Breadth-First Search Multi-Dimensional Binary Search Tree based Algorithms for Structural

This research proposes a set of novel algorithms for structural reliability estimation based on muti-dimensional binary search tree and breadth-first search, namely the reliability accuracy supervised searching algorithm, the limit-state surface resolution supervised searching algorithm and the reliability index precision supervised fast searching algorithm. The proposed algorithms have the following strengths: 1, all the proposed algorithms have satisfactory computational efficiency by reducing redundant samplings; 2, their computational costs are stable and computable; 3, performance functions of high non-linearity can be will handled; 4, the reliability accuracy supervised searching algorithm can adapt its computational cost according to a prescribed accuracy; 5, the limit-state surface resolution supervised searching algorithm is able to probe sharp changes on limit-state surfaces; 6, the reliability index precision supervised fast searching algorithm computes the reliability index with sufficient precision in a fast way.

A Comparison of the Effectiveness of the RRT, PRM, and Novel Hybrid RRT-PRM Path Planners

Sampling-based path planners develop paths for robots to journey to their destinations. The two main types of sampling-based techniques are the probabilistic roadmap (PRM) and the Rapidly Exploring Random Tree (RRT). PRMs are multi-query methods that construct roadmaps to find routes, while RRTs are single-query techniques that grow search trees to find paths. This investigation evaluated the effectiveness of the PRM, the RRT, and the novel Hybrid RRT-PRM methods. This novel path planner was developed to improve the performance of the RRT and PRM techniques. It is a fusion of the RRT and PRM methods, and its goal is to reduce the path length. Experiments were conducted to evaluate the effectiveness of these path planners. The performance metrics included the path length, runtime, number of nodes in the path, number of nodes in the search tree or roadmap, and the number of iterations required to obtain the path. Results showed that the Hybrid RRT-PRM method was more effective than the PRM and RRT techniques because of the shorter path length. This new technique searched for a path in the convex hull region, which is a subset of the search area near to the start and end locations. The roadmap for the Hybrid RRT-PRM could also be re-used to find pathways for other sets of initial and final positions. Keywords: Path Planning, Sampling-based algorithms, search tree, roadmap, single-query planners, multi-query planners, Rapidly Exploring Random Tree (RRT), Probabilistic Roadmap (PRM), Hybrid RRT-PRM

Improving the Red-Black tree delete algorithm

Today, Red-Black trees are becoming a popular data structure typically used to implement dictionaries, associative arrays, symbol tables within some compilers (C++, Java …) and many other systems. In this paper, we present an improvement of the delete algorithm of this kind of binary search tree. The proposed algorithm is very promising since it colors differently the tree while reducing color changes by a factor of about 29%. Moreover, the maintenance operations re-establishing Red-Black tree balance properties are reduced by a factor of about 11%. As a consequence, the proposed algorithm saves about 4% on running time when insert and delete operations are used together while conserving search performance of the standard algorithm.

A novel RSW&TST framework of MCPs detection for abnormal pattern recognition on large-scale time series and pathological signals in epilepsy

To quickly and efficiently recognize abnormal patterns from large-scale time series and pathological signals in epilepsy, this paper presents here a preliminary RSW&TST framework for Multiple Change-Points (MCPs) detection based on the Random Slide Window (RSW) and Trigeminal Search Tree (TST) methods. To avoid the remaining local optima, the proposed framework applies a random strategy for selecting the size of each slide window from a predefined collection, in terms of data feature and experimental knowledge. For each data segment to be diagnosed in a current slide window, an optimal path towards a potential change point is detected by TST methods from the top root to leaf nodes with O(log3(N)). Then, the resulting MCPs vector is assembled by means of TST-based single CP detection on data segments within each of the slide windows. In our experiments, the RSW&TST framework was tested by using large-scale synthetic time series, and then its performance was evaluated by comparing it with existing binary search tree (BST), Kolmogorov-Smirnov (KS)-statistics, and T-test under the fixed slide window (FSW) approach, as well as the integrated method of wild binary segmentation and CUSUM test (WBS&CUSUM). The simulation results indicate that our RSW&TST is both more efficient and effective, with a higher hit rate, shorter computing time, and lower missed, error and redundancy rates. When the proposed RSW&TST framework is executed for MCPs detection on pathological ECG (electrocardiogram)/EEG (electroencephalogram) recordings of people in epileptic states, the abnormal patterns are roughly recognized in terms of the number and position of the resultant MCPs. Furthermore, the severity of epilepsy is roughly analyzed based on the strength and period of signal fluctuations among multiple change points in the stage of a sudden epileptic attack. The purpose of our RSW&TST framework is to provide an encouraging platform for abnormal pattern recognition through MCPs detection on large-scale time series quickly and efficiently.

Maintaining AUC and H-measure over time

Measuring the performance of a classifier is a vital task in machine learning. The running time of an algorithm that computes the measure plays a very small role in an offline setting, for example, when the classifier is being developed by a researcher. However, the running time becomes more crucial if our goal is to monitor the performance of a classifier over time. In this paper we study three algorithms for maintaining two measures. The first algorithm maintains area under the ROC curve (AUC) under addition and deletion of data points in $$\mathcal {O} \mathopen {}\left( \log n\right)$$ O log n time. This is done by maintaining the data points sorted in a self-balanced search tree. In addition, we augment the search tree that allows us to query the ROC coordinates of a data point in $$\mathcal {O} \mathopen {}\left( \log n\right)$$ O log n time. In doing so we are able to maintain AUC in $$\mathcal {O} \mathopen {}\left( \log n\right)$$ O log n time. Our next two algorithms involve in maintaining H-measure, an alternative measure based on the ROC curve. Computing the measure is a two-step process: first we need to compute a convex hull of the ROC curve, followed by a sum over the convex hull. We demonstrate that we can maintain the convex hull using a minor modification of the classic convex hull maintenance algorithm. We then show that under certain conditions, we can compute the H-measure exactly in $$\mathcal {O} \mathopen {}\left( \log ^2 n\right)$$ O log 2 n time, and if the conditions are not met, then we can estimate the H-measure in $$\mathcal {O} \mathopen {}\left( (\log n + \epsilon ^{-1})\log n\right)$$ O ( log n + ϵ - 1 ) log n time. We show empirically that our methods are significantly faster than the baselines.

CMash: fast, multi-resolution estimation of k-mer-based Jaccard and containment indices

K-mer based methods are used ubiquitously in the field of computational biology. However, determining the optimal value of k for a specific application often remains heuristic. Simply reconstructing a new k-mer set with another k-mer size is computationally expensive, especially in metagenomic analysis where data sets are large. Here, we introduce a hashing-based technique that leverages a kind of bottom-m sketch as well as a k-mer ternary search tree (KTST) to obtain k-mer based similarity estimates for a range of k values. By truncating k-mers stored in a pre-built KTST with a large k = kmax value, we can simultaneously obtain k-mer based estimates for all k values up to kmax. This truncation approach circumvents the reconstruction of new k-mer sets when changing k values, making analysis more time and space-efficient. For example, we show that when using a KTST to estimate the containment index between a RefSeq-based microbial reference database and simulated metagenome data for 10 values of k, the running time is close to 10x faster compared to a classic MinHash approach while using less than one-fifth the space to store the data structure. A python implementation of this method, CMash, is available at https://github.com/dkoslicki/CMash. The reproduction of all experiments presented herein can be accessed via https://github.com/KoslickiLab/CMASH-reproducibles.

Guidance system based on Dijkstra-ant colony algorithm with binary search tree for indoor parking system

A common algorithm to solve the single-source shortest path (SSSP) is the Dijkstra algorithm. However, the traditional Dijkstra’s is not accurate and need more time to perform the path in order it should visit all the nodes in the graph. In this paper, the Dijkstra-ant colony algorithm (ACO) with binary search tree (BST) has been proposed. Dijkstra and ACO are integrated to produce the smart guidance algorithm for the indoor parking system. Dijkstra algorithm initials the paths to finding the shortest path while ACO optimizes the paths. BST has been used to store the paths that Dijkstra algorithm initialled. The proposed algorithm is aimed to control the shortest path as well as guide the driver towards the nearest vacant available space near the entrance. This solution depending on applying the optimization on an optimal path while the traditional ACO is optimizing the random path based on the greedy algorithm hence we get the most optimal path. Moreover, the reason behind using the BST is to make the generation of the path by Dijkstra’s algorithm more accurate and less time performance. The results show a range of 8.3% to 26.8% improvement in the proposed path compared to the traditional Dijkstra’s algorithm.

Zip Trees

We introduce the zip tree , 1 a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank and the tree is (max)-heap-ordered with respect to ranks, with rank ties broken in favor of smaller keys. Zip trees are essentially treaps [8], except that ranks are drawn from a geometric distribution instead of a uniform distribution, and we allow rank ties. These changes enable us to use fewer random bits per node. We perform insertions and deletions by unmerging and merging paths ( unzipping and zipping ) rather than by doing rotations, which avoids some pointer changes and improves efficiency. The methods of zipping and unzipping take inspiration from previous top-down approaches to insertion and deletion by Stephenson [10], Martínez and Roura [5], and Sprugnoli [9]. From a theoretical standpoint, this work provides two main results. First, zip trees require only O (log log n ) bits (with high probability) to represent the largest rank in an n -node binary search tree; previous data structures require O (log n ) bits for the largest rank. Second, zip trees are naturally isomorphic to skip lists [7], and simplify Dean and Jones’ mapping between skip lists

Retrieving Mobile Phone Information Based on Digital Search Tree

The current study primarily aims to develop a dictionary system for tracing mobile phone numbers for call centers of mobile communication companies. This system tries to save the numbers using a digital search tree in order to make the processes of searching and retrieving customers’ information easier and faster. Several shrubs that represent digits of the total phone numbers will be built through following the phone number digits to be added to the dictionary, with the owner name being at the last node in the tree. Thus, by such searching process, every phone number can be tracked digit-by-digit according to a required path inside its tree, until reaching the leaf. Then, the value stored in the node, that represents the name of phone number’s owner, is returned. Consequently, the amount of memory required to store data will be reduced and data retrieval will be faster.