Intersection Operations Research Articles

Per Segment Plane Sweep Line Segment Intersection on the GPU

Polygon overlay operations are used for various purposes such as GIS searches and queries, VLSI and basic geometric operations of intersection, union and difference. There have been recent research articles presenting algorithms using the GPU to perform line segment intersection for geometric operations. We present two parallel algorithms implemented on the GPU that focus on the active list portion of the traditional serial plane sweep algorithm. The first algorithm uses a single block of threads to simulate the active list data structure in hardware; this algorithm is slow due to GPU thread block size limitations and synchronization points, but demonstrates favorable time complexity. The second algorithm uses dynamic parallelism to remove synchronization and scales to utilize available GPU hardware (single GPU). We perform experiments on both synthetic and real world data sets. The presented results show improvement in execution time with respect to recent algorithms, and low memory usage compared to recent algorithms. We achieve speedups of up to 38.8 over the serial sweep line algorithm on real world data.

Comparative Sensitivity Analysis on Intersection Crash Prediction Models by Control Type: Highway Safety Manual Approach

A comprehensive, in-depth investigation into the comparative safety of different intersection control types is presented, specifically signalized and minor road stop-controlled intersections across facility types. Employing a rigorous sensitivity analysis, the study scrutinizes intersection crash prediction models (CPMs) rooted in the Highway Safety Manual (HSM) methodology. Through meticulous data analyses and thorough comparisons of predictive models across a range of major and minor road traffic volumes, the paper critically examines the portrayal of signalized and stop-controlled intersections within the default HSM Part C CPMs. Additionally, the study delves into the effects of certain crash modification factors on CPMs, further exploring the impacts of calibration factors and locally developed models on crash prediction results. CPMs for signalized intersections do not uniformly lead to fewer crashes compared with stop-controlled intersections, especially under certain traffic volumes and when considering fatal and injury crashes. Therefore, the choice of intersection control should be based on more nuanced criteria than traffic volume alone. Additionally, the research emphasizes the role of intersection geometry and operations, for example, the benefits of adding turn lanes and varying left-turn phasing, in influencing safety outcomes. This study significantly contributes to the understanding of intersection safety and HSM modeling approaches, providing a valuable resource for transportation professionals dedicated to advancing intersection safety. Examining strengths and limitations of existing models provides valuable input for researchers developing future intersection CPMs, and offers essential insights for transportation planners and engineers, informing decision-making for optimizing intersection control strategies and enhancing overall intersection safety and traffic management.

A New Type of Extended Soft Set Operation: Complementary Extended Intersection Operation

A New Type of Extended Soft Set Operation: Complementary Extended Intersection Operation

PimPam: Efficient Graph Pattern Matching on Real Processing-in-Memory Hardware

Graph pattern matching is powerful and widely applicable to many application domains. Despite the recent algorithm advances, matching patterns in large-scale real-world graphs still faces the memory access bottleneck on conventional computing systems. Processing-in-memory (PIM) is an emerging hardware architecture paradigm that puts computing cores into memory devices to alleviate the memory wall issues. Real PIM hardware has recently become commercially accessible to the public. In this work, we leverage the real PIM hardware platform to build a graph pattern matching framework, PimPam, to benefit from its abundant computation and memory bandwidth resources. We propose four key optimizations in PimPam to improve its efficiency, including (1) load-aware task assignment to ensure load balance, (2) space-efficient and parallel data partitioning to prepare input data for PIM cores, (3) adaptive multi-threading collaboration to automatically select the best parallelization strategy during processing, and (4) dynamic bitmap structures that accelerate the key operations of set intersection. When evaluated on five patterns and six real-world graphs, PimPam outperforms the state-of-the-art CPU baseline system by 22.5x on average and up to 71.7x, demonstrating significant performance improvements.

Methodological issues of the fuzzy set theory (generalizing article)

The theory of fuzziness is an important area of modern theoretical and applied mathematics. The methodology of the theory of fuzziness is a doctrine of organizing activities in the field of development and application of the scientific results of this theory. We discuss some methodological issues of the theory of fuzziness, i.e., individual components of the methodology in the area under consideration. The theory of fuzziness is a science of pragmatic (fuzzy) numbers and sets. The ancient Greek philosopher Eubulides showed that the concepts «Heap» and «Bald» cannot be described using natural numbers. E. Borel proposed to define a fuzzy set using a membership function. A fundamentally important step was taken by L. A. Zadeh in 1965. He gave the basic definitions of the algebra of fuzzy sets and introduced the operations of intersection, product, union, sum, negation of fuzzy sets. The main thing he did was demonstration of the possibilities of expanding («doubling») mathematics: by replacing the numbers and sets used in mathematics with their fuzzy counterparts, we obtain new mathematical formulations. In the statistics of non-numerical data, methods of statistical analysis of fuzzy sets have been developed. Interval and triangular fuzzy numbers are often used specific types of membership functions. The theory of fuzzy sets in a certain sense is reduced to the theory of random sets. We think fuzzy and that is the only reason we understand each other. The paradox of the fuzzy theory is that it is impossible to consistently implement the thesis «Everything in the world is fuzzy». For ordinary fuzzy sets, the argument and values of the membership function are crisp. If they are replaced by fuzzy analogues, then their description will require their own clear arguments and membership functions, and so on ad infinitum. System fuzzy interval mathematics proceeds from the need to take into account the fuzziness of the initial data and the prerequisites of the mathematical model. One of the options for its practical implementation is an automated system-cognitive analysis and the intellectual system «Eidos».

Fault diagnosis method via one vs rest evidence classifier considering imprecise feature samples

The key task of fault diagnosis is to establish the nonlinear mapping relationship between fault feature sequences (FFSs) and fault modes (FMs). Therefore, it is usually necessary to detect transit jump points of FFS to separate feature samples with the different trends. These samples and the their fault labels are combined to form training samples for a fault diagnosis model (FDM). However, due to changes in fault status and uncertainty in measurement, some feature samples will imprecisely point to multiple FMs (fault labels), hardly adopted in FDM. In order to solve such imprecision problem, this paper presents an information fusion method via One vs Rest (OvR) evidence classifiers. For each FFS, the multiple OvR evidence classifiers are designed to model the imprecise relationship between the samples and FMs. Then, a two-level fusion framework is proposed to integrate the evidence of all FFSs. By using the intersection operation between One (one FM) and Rest (the other FMs), the imprecision can be significantly reduced. A rotating machinery fault diagnosis experiment is given to illustrate that the proposed method have better fault classification accuracy compared with the traditional FDMs including SVM, BPNN, KNN, FCNN, RF and Bayes.

A Novel Approach to Enhance the Efficiency of Apriori Algorithm

Data mining is the process of obtaining valuable or significant information from a large-scale database. One significantarea of research in the field of data mining is association rules mining. Apriori algorithm is one of the classical algorithmsin the association rule mining field. This research analyses the basic ideas and shortcomings of the Apriori algorithm andcompares several different styles of its major improvement strategies. Then it suggests an improved version of the Apriorialgorithm that utilizes a dataset summarization method, an optimized database mapping technique, an intersection operation,and a joined optimization strategy. These enhancements aim to address the low performance and efficiency by reducing thegeneration of candidate itemsets and minimizing the execution time. This addresses the issues of generating numerous candidate itemsets and repeatedly scanning the transaction database. After implementing the optimized algorithm, to verify its effectiveness, it has been applied to a groceries dataset, which is for market basket analysis. The improved Apriori algorithm demonstrated significant enhancements over the original algorithm in terms of reduced candidate itemsets and running time, leading to improved algorithm efficiency.

Real-world black carbon emissions of gasoline vehicles at urban intersections

To gain insight into the real-world black carbon (BC) emission patterns at urban intersections, we employed a portable emission measurement system (PEMS) to assess the BC emissions from three light-duty gasoline vehicles along a designated urban route. The BC emission factors were evaluated, and the contributions of vehicle operating conditions at the intersections to the total BC emissions were quantified. The results show that the BC emission factors in an intersection area range from 0.045 to 0.291 mg/km, higher than those at an intersection's connecting sections. The average BC emission factor at signalized intersections is 17.07% higher than at roundabouts. Emission contribution analysis of driving conditions showed that in a state of non-free traffic flow, acceleration and deceleration conditions are responsible for 39% ∼ 56% and 24% ∼ 33% of BC emissions at intersections, respectively. We also found that vehicle specific power (VSP) and delay time are almost equally crucial for BC emissions from vehicles at intersections in the multiple linear regression. Our research reveals the significant impact of vehicle delay time and acceleration conditions on black carbon emissions at urban intersections, further emphasizing the importance of smooth (congestion-free) intersection operation and steady driving in reducing urban black carbon emissions.

Efficient List Intersection Algorithm for Short Documents by Document Reordering

List intersection plays a pivotal role in various domains such as search engines, database systems, and social networks. Efficient indexes and query strategies can significantly enhance the efficiency of list intersection. Existing inverted index-based algorithms fail to utilize the length information of documents and require excessive list intersections, resulting in lower efficiency. To address this issue, in this paper, we propose the LDRpV (Length-based Document Reordering plus Verification) algorithm. LDRpV filters out documents that are unlikely to satisfy the intersection results by reordering documents based on their length, thereby reducing the number of candidates. Additionally, to minimize the number of list intersection operations, an intersection and verification strategy is designed, where only the first m lists are intersected, and the resulting candidate set is directly verified. This approach effectively improves the efficiency of list intersection. Experimental results on four real datasets demonstrate that LDRpV can achieve a maximum efficiency improvement of 46.69% compared to the most competitive counterparts.

Introduction to Possibility Plithogenic Soft Sets

Plithogenic sets are versatile in nature, and they are widely applied in decision making. However, the generalization of Plithogenic sets is essential to make the process of deriving optimal solutions more comprehensive. Hence, this paper introduces the concept of Possibility Plithogenic Soft Sets (PPSS) with the aim of developing a generalized form of Plithogenic soft sets. The types of PPSS,union and intersection operations, and similarity measures with possibility degrees are discussed. A practical application of Possibility Plithogenic Soft Sets is also presented in this research work to illustrate the advantages of PPSS in constructing solutions to decision-making problems.

ВЛИЯНИЕ ОСТАТОЧНОЙ АВТОТРАНСПОРТНОЙ ОЧЕРЕДИ НА ПРОЦЕСС ДВИЖЕНИЯ АВТОМОБИЛЕЙ НА ГОРОДСКИХ РЕГУЛИРУЕМЫХ ПЕРЕСЕЧЕНИЯХ

This paper continues to investigate methods for separating turning vehicle flows at urban light-controlled intersections. The authors carried out mathematical modelling of the process of left-turn transport queue formation on the basis of existing dependencies, as well as the indicator of "residual motor transport queue". After studying the processes and existing mathematical models describing the formation of a vehicle queue at a light-controlled intersection, as well as modelling of the process depending on the "residual vehicle queue" parameter, we made an assumption about the type of mathematical model describing the process. To confirm the assumptions, we carried out studies of urban light-controlled intersections in Russian cities. Based on passive experiment, it was found that the value of the residual vehicle queue obeyed the exponential distribution law of a random variable. The length of the vehicle queue formed at the intersection depends on the residual vehicle queue parameter. A linear mathematical model describes the dependence. It was found that for an average urban regulated intersection, the required rotary-accumulative lane capacity was 9 and 5 automobiles with loading factor more than and less than 1, respectively. When the residual vehicle queue increases from 5 to 50 vehicles, the size of the vehicle queue at the regulated intersection in the left-turn direction increases in 5 times. The results of the study can be used to adjust the modes of operation of urban light-controlled intersections, as well as to estimate the length of turn-accumulative lanes.

HERO: A Hierarchical Set Partitioning and Join Framework for Speeding up the Set Intersection Over Graphs

As one of the most primitive operators in graph algorithms, such as the triangle counting, maximal clique enumeration, and subgraph listing, a set intersection operator returns common vertices between any two given sets of vertices in data graphs. It is therefore very important to accelerate the set intersection, which will benefit a bunch of tasks that take it as a built-in block. Existing works on the set intersection usually followed the merge intersection or galloping-search framework, and most optimization research focused on how to leverage the SIMD hardware instructions. In this paper, we propose a novel multi-level set intersection framework, namely hierarchical set partitioning and join (HERO), by using our well-designed set intersection bitmap tree (SIB-tree) index, which is independent of SIMD instructions and completely orthogonal to the merge intersection framework. We recursively decompose the set intersection task into small-sized subtasks and solve each subtask using bitmap and boolean AND operations. To sufficiently achieve the acceleration brought by our proposed intersection approach, we formulate a graph reordering problem, prove its NP-hardness, and then develop a heuristic algorithm to tackle this problem. Extensive experiments on real-world graphs have been conducted to confirm the efficiency and effectiveness of our HERO approach. The speedup over classic merge intersection achieves up to 188x and 176x for triangle counting and maximal clique enumeration, respectively.

Multicore Parallelized Spatial Overlay Analysis Algorithm Using Vector Polygon Shape Complexity Index Optimization

As core algorithms of geographic computing, overlay analysis algorithms typically have computation-intensive and data-intensive characteristics. It is highly important to optimize overlay analysis algorithms by parallelizing the vector polygons after reasonable data division. To address the problem of unbalanced data partitioning in the task decomposition process for parallel polygon overlay analysis and calculation, this paper presents a data partitioning method based on shape complexity index optimization, which achieves data equalization among multicore parallel computing tasks. Taking the intersection operator and difference operator of the Vatti algorithm as examples, six polygon shape indexes are selected to construct the shape complexity model, and the vector data are divided in accordance with the calculated shape complexity results. Finally, multicore parallelism is achieved based on OpenMP. The experimental results show that when a data set with a large amount of data is used, the effect of the multicore parallel execution of the Vatti algorithm’s intersection operator and difference operator based on shape complexity division is clearly improved. With 16 threads, compared with the serial algorithm, speedups of 29 times and 32 times can be obtained. Compared with the traditional multicore parallel algorithm based on polygon number division, the speed can be improved by 33% and 29%, and the load balancing index is reduced. For a data set with a small amount of data, the acceleration effect of this method is similar to that of traditional methods involving multicore parallelism.

T2FM: A novel hashtable based type-2 fuzzy frequent itemsets mining

Association rule mining (ARM) is an important research issue in the field of data mining that aims to find relations among different items in binary databases. The conventional ARM algorithms consider the frequency of the items in binary databases, which is not sufficient for real time applications. In this paper, a novel hash table based Type-2 fuzzy mining algorithm (T2FM) with an efficient pruning strategy is presented for discovering multiple fuzzy frequent itemsets from quantitative databases. The algorithm employs a hash table based structure for efficient storage and retrieval of item/itemset which reduces the search efficiency to O(1) or constant time. Previously, type-2 based Apriori and FP-growth based fuzzy frequent itemsets mining were proposed, which required large amounts of computation and a greater number of candidate generation and processing. Meanwhile, the proposed approach reduces a huge amount of computation by finding the common keys before the actual intersection operation takes place. An efficient pruning strategy is proposed to avoid unpromising candidates in order to speed up the computations. Several experiments are carried out to verify the efficiency of the approach in terms of runtime and memory for different minimum support threshold and the results show that the designed approach provides better performance compared to the state-of-the-art algorithms.

Diagnosing Overlapping and Differing Information for SPEAR and CFSv2 Global Precipitation Forecasts

Global climate models (GCMs) provide valuable forecasts of precipitation around the world. This paper has presented an in-depth investigation of the overlapping versus differing information for 2 sets of GCM forecasts based on the classic set operations. Specifically, by using the coefficient of determination to measure the amount of information of precipitation observations contained in GCM forecast, the common part of the 2 sets of forecasts is quantified by the intersection operation and the unique part of 1 set of forecasts is quantified by the difference operation. A case study is devised for the global precipitation forecasts in December-January-February generated by the Seamless System for Prediction and EArth System Research (SPEAR) and the Climate Forecast System version 2 (CFSv2). Their overlapping and differing information are diagnosed. It is found that significant information common to the 2 sets of forecasts exists over 54.61% of global land grid cells, significant information unique to SPEAR forecasts over 23.59% of global land grid cells, and significant information unique to CFSv2 forecasts over 18.15% of global land grid cells. While the information unique to the SPEAR forecasts suggests that the SPEAR forecasts provide new information compared to the CFSv2 forecasts and the information unique to the CFSv2 forecasts suggests that the CFSv2 forecasts also provide new information compared to the SPEAR forecasts, the common information of the 2 sets of forecasts indicates that they present substantial amount of similar information. Overall, the diagnosis of the overlapping and differing information for different sets of GCM forecasts yields insights into GCM predictive performances.

Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius

<abstract><p>The circular intuitionistic fuzzy set (<italic>CIFS</italic>) extends the concept of <italic>IFS</italic>, representing each set element with a circular area on the <italic>IFS</italic> interpretation triangle (<italic>IFIT</italic>). Each element in <italic>CIFS</italic> is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecise areas of these degrees. While some basic operations have been defined for <italic>CIFS</italic>, not all have been thoroughly explored and generalized. The radius domain has been extended from $ [0, 1] $ to $ [0, \sqrt{2}] $. However, the operations on the radius domain are limited to $ min $ and $ max $. We aimed to address these limitations and further explore the theory of <italic>CIFS</italic>, focusing on operations for membership and non-membership degrees as well as radius domains. First, we proposed new radius operations on <italic>CIFS</italic> with a domain $ [0, \psi] $, where $ \psi \in [1, \sqrt{2}] $, called a radius algebraic product (<italic>RAP</italic>) and radius algebraic sum (<italic>RAS</italic>). Second, we developed basic operators for generalized union and intersection operations on <italic>CIFS</italic> based on triangular norms and conorms, investigating their algebraic properties. Finally, we explored negation and modal operators based on proposed radius conditions and examined their characteristics. This research contributes to a more explicit understanding of the properties and capabilities of <italic>CIFS</italic>, providing valuable insights into its potential applications, particularly in decision-making theory.</p></abstract>

Many-Objective Jaccard-based Evolutionary Feature Selection for High-Dimensional Imbalanced Data Classification.

Filters and wrappers represent two mainstream approaches to feature selection (FS). Although evolutionary wrapper-based FS outperforms filters in addressing real-world classification problems, extending these methods to high-dimensional, many-objective optimization problems with imbalanced data poses substantial challenges. Overcoming computational costs and identifying suitable performance metrics are vital for navigating search operation complexities. Here, we propose using the Jaccard similarity (JS) in a set-based evolutionary many-objective (JSEMO) FS search, addressing both evolutionary FS and imbalanced classifier choice concurrently. This study highlights the mutual influence between these aspects, impacting overall algorithm performance. JSEMO integrates JS into population initialization, reproduction, and elitism steps, enhancing diversity and avoiding duplicate solutions. The set-based variation operator utilizes intersection and union operators for compatibility with binary coding. We also introduce a double-weighted KNN (KNN2W) classifier with four supportive objectives as a many-objective FS problem to handle imbalanced distributions. Compared with 20 methods on 15 benchmark problems, JSEMO produces distinct optimal features, significantly improving overall accuracy, balance accuracy, and g-mean metrics with comparable feature set size and computational cost. The ablation study underscores the positive impact of all JSEMO components, highlighting the set-based variation operation with JS and KNN2W with relevant evaluation metrics as the most influential aspects.

Research on the Path of Civic-Political Construction of Music Appreciation Courses in Public Art Education in Colleges and Universities under the Perspective of the Internet

Abstract In this paper, the association rule algorithm is used to mine all the strong association rules in the public art education music appreciation course, and the course Civics, and the Inter-transaction algorithm is utilized to decompose the mining task into two parts of long and short itemsets according to the time-consuming time, so as to reduce the number of transactional intersection operations. A new pruning strategy has been adopted to effectively limit the number of candidate sets and improve the performance of the algorithm. Finally, based on the model of this paper, we analyzed the relevance of the music appreciation courses in public art education in colleges and universities to Civics and the change in students’ Civics literacy after integrated teaching. The results show that the mean value of students’ moral quality after teaching increased by 3.24 from 18.07±2.08, and the p-value of each index except music literacy is 0.000, which is significantly different. And sup=0.05, conf=0.622, lift=4.499 for Music Art A and Introduction to Basic Marxist Principles A. There is a strong correlation between teaching music and Civic and Political Science courses.

Constructing a screening model to obtain the functional herbs for the treatment of active ulcerative colitis based on herb-compound-target network and immuno-infiltration analysis

The therapeutic effect of most traditional Chinese medicines (TCM) on ulcerative colitis is unclear, The objective of this study was to develop a core herbal screening model aimed at facilitating the transition from active ulcerative colitis (UC) to inactive. We obtained the gene expression dataset GSE75214 for UC from the GEO database and analysed the differentially expressed genes (DEGs) between active and inactive groups. Gene modules associated with the active group were screened using WGCNA, and immune-related genes (IRGs) were obtained from the ImmPort database. The TCMSP database was utilized to acquire the herb-molecule-target network and identify the herb-related targets (HRT). We performed intersection operations on HRTs, DEGs, IRGs, and module genes to identify candidate genes and conducted enrichment analyses. Subsequently, three machine learning algorithms (SVM-REF analysis, Random Forest analysis, and LASSO regression analysis) were employed to refine the hubgene from the candidate genes. Based on the hub genes identified in this study, we conducted compound and herb matching and further screened herbs related to abdominal pain and blood in stool using the Symmap database.Besides, the stability between molecules and targets were assessed using molecular docking and molecular dynamic simulation methods. An intersection operation was performed on HRT, DEGs, IRGs, and module genes, leading to the identification of 23 candidate genes. Utilizing three algorithms (RandomForest, SVM-REF, and LASSO) for analyzing the candidate genes and identifying the intersection, we identified five core targets (CXCL2, DUOX2, LYZ, MMP9, and AGT) and 243 associated herbs. Hedysarum Multijugum Maxim. (Huangqi), Sophorae Flavescentis Radix (Kushen), Cotyledon Fimbriata Turcz. (Wasong), and Granati Pericarpium (Shiliupi) were found to be capable of relieving abdominal pain and hematochezia during active UC. Molecular docking demonstrated that the compounds of the four aforementioned herbs showed positive docking activity with their core targets. The results of molecular dynamic simulations indicated that well-docked active molecules had a more stable structure when bound to their target complexes. The study has shed light on the potential of TCMs in treating active UC from an immunomodulatory perspective, consequently, 5 core targets and 4 key herbs has been identified. These findings can provide a theoretical basis for subsequent management and treatment of active UC with TCM, as well as offer original ideas for further research and development of innovative drugs for alleviating UC.

The Algebra of Signatures for Extreme Two-Uniform Hypergraphs

In the last decade, several characterizations have been constructed for constructions such as extreme hypergraphs. One of the most recently described features is the signature. A signature is a number that uniquely describes an extremal and allows one to efficiently store the extremal two-uniform hypergraph itself. However, for the signature, although various algorithms have been derived for transforming it into other object-characteristics such as the base, the adjacency matrix, and the vector of vertex degrees, no isolated signature union and intersection apparatus has been constructed. This allows us to build efficient algorithms based on signatures, the most compact representation of extremal two-uniform hypergraphs. The nature of the algebraic construction that can be built on a set of signatures using union and intersection operations has also been defined. It is proved that an algebra on a set of signatures with either the union or intersection operation forms a monoid; if the algebra is defined on a set of signatures with both union and intersection operations, it forms a distributive lattice.