Multidimensional Databases Research Articles

Development of a 3D Online System for Comparative Study of Architectural Elements in Thai Stupas

Understanding architectural names and semantics is essential for studying historical sites. New educational media in 3D and 2D formats, available online and offline, supports this by using specific buildings to illustrate shapes, positions, and proportions along with names and semantics. This approach works well for initial education, but in-depth study requires comparing architectural elements to identify similarities and differences. Today, comparative learning is recognized as an effective method for enhancing understanding. Therefore, this research focuses on developing a 3D online system for studying the names and semantics of architectural elements in Thai stupas and their architectural elements. The system features a multi-dimensional database and a real-time interactive online interface. It includes the ability to simultaneously view and compare up to three stupa models, enhancing comparative analysis and facilitating a comprehensive understanding of architectural variations. The system is tested using stupas from the Sukhothai, Si Satchanalai, and Kamphaeng Phet Historical Parks to help users appreciate Thai historical sites better. The developed system has been evaluated through teaching experiments, revealing that comparative learning deepens students' understanding. They can predict the names of stupa components, even if they have never seen that particular stupa before, by using the similarities or differences in elements as preliminary information to guess the semantics. Students who participated in the comparative interface were also able to improve their knowledge retention compared to learning with a single 3D interface.

TCM-ADIP: A Multidimensional Database Linking Traditional Chinese Medicine to Functional Brain Zones of Alzheimer’s Disease

Alzheimer’s disease (AD) is a complex neurodegenerative disorder, with existing therapeutic drugs typically targeting specific disease stages. Traditional Chinese medicine (TCM), known for its multi-target and multi-mechanism therapeutic approach, has demonstrated efficacy in treating various stages of AD. In the present work, through a systematic review of classical Chinese medical texts, the formulae for preventing and treating AD were identified. Meanwhile, the active ingredients within these formulae were extracted and cataloged. A comprehensive bioinformatics analysis of omics data was performed to identify differentially expressed genes across different functional brain zones in AD patients at various stages. Finally, by integrating the multidimensional data, we proposed the first database, TCM-ADIP, dedicated to TCM based AD prevention and treatment, which is freely available at https://cbcb.cdutcm.edu.cn/TCM-ADIP/. TCM-ADIP not only supports interactive searching of multidimensional data, but also provides tools for gene localization and functional enrichment analysis of formulae, herbs, and ingredients for AD intervention in specific brain zones. TCM-ADIP fills a crucial gap in existing databases, offering a comprehensive resource for TCM in the treatment of AD.

Recent additions and access to a multidimensional lipidomic database containing liquid chromatography, ion mobility spectrometry, and tandem mass spectrometry information.

The importance of lipids in biology continues to grow with their recent linkages to more diseases and conditions, microbiome fluctuations, and environmental exposures. These associations have motivated researchers to evaluate lipidomic changes in numerous matrices and studies. Lipidomic analyses, however, present numerous challenges as lipid species have broad chemistries that require different extraction methods and instrumental analyses to evaluate and separate their many isomers and isobars. Increasing knowledge about different lipid characteristics is therefore crucial for improving their separation and identification. Here, we present a multidimensional database for lipids analyzed on a platform combining reversed-phase liquid chromatography, drift tube ion mobility spectrometry, collision-induced dissociation, and mass spectrometry (RPLC-DTIMS-CID-MS). This platform and the different separation characteristics it provides enables more confident lipid annotations when compared to traditional tandem mass spectrometry platforms, especially when analyzing highly isomeric molecules such as lipids. This database expands on our previous publication containing only human plasma and bronchoalveolar lavage fluid lipids and provides experimental RPLC retention times, IMS collision cross section (CCS) values, and m/z information for 877 unique lipids from additional biofluids and tissues. Specifically, the database contains 1504 precursor [M + H]+, [M + NH4]+, [M + Na]+, [M-H]-, [M-2H]2-, [M + HCOO]-, and [M + CH3COO]- ion species and their associated CID fragments which are commonly targeted in clinical and environmental studies, in addition to being present in the chloroform layer of Folch extractions. Furthermore, this multidimensional RPLC-DTIMS-CID-MS database spans 5 lipid categories (fatty acids, sterols, sphingolipids, glycerolipids, and glycerophospholipids) and 24 lipid classes. We have also created a webpage (tarheels.live/bakerlab/databases/) to enhance the accessibility of this resource which will be populated regularly with new lipids as we identify additional species and integrate novel standards.

DPKnob: A visual analysis approach to risk-aware formulation of differential privacy schemes for data query scenarios

Differential privacy is an essential approach for privacy preservation in data queries. However, users face a significant challenge in selecting an appropriate privacy scheme, as they struggle to balance the utility of query results with the preservation of diverse individual privacy. Customizing a privacy scheme becomes even more complex in dealing with queries that involve multiple data attributes. When adversaries attempt to breach privacy firewalls by conducting multiple regular data queries with various attribute values, data owners must arduously discern unpredictable disclosure risks and construct suitable privacy schemes. In this paper, we propose a visual analysis approach for formulating privacy schemes of differential privacy. Our approach supports the identification and simulation of potential privacy attacks in querying statistical results of multi-dimensional databases. We also developed a prototype system, called DPKnob, which integrates multiple coordinated views. DPKnob not only allows users to interactively assess and explore privacy exposure risks by browsing high-risk attacks, but also facilitates an iterative process for formulating and optimizing privacy schemes based on differential privacy. This iterative process allows users to compare different schemes, refine their expectations of privacy and utility, and ultimately establish a well-balanced privacy scheme. The effectiveness of this study is verified by a user study and two case studies with real-world datasets.

Machine Learning in FTIR Spectrum for the Identification of Antibiotic Resistance: A Demonstration with Different Species of Microorganisms.

Recent studies introduced the importance of using machine learning algorithms in research focused on the identification of antibiotic resistance. In this study, we highlight the importance of building solid machine learning foundations to differentiate antimicrobial resistance among microorganisms. Using advanced machine learning algorithms, we established a methodology capable of analyzing the FTIR structural profile of the samples of Streptococcus pyogenes and Streptococcus mutans (Gram-positive), as well as Escherichia coli and Klebsiella pneumoniae (Gram-negative), demonstrating cross-sectional applicability in this focus on different microorganisms. The analysis focuses on specific biomolecules-Carbohydrates, Fatty Acids, and Proteins-in FTIR spectra, providing a multidimensional database that transcends microbial variability. The results highlight the ability of the method to consistently identify resistance patterns, regardless of the Gram classification of the bacteria and the species involved, reinforcing the premise that the structural characteristics identified are universal among the microorganisms tested. By validating this approach in four distinct species, our study proves the versatility and precision of the methodology used, in addition to bringing support to the development of an innovative protocol for the rapid and safe identification of antimicrobial resistance. This advance is crucial for optimizing treatment strategies and avoiding the spread of resistance. This emphasizes the relevance of specialized machine learning bases in effectively differentiating between resistance profiles in Gram-negative and Gram-positive bacteria to be implemented in the identification of antibiotic resistance. The obtained result has a high potential to be applied to clinical procedures.

Identification of key eRNAs for intervertebral disc degeneration by integrated multinomial bioinformatics analysis

BackgroundIntervertebral disc degeneration (IVDD) is a common degenerative condition leading to abnormal stress distribution under load, causing intervertebral stenosis, facet joint degeneration, and foraminal stenosis. Very little is known about the molecular mechanism of eRNAs in IVDD.MethodsGene expression profiles of 38 annulus disc samples composed of 27 less degenerated discs (LDs) and 11 more degenerated discs (MDs) were retrieved from the GEO database. Then, differentially expressed enhancer RNAs (DEeRNAs), differentially expressed target genes (DETGs), and differentially expressed transcription factors (DETFs), hallmark of cancer signalling pathways according to GSVA; the types and quantity of immune cells according to CIBERSORT; and immune gene sets according to ssGSEA were analysed to construct an IVDD-related eRNA network. Then, multidimensional validation was performed to explore the interactions among DEeRNAs, DETFs and DEGs in space.ResultsA total of 53 components, 14 DETGs, 15 DEeRNAs, 3 DETFs, 5 immune cells, 9 hallmarks, and 7 immune gene sets, were selected to construct the regulatory network. After validation by online multidimensional databases, 21 interactive DEeRNA-DEG-DETF axes related to IVDD exacerbation were identified, among which the C1S-CTNNB1-CHD4 axis was the most significant.ConclusionBased upon the results of our study, we theorize that the C1S-CTNNB1-CHD4 axis plays a vital role in IVDD exacerbation. Specifically, C1S recruits CTNNB1 and upregulates the expression of CHD4 in IVDD, and subsequently, CHD4 suppresses glycolysis and activates oxidative phosphorylation, thus generating insoluble collagen fibre deposits and leading to the progression of IVDD. Overall, these DEeRNAs could comprise promising therapeutic targets for IVDD due to their high tissue specificity.

Bioinformatics database and production layout visual analysis platform of medicinal plants:a case study of Dao-di medicinal materials in Sichuan province

In the new stage of trans-omics and trans-subjects for medicinal plants, it is an urgent need to integrate big data, provide interactive applications, and form a unified and multi-level research system and big data platform. Dao-di medicinal material, as an important source of medicinal plants, is a unique quality concept and comprehensive standard of tranditional Chinese medicine(TCM). Several databases have been developed in China and abroad, such as the Encyclopedia of Traditional Chinese Medicine(ETCM) and the Global Pharmacopoeia Genome Database(GPGD). Yet, most databases do not provide multi-dimensional data, including geographic data, phenotype data, compound data, and genetic data. Sichuan, known as the hometown of TCM therapies and the treasure trove of TCM, is the most representative region of medicinal plant diversity in China. According to the latest data of the fourth national survey of TCM resources, there are more than 8 000 TCM and 86 Dao-di medicinal materials in Sichuan province. Based on resource census data and relevant achievements, this study constructed the bioinformatics database of medicinal plants and the visual analysis platform of production layout by taking the Dao-di medicinal materials in Sichuan province as an example, covering geographic data, phenotype data, compound data, and genetic data. It effectively integrates multi-dimensional data of Dao-di medicinal materials and provides different levels of data interaction applications. The platform is the first large-scale multi-dimensional database and visual platform of Dao-di medicinal materials in Sichuan province, which serves as an essential resource for germplasm resources identification, decomposition of biosynthetic pathways, molecular breeding of varieties and provides medicinal plant resource information and data support for development and utilization of medicinal plants in China and abroad.

Development and Application of a Multidimensional Database for the Detection of Quaternary Ammonium Compounds and Their Phase I Hepatic Metabolites in Humans.

The COVID-19 pandemic has led to significantly increased human exposure to the widely used disinfectants quaternary ammonium compounds (QACs). Xenobiotic metabolism serves a critical role in the clearance of environmental molecules, yet limited data are available on the routes of QAC metabolism or metabolite levels in humans. To address this gap and to advance QAC biomonitoring capabilities, we analyzed 19 commonly used QACs and their phase I metabolites by liquid chromatography-ion mobility-tandem mass spectrometry (LC-IM-MS/MS). In vitro generation of QAC metabolites by human liver microsomes produced a series of oxidized metabolites, with metabolism generally occurring on the alkyl chain group, as supported by MS/MS fragmentation. Discernible trends were observed in the gas-phase IM behavior of QAC metabolites, which, despite their increased mass, displayed smaller collision cross-section (CCS) values than those of their respective parent compounds. We then constructed a multidimensional reference SQLite database consisting of m/z, CCS, retention time (rt), and MS/MS spectra for 19 parent QACs and 81 QAC metabolites. Using this database, we confidently identified 13 parent QACs and 35 metabolites in de-identified human fecal samples. This is the first study to integrate in vitro metabolite biosynthesis with LC-IM-MS/MS for the simultaneous monitoring of parent QACs and their metabolites in humans.

Cube query interestingness: Novelty, relevance, peculiarity and surprise

In this paper, we discuss methods to assess the interestingness of a query in an environment of data cubes. We assume a hierarchical multidimensional database, storing data cubes and level hierarchies. We start with a comprehensive review of related work in the fields of human behavior studies and computer science. We define the interestingness of a query as a vector of scores along different aspects, like novelty, relevance, surprise and peculiarity and complement this definition with a taxonomy of the information that can be used to assess each of these aspects of interestingness. We provide both syntactic (result-independent) and extensional (result-dependent) checks, measures and algorithms for assessing the different aspects of interestingness in a quantitative fashion. We also report our findings from a user study that we conducted, analyzing the significance of each aspect, its evolution over time and the behavior of the study’s participants.

Fuzzy Evolutionary Algorithm in Construction Project for Valuation

Clustering algorithms has emerged as an important data mining technique for pattern recognition, data analysis and dimensionality reduction. Clustering is usually used in all fields to merge the same feature objects into a single group. The clustering method is incorporated with search algorithms to search the dataset from the databases. For large databases, there is a need of good clustering algorithm with high accuracy. Despite its high performance, the existing methods show some limitations. This paper focused on optimize the clustering method with a search structure for large multidimensional databases with dynamic indexes for the effective validation of construction projects. In the construction project validation to improve the clustering methods using Evolutionary Constrained Differential Optimization (ECDO) and Distributed Weighted Fuzzy C-Means algorithm to improve clustering performance than the centralized clustering approaches. The proposed methodology includes ECDO which presents new cluster tree indexing approach with cluster speed improvement in the validation of the construction projects. Distributed Fuzzy Possibilistic C-Means algorithm is proposed in improvement of cluster centre to overcome coincidence cluster problems. The comparative analysis stated that proposed ECDO model exhibits ~6% reduced memory utilization ~11% reduced scalability and ~8% minimized selectivity than the conventional WPCM model.

Modern technological tools for creating multidimensional matrix database machines

The article discusses a group of tasks that require online analytical data processing. The authors analyze the components of OLAP technology: multidimensional cubes, implementation methods and methods for accessing them. Based on the analysis, it is concluded that truly multidimensional databases do not exist. An algebra of multidimensional matrices is proposed, which corresponds to relational algebra. It is shown that on the basis of this algebra it is possible to develop a DBMS that will provide an effective parallel implementation of OLAP technology. A method for constructing a multidimensional matrix database engine based on available software and hardware is proposed.

СИСТЕМЫ ПОДДЕРЖКИ ПРИНЯТИЯ РЕШЕНИЙ ДЛЯ РЕГИОНАЛЬНЫХ ПРЕДПРИЯТИЙ И ОРГАНИЗАЦИЙ РАЗЛИЧНЫХ СФЕР БИЗНЕСА

Currently, one can observe the rapid expansion and spread of the idea of using decision support systems (DSS). The new tasks set by the developers of the system are directly related to the universalization of the product, and without compromising the quality of development. The technologies and tools currently being implemented to improve the work of the DSS include: applied mathematical developments, multidimensional databases, artificial intelligence methods, telecommunications technologies, OLAP, data warehouses and others. Today, the DSS is becoming a necessary component in the life of the organization. In this regard, it is worth shifting the focus of the system’s application to specific individual differences of economic entities, that is, from actual indicators to subjective factors, primarily related to human resources, as well as the uncertainty of external influences. We can say that business units are becoming less impersonal, managers endow organizations with human qualities of behavior, in an exaggerated sense. Adapting the DSS to the changing reality is a necessary component of its competitiveness among other information systems.

First-principles and machine learning investigation on A4BX6 halide perovskites

The A4BX6 molecular halide perovskites have received attention owing to their interesting optoelectronic properties at the molecular scale; however, a comprehensive dataset of their atomic structures and electronic properties and associated data-driven investigation are still unavailable now, which makes it difficult for inverse materials design for semiconductor applications (e.g. wide band gap semiconductor). In this manuscript, we employ data-driven methods to predict band gaps of A4BX6 molecular halide perovskites via machine learning. A large virtual design database including 246 904 A4BX6 perovskite samples is predicted via machine learning, based on the model trained using 2740 first-principles results of A4BX6 molecular halide perovskites. In addition, symbolic regression-based machine learning is employed to identify more physically intuitive descriptors based on the starting first-principles dataset of A4BX6 molecular halide perovskites. In addition, different ranking methods are employed to offer a comprehensive feature importance analysis for the halide perovskite materials. This study highlights the efficacy of machine learning-assisted compositional design of A4BX6 perovskites, and the multi-dimensional database established here is valuable for future experimental validation toward perovskite-based wide band gap semiconductor materials.

Energy justice and gaps in sustainable development: A convergence testing and clustering study

The purpose of the study is to examine the dynamics of carbon emissions inequality and its effect on energy justice, whether carbon footprints have increased or decreased across countries, sectors, and households over time. We use convergence analysis, which is a methodology that effectively reveals carbon footprint dynamics. Our database contained carbon footprint data from different sectors across 180 countries between 1980 and 2020. We account for the non-linearity of the carbon footprint convergence or divergence process over time and individual heterogeneity across countries and sectors (data pre-filtering, carbon footprint convergence testing, and club clustering). Our results demonstrate a significant disparity in carbon footprints across various sectors and countries, especially among the top 1 % of earners. The wealthiest individuals worldwide have not converged towards a common trajectory, indicating high levels of carbon footprint inequality. This investigation assumes that the carbon footprint convergence or divergence process is not linear over time, allowing for fluctuations in carbon emissions inequality. Future research may explore the factors contributing to this non-linearity and its implications for energy justice. Our findings highlight global cooperation's importance in promoting sustainable production practices and a fair distribution of energy-related responsibilities. Energy production and consumption burdens are not equitably distributed, posing a significant challenge to achieving energy justice. This study provides a comprehensive understanding of the dynamics of carbon emissions inequality and its impact on energy justice. It employs a unique methodology and a multidimensional database, providing new insights into the carbon footprint disparity across sectors and countries.

Statistical Analysis of Long GRBs’ Prompt Emission and X-Ray Flares: Multivariate Clustering and Correlations

The extensive observations done by the X-ray Telescope on board Neil Gehrels Swift Observatory have revealed the presence of late-time flares concurrent with the decaying afterglow emission. However, the origins of these flares are elusive. In this work, we make use of the large database of Swift observations (2005–2020) of long gamma-ray bursts (GRBs) to conduct a systematic statistical study between the prompt gamma-ray emission and X-ray flares by characterizing their temporal and spectral properties of duration, quiescent period, peak flux, fluence, minimum variability timescale, and spectral power-law index. The multidimensional database of parameters thereby generated was investigated by principal component analysis, which revealed there is no evident correlation between the different parameters of the prompt emission and X-ray flares. Furthermore, the correlation studies revealed that while there is a trend of positive correlation between the minimum variability timescale of the flare and its duration, and of strong negative correlation with its peak flux, there are no such correlations observed in the prompt emission. Similarly, we find a positive correlation between the quiescent period and the flare duration, and a negative correlation with the flare peak flux, while no such correlations are observed for the prompt emission of the GRBs. Finally, among the X-ray flares, we find two dominant classes, whose variations are driven by the minimum variability timescale, peak flux, and fluence of the flares. A catalog of these different parameters characterizing the prompt and flare emissions is presented.

Pan-cancer analysis of promoter activity quantitative trait loci.

Altered promoter activity has been generally observed in diverse biological processes, including tumorigenesis. Accumulating evidence suggests that employing a quantitative trait locus mapping approach is effective in comprehending the genetic basis of promoter activity. By utilizing genotype data from The Cancer Genome Atlas and calculating corresponding promoter activity values using proActiv, we systematically evaluated the impact of genetic variants on promoter activity and identified >1.0 million promoter activity quantitative trait loci (paQTLs) as both cis- and trans-acting. Additionally, leveraging data from the genome-wide association study (GWAS) catalog, we discovered >1.3 million paQTLs that overlap with known GWAS linkage disequilibrium regions. Remarkably, ∼9324 paQTLs exhibited significant associations with patient prognosis. Moreover, investigating the impact of promoter activity on >1000 imputed antitumor therapy responses among pan-cancer patients revealed >43000 million significant associations. Furthermore, ∼25000 significant associations were identified between promoter activity and immune cell abundance. Finally, a user-friendly data portal, Pancan-paQTL (https://www.hbpding.com/PancanPaQTL/), was constructed for users to browse, search and download data of interest. Pancan-paQTL serves as a comprehensive multidimensional database, enabling functional and clinical investigations into genetic variants associated with promoter activity, drug responses and immune infiltration across multiple cancer types.

CLIM4OMICS: a geospatially comprehensive climate and multi-OMICS database for maize phenotype predictability in the United States and Canada

Abstract. The performance of numerical, statistical, and data-driven diagnostic and predictive crop production modeling relies heavily on data quality for input and calibration or validation processes. This study presents a comprehensive database and the analytics used to consolidate it as a homogeneous, consistent, multidimensional genotype, phenotypic, and environmental database for maize phenotype modeling, diagnostics, and prediction. The data used are obtained from the Genomes to Fields (G2F) initiative, which provides multiyear genomic (G), environmental (E), and phenotypic (P) datasets that can be used to train and test crop growth models to understand the genotype by environment (GxE) interaction phenomenon. A particular advantage of the G2F database is its diverse set of maize genotype DNA sequences (G2F-G), phenotypic measurements (G2F-P), station-based environmental time series (mainly climatic data) observations collected during the maize-growing season (G2F-E), and metadata for each field trial (G2F-M) across the United States (US), the province of Ontario in Canada, and the state of Lower Saxony in Germany. The construction of this comprehensive climate and genomic database incorporates the analytics for data quality control (QC) and consistency control (CC) to consolidate the digital representation of geospatially distributed environmental and genomic data required for phenotype predictive analytics and modeling of the GxE interaction. The two-phase QC–CC preprocessing algorithm also includes a module to estimate environmental uncertainties. Generally, this data pipeline collects raw files, checks their formats, corrects data structures, and identifies and cures or imputes missing data. This pipeline uses machine-learning techniques to fill the environmental time series gaps, quantifies the uncertainty introduced by using other data sources for gap imputation in G2F-E, discards the missing values in G2F-P, and removes rare variants in G2F-G. Finally, an integrated and enhanced multidimensional database was generated. The analytics for improving the G2F database and the improved database called Climate for OMICS (CLIM4OMICS) follow findability, accessibility, interoperability, and reusability (FAIR) principles, and all data and codes are available at https://doi.org/10.5281/zenodo.8002909 (Aslam et al., 2023a) and https://doi.org/10.5281/zenodo.8161662 (Aslam et al., 2023b), respectively.

A process-oriented data warehouse to support decision making process in crop production

The data available at the right time and in the right way and the economic calculations that can be produced from them, as well as the presentation of the produced information to managers, are crucial in the decision-making process for the organizations. Wide range of digital solutions has an important role to support the business activities and the decision making in the case of farm management as well.
 It is important to determine the structure of the data required to base the economic calculations, build a data model and create a multidimensional database, this lays the foundation for the calculation of economic and financial indicators, which can help in making economic decisions.
 In our article, we present the structure of a process-oriented data warehouse created according to the OLAP (online analytical processing) principle, which is suitable for displaying immediate results and creating analytical queries, as well as for displaying different combinations of variables for making economic decisions.

SAP BusinessObjects in Medical Informatics.

Electronic health record (EHR) generates a large amount of data filled with opportunities to enhance documentation compliance, quality improvement, and other metrics. Various software tools exist, but many clinicians are unaware of them. Our institution switched from a hybrid of paper and multiple small EHRs to one all-inclusive EHR system. We faced significant challenges beyond the typical new software deployment phase that affected our departmental regulatory compliance, quality measures, and research initiatives. We aimed to navigate these issues through the use of medical informatics. We used a multidimensional database software analysis tool called SAP BusinessObjects® (SAP SE. Released 2020. SAP BusinessObjects, Version 14.2.8.3671. Waldorf, Germany) to design automated queries for the patient database to generate various reports for our department. As a result, We improved our anesthesia documentation non-compliance from 13-17% of all cases to 4% within months. We have also used this tool to automatically generate various reports such as preoperative beta-blocker administrations, caseloads, case complications, procedure logs, and medication records. Even today many departments rely on manual checks for even the most basic documentation and quality metric compliance, which can be time consuming and costly. Using medical informatics tools is a highly efficient alternative. Fortunately, many software tools exist within most modern EHR packages, and most people can learn to use these tools productively.

Efficient Approximate Nearest Neighbor Search in Multi-dimensional Databases

Approximate nearest neighbor (ANN) search is a fundamental search in multi-dimensional databases, which has numerous real-world applications, such as image retrieval, recommendation, entity resolution, and sequence matching. Proximity graph (PG) has been the state-of-the-art index for ANN search. However, the search on existing PGs either suffers from a high time complexity or has no performance guarantee on the search result. In this paper, we propose a novel τ-monotonic graph (τ- MG) to address the limitations. The novelty of τ-MG lies in a τ-monotonic property. Based on this property, we prove that if the distance between a query q and its nearest neighbor is less than a constant τ, the search on τ-MG guarantees to find the exact nearest neighbor of q and the time complexity of the search is smaller than all existing PG-based methods. For index construction efficiency, we propose an approximate variant of τ-MG, namely τ-monotonic neighborhood graph (τ- MNG), which only requires the neighborhood of each node to be τ-monotonic. We further propose an optimization to reduce the number of distance computations in search. Our extensive experiments show that our techniques outperform all existing methods on well-known real-world datasets.