now, in this paper, an effort is made to develop a novel fast searching algorithm based on the least square regression curve fitting method. The algorithm is implemented and its execution results are analyzed and compared with binary search and interpolation search performance. The proposed model is compared with the traditional methods and the proposed fast searching algorithm exhibits better performance than the traditional models.

Interpolation search-based malicious user detection in smart grids

Nowadays energy theft in smart grids has led to severe economic loss to utility companies and countries across the world. Malicious users who illegally steal electricity from the distribution centre without getting noticed lead to unplanned power loss and blackouts in many developing countries. In order to prevent and find the malicious users who steal electricity, a system must be introduced in such a way that the malicious users will be identified easily in a large neighbourhood area network. In this work, to detect energy theft, a decision-making system using the Hadoop multi-cluster model with interpolation search algorithm has been proposed to calculate the actual energy consumed by every user and classify the user as the honest user or malicious user. The proposed interpolation-based approach is lightweight in its operation, which reduces the time complexity for predicting the malicious users in the NAN. The simulation results indicate that the proposed algorithm performs better than the existing approaches in terms of number of inspection steps, execution speed, detection accuracy and false-negative rate.

Application of hybrid multi-agent interpolation search method to the satellite stabilization problem

Application of hybrid multi-agent interpolation search method to the satellite stabilization problem

Adaptive Powell’s Identification of Elastic Constants of Composite Glass Girder with Layered Shell Element Theory

For the composite glass box girder, the generalized Bayesian objective function of elastic constants of the structure was derived based on layered shell element theory. Mechanical performances of the composite glass box girder were solved by layered shell element method. Combined with quadratic parabolic interpolation search scheme of optimized step length, the adaptive Powell’s optimization theory was taken to complete the stochastic identification of elastic constants of composite glass box girder. Then the adaptive Powell’s identification steps of elastic constants of the structure were presented in detail and the adaptive Powell’s identification procedure was accomplished. From some classic examples, it is finally achieved that the adaptive Powell’s identification of elastic constants of composite glass box girder has perfect convergence and numerical stability, which testifies that the adaptive Powell’s identification theory of elastic constants of composite glass box girder is correct and reliable. The stochastic characteristics of systematic responses and elastic constants are well deliberated in generalized Bayesian objective function. And in iterative processes, the adaptive Powell’s identification is irrelevant with the complicated partial differentiation of the systematic responses from the layered shell element model to the elastic constants, which proves high computation efficiency.

Pricing European Option Under Fuzzy Mixed Fractional Brownian Motion Model with Jumps

As we all know, the financial environment on which option prices depend is very complex and fuzzy, which is mainly affected by the risk preferences of investors, economic policies, markets and other non-random uncertainty. Thus, the input data in the options pricing formula cannot be expected to be precise. However, fuzzy set theory has been introduced as a main method for modeling the uncertainties of the input parameters in the option pricing model. In this paper, we discuss the pricing problem of European options under the fuzzy environment. Specifically, to capture the features of long memory and jump behaviour in financial assets, we propose a fuzzy mixed fractional Brownian motion model with jumps. Subsequently, we present the fuzzy prices of European options under the assumption that the underlying stock price, the risk-free interest rate, the volatility, the jump intensity and the mean value and variance of jump magnitudes are all fuzzy numbers. This assumption allows the financial investors to pick any option price with an acceptable belief degree to make investment decisions based on their risk preferences. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Numerical analysis and examples are also presented to illustrate the performance of our proposed model and the designed algorithm. Finally, empirically studies are performed by utilizing the underlying SSE 50 ETF returns and European options written on SSE 50 ETF. The empirical results indicate that the proposed pricing model is reasonable and can be treated as a reference pricing tool for financial analysts or investors.

Novel Leakage Detection and Localization Method Based on Line Spectrum Pair and Cubic Interpolation Search

Leakage detection in water distribution systems (WDS) is critical to ensuring the security of urban water supplies. Acoustic detection methods have been used for leakage detection in water utilities, but ambient noise in real cases interferes with their detection accuracy, and the localization process in meshed or looped pipe networks requires significant computational costs. To increase the effectiveness of acoustic detection methods in practical applications, the current work proposes a novel leakage detection and localization method. This method extracts line spectrum pairs (LSP) of leakage signals and uses a random forest (RF) model to detect leaks; then, a cubic interpolation search (CIS) algorithm is developed to locate leaks. The LSP-based leakage detection method shows a clear advantage over the detection methods based on linear prediction coefficients (LPC) and time or frequency domain features. The proposed leakage detection method achieves 99.45% accuracy. In the case of −5 dB, the detection accuracy reaches 93.89%. The CIS algorithm is found to be more stable and shows a faster convergence speed than a commonly used graph-based search algorithm. The localization error is low (i.e., 2.22 m to 9.99 m). The LSP-CIS combined algorithm provides a more effective solution for leakage detection and localization.

A Fast Bistatic ISAR Imaging Approach for Rapidly Spinning Targets via Exploiting SAR Technique

Because of the large range of cell migration (RCM) and nonstationary Doppler frequency modulation (DFM) produced by non-cooperative targets with rapid spinning motions, it is difficult to efficiently generate a well-focused bistatic inverse synthetic aperture radar (ISAR) by use of the conventional imaging algorithms. Utilizing the property of the inherent azimuth spatial invariance in strip-map synthetic aperture radar (SAR) imaging mode, in this work, an efficient bistatic ISAR imaging approach based on circular shift operation in the range-Doppler (RD) domain is proposed. First, echoes of rapidly spinning targets are transformed into the RD domain, whose exact analytical is derived on the basis of the principle of stationary phase (POSP). Second, the RCM is corrected by using an efficient circular shift operation in the RD domain. By doing so, the energies of a scatterer that span multiple range cells are concentrated into the same range cell, and the time-varying DFM can also be compensated along the rotating radius direction. Compared with existing methods, the proposed method has advantages in its computational complexity, avoiding the interpolation and multi-dimensional search operation, and in its satisfactory imaging performance under low signal to noise ratio (SNR) conditions thanks to the two-dimensional coherent integration gain utilized. Finally, several numerical simulations are conducted to show the validity of the proposed algorithm.