Accommodating Hierarchies in Relational Databases

2001 ◽  
pp. 194-209
Author(s):  
Ido Millet
Keyword(s):  
Data Structure ◽  
Relational Databases ◽  
Data Retrieval ◽  
Hierarchical Data ◽  
Inconsistent Data ◽  
The Cost

Relational databases and the current SQL standard are poorly suited to retrieval of hierarchical data. After demonstrating the problem, this chapter describes how two approaches to data denormalization can facilitate hierarchical data retrieval. Both approaches solve the problem of data retrieval, but as expected, come at the cost of difficult and potentially inconsistent data updates. This chapter then describes how we can address these update-related shortcomings via back-end (triggers) logic. Using a proper combination of denormalized data structure and back-end logic, we can have the best of both worlds: easy data retrieval and simple, consistent data updates.

scholarly journals Computing the Exact Number of Similarity Classes in the Longest Edge Bisection of Tetrahedra

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1447
Author(s):  
Jose P. Suárez ◽  
Agustín Trujillo ◽  
Tania Moreno
Keyword(s):  
Data Structure ◽  
Stability Condition ◽  
Open Problem ◽  
Integer Arithmetic ◽  
Exact Number ◽  
Similarity Class ◽  
The Stability ◽  
High Level ◽  
The Cost

Showing whether the longest-edge (LE) bisection of tetrahedra meshes degenerates the stability condition or not is still an open problem. Some reasons, in part, are due to the cost for achieving the computation of similarity classes of millions of tetrahedra. We prove the existence of tetrahedra where the LE bisection introduces, at most, 37 similarity classes. This family of new tetrahedra was roughly pointed out by Adler in 1983. However, as far as we know, there has been no evidence confirming its existence. We also introduce a new data structure and algorithm for computing the number of similarity tetrahedral classes based on integer arithmetic, storing only the square of edges. The algorithm lets us perform compact and efficient high-level similarity class computations with a cost that is only dependent on the number of similarity classes.

scholarly journals Calculate Accurate 3D Cost Distance Efficiently

2019 ◽  
Vol 1 ◽  
pp. 1-1
Author(s):  
Yaqian Chen ◽  
Jiangfeng She ◽  
Xingong Li
Keyword(s):  
Data Structure ◽  
Distance Function ◽  
Friction Surface ◽  
Hash Table ◽  
Route Planning ◽  
Weighted Interpolation ◽  
Cost Distance ◽  
Distance Weighted ◽  
Cost Paths ◽  
The Cost

<p><strong>Abstract.</strong> Cost distance is one of the fundamental functions in geographic information systems (GIS), which has been used in various applications such as route planning, construction of Thiessen polygons and distance weighted interpolation. Conventional 2D cost distance function, due to its limited movement directions (either 4 or 8 neighbourhood cells) in the raster data model, overestimates the least cost and the problem is especially severe with a homogeneous friction surface. 3D cost distance function removes the limitation that movement must occur on a planar surface. It can therefore take into account tunnels and bridges when calculating least cost paths. In addition, it can also be used in many other application domains which deal with 3D geospatial data such as in atmospheric science, geology, and oceanography. Based on the method in Tomlin (2010), which can completely eliminate the overestimation when traveling on a homogeneous friction surface, this research proposes an algorithm that calculates accurate least cost with both homogeneous and heterogeneous friction in 3D space. When extending the cost distance function from 2D to 3D, the number of voxels in the propagation front increases significantly and efficiency is an imperative issue. This research also improves the computational efficiency by developing a data structure that combines a binary heap and a hash table. Our results show that the proposed algorithm can calculate accurate 3D cost distance in a homogeneous friction space, and the proposed data structure (i.e., heap plus hash table) not only significantly reduces the algorithm’s runtime but also benefits more in 3D than in 2D. In addition, we have applied the method in a 3D drone delivery routing application in a city environment (Figure 1). Additional applications, such as calculating groundwater flow paths of least hydraulic resistance in a heterogeneous 3D hydraulic conductivity field, are currently under development.</p>

Cost Modeling and Range Estimation for Top-k Retrieval in Relational Databases

2011 ◽  
pp. 295-315
Author(s):  
Anteneh Ayanso ◽  
Paulo B. Goes ◽  
Kumar Mehta
Keyword(s):  
Relational Databases ◽  
Estimation Method ◽  
Synthetic Data ◽  
Cost Modeling ◽  
Data Sets ◽  
Range Estimation ◽  
Mapping Techniques ◽  
The Cost ◽  
Query Estimation ◽  
Query Mapping

Relational databases have increasingly become the basis for a wide range of applications that require efficient methods for exploratory search and retrieval. Top-k retrieval addresses this need and involves finding a limited number of records whose attribute values are the closest to those specified in a query. One of the approaches in the recent literature is query-mapping which deals with converting top-k queries into equivalent range queries that relational database management systems (RDBMSs) normally support. This approach combines the advantages of simplicity as well as practicality by avoiding the need for modifications to the query engine, or specialized data structures and indexing techniques to handle top-k queries separately. This paper reviews existing query-mapping techniques in the literature and presents a range query estimation method based on cost modeling. Experiments on real world and synthetic data sets show that the cost-based range estimation method performs at least as well as prior methods and avoids the need to calibrate workloads on specific database contents.

scholarly journals Fast Closed-Form Matting Using a Hierarchical Data Structure

2014 ◽  
Vol 24 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Chunxia Xiao ◽  
Meng Liu ◽  
Donglin Xiao ◽  
Zhao Dong ◽  
Kwan-Liu Ma
Keyword(s):  
Data Structure ◽  
Closed Form ◽  
Hierarchical Data ◽  
Hierarchical Data Structure

scholarly journals Ordinal Distance Metric Learning with MDS for Image Ranking

2018 ◽  
Vol 35 (01) ◽  
pp. 1850007 ◽  
Author(s):  
Panpan Yu ◽  
Qingna Li
Keyword(s):  
Data Structure ◽  
Metric Learning ◽  
Learning Model ◽  
Distance Metric Learning ◽  
Distance Metric ◽  
Local Data ◽  
Linear Distance ◽  
Image Ranking ◽  
Unconstrained Problem ◽  
The Cost

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric [Formula: see text] as [Formula: see text], the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

scholarly journals AVBH: Asymmetric Learning to Hash with Variable Bit Encoding

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yanduo Ren ◽  
Jiangbo Qian ◽  
Yihong Dong ◽  
Yu Xin ◽  
Huahui Chen
Keyword(s):  
Low Frequency ◽  
Large Data ◽  
Data Retrieval ◽  
Query Point ◽  
Compact Binary ◽  
Hash Code ◽  
Asymmetric Learning ◽  
Learning To Hash ◽  
Public Datasets ◽  
The Cost

Nearest neighbour search (NNS) is the core of large data retrieval. Learning to hash is an effective way to solve the problems by representing high-dimensional data into a compact binary code. However, existing learning to hash methods needs long bit encoding to ensure the accuracy of query, and long bit encoding brings large cost of storage, which severely restricts the long bit encoding in the application of big data. An asymmetric learning to hash with variable bit encoding algorithm (AVBH) is proposed to solve the problem. The AVBH hash algorithm uses two types of hash mapping functions to encode the dataset and the query set into different length bits. For datasets, the hash code frequencies of datasets after random Fourier feature encoding are statistically analysed. The hash code with high frequency is compressed into a longer coding representation, and the hash code with low frequency is compressed into a shorter coding representation. The query point is quantized to a long bit hash code and compared with the same length cascade concatenated data point. Experiments on public datasets show that the proposed algorithm effectively reduces the cost of storage and improves the accuracy of query.

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