scholarly journals On Space Efficient Two Dimensional Range Minimum Data Structures

2010 ◽  
pp. 171-182 ◽  
Author(s):  
Gerth Stølting Brodal ◽  
Pooya Davoodi ◽  
S. Srinivasa Rao
Keyword(s):  
Data Structures ◽  
Two Dimensional ◽  
Minimum Data ◽  
Dimensional Range

scholarly journals On Space Efficient Two Dimensional Range Minimum Data Structures

Algorithmica ◽  
2011 ◽  
Vol 63 (4) ◽  
pp. 815-830 ◽  
Author(s):  
Gerth Stølting Brodal ◽  
Pooya Davoodi ◽  
S. Srinivasa Rao
Keyword(s):  
Data Structures ◽  
Two Dimensional ◽  
Minimum Data ◽  
Dimensional Range

A Constrained Delaunay Triangulation Algorithm Based on Incremental Points

2011 ◽  
Vol 90-93 ◽  
pp. 3277-3282 ◽  
Author(s):  
Bai Chao Wu ◽  
Ai Ping Tang ◽  
Lian Fa Wang
Keyword(s):  
Information System ◽  
Data Structures ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Three Dimensional ◽  
Geographical Information ◽  
Two Dimensional ◽  
Data Set ◽  
Constrained Delaunay Triangulation

The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation ofconstrained delaunay triangulationis showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.

scholarly journals Encoding Two-Dimensional Range Top-k Queries

Algorithmica ◽  
2021 ◽  
Author(s):  
Seungbum Jo ◽  
Rahul Lingala ◽  
Srinivasa Rao Satti
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Total Order ◽  
Two Dimensional ◽  
Information Theoretic ◽  
Cartesian Tree ◽  
Dimensional Range

AbstractWe consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering $${\text{Top-}}{k}$$ Top- k queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be constructed efficiently. For an $$m \times n$$ m × n array, with $$m \le n$$ m ≤ n , we first propose an encoding for answering 1-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, whose query range is restricted to $$[1 \dots m][1 \dots a]$$ [ 1 ⋯ m ] [ 1 ⋯ a ] , for $$1 \le a \le n$$ 1 ≤ a ≤ n . Next, we propose an encoding for answering for the general (4-sided) $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries that takes $$(m\lg {{(k+1)n \atopwithdelims ()n}}+2nm(m-1)+o(n))$$ ( m lg ( k + 1 ) n n + 2 n m ( m - 1 ) + o ( n ) ) bits, which generalizes the joint Cartesian tree of Golin et al. [TCS 2016]. Compared with trivial $$O(nm\lg {n})$$ O ( n m lg n ) -bit encoding, our encoding takes less space when $$m = o(\lg {n})$$ m = o ( lg n ) . In addition to the upper bound results for the encodings, we also give lower bounds on encodings for answering 1 and 4-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, which show that our upper bound results are almost optimal.

scholarly journals The reliability and validity of upper quadrant posture and two-dimensional range of motion measurement tools

2008 ◽  
Vol 64 (3) ◽  
Author(s):  
S. Van Niekerk ◽  
Q. Louw
Keyword(s):  
Reliability And Validity ◽  
Two Dimensional ◽  
Research Projects ◽  
Validity And Reliability ◽  
Research Setting ◽  
Motion Measurement ◽  
Measurement Tools ◽  
Specific Project ◽  
Posture Measurement ◽  
Dimensional Range

Measuring upper quadrant posture and movement is a challenge to researchers and clinicians. A  range of postural measurement tools is commonly used in the clinical setting and in research projects to evaluate postural align-ment, but information about the validity and reliability of these tools and thus as election of the optimal tool for a specific project is often uncertain. This reviewaims to make recommendations to clinicians and researchers regarding practical,valid and reliable tools to assess upper quadrant posture and range of motion.Electronic databases and key journals were searched. An adapted appraisal toolwas utilised to assess the methodology for each of the nine selected articles. Nine eligible articles reporting on thegoniometer, flexicurve and inclinometer were included. This review highlights the fact that a range of two-dimensional(2D) posture measurement tools are being used in clinical practice and research. Although the findings for the reliability and validity of the tools included in this review appear to be promising, strong recommendations are limited by the imprecision of the results. Thus, the primary issue hampering the recommendation for the most reliable and valid tool to use in the clinical or research setting is due to the limitations pertaining the analysis of the data, and the interpretation thereof.

Deep Person Detection in Two-Dimensional Range Data

2018 ◽  
Vol 3 (3) ◽  
pp. 2726-2733 ◽  
Author(s):  
Lucas Beyer ◽  
Alexander Hermans ◽  
Timm Linder ◽  
Kai O. Arras ◽  
Bastian Leibe
Keyword(s):  
Range Data ◽  
Two Dimensional ◽  
Person Detection ◽  
Dimensional Range

TWO-DIMENSIONAL RANGE SEARCH BASED ON THE VORONOI DIAGRAM

2005 ◽  
Vol 15 (02) ◽  
pp. 151-166
Author(s):  
TAKESHI KANDA ◽  
KOKICHI SUGIHARA
Keyword(s):  
Voronoi Diagram ◽  
Dimensional Space ◽  
Search Problem ◽  
Two Dimensional ◽  
Worst Case ◽  
Average Case ◽  
Range Search ◽  
Almost All ◽  
Set Of Points ◽  
Dimensional Range

This paper studies the two-dimensional range search problem, and constructs a simple and efficient algorithm based on the Voronoi diagram. In this problem, a set of points and a query range are given, and we want to enumerate all the points which are inside the query range as quickly as possible. In most of the previous researches on this problem, the shape of the query range is restricted to particular ones such as circles, rectangles and triangles, and the improvement on the worst-case performance has been pursued. On the other hand, the algorithm proposed in this paper is designed for a general shape of the query range in the two-dimensional space, and is intended to accomplish a good average-case performance. This performance is actually observed by numerical experiments. In these experiments, we compare the execution time of the proposed algorithm with those of other representative algorithms such as those based on the bucketing technique and the k-d tree. We can observe that our algorithm shows the better performance in almost all the cases.

A THREE-DIMENSIONAL AZIMUTHAL WIDE-ANGLE MODEL FOR THE PARABOLIC WAVE EQUATION

1999 ◽  
Vol 07 (04) ◽  
pp. 269-286 ◽  
Author(s):  
CHIFANG CHEN ◽  
YING-TSONG LIN ◽  
DING LEE
Keyword(s):  
Wave Equation ◽  
Prediction Models ◽  
Three Dimensional ◽  
3D Models ◽  
Theoretical Development ◽  
Wide Angle ◽  
Two Dimensional ◽  
Narrow Angle ◽  
Propagation Prediction ◽  
Dimensional Range

In predicting wave propagations in either direction, the size of the angle of propagation plays an important role; thus, the concept of wide-angle is introduced. Most existing acoustic propagation prediction models do have the capability of treating the wide-angle but the treatment, in practice, is vertical. This is desirable for solving two-dimensional (range and depth) problems. In extending the two-dimensional treatment to 3 dimensions, even though the wide-angle capability is maintained in most 3D models, it is still vertical. Owing to the need of a wide-angle capability in the azimuth direction, this paper formulates an azimuthal wide-angle wave equation whose theoretical development is presented. An illustrative example is included to demonstrate the need for such azimuthal wide-angle capability. Also, a comparison is shown between results using narrow-angle and wide-angle equations separately.

Two dimensional Range Minimum/Maximum Query revisited

2010 ◽  
Author(s):  
Maxime Crochemore ◽  
Masud Hasan ◽  
Tanaeem M Moosa ◽  
M. Sohel Rahman
Keyword(s):  
Two Dimensional ◽  
Dimensional Range
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