Computational approach to solving problems of spatial processing of point sets on two-dimensional regular grids

2021 ◽  
Vol 1 (2 (6)) ◽  
Author(s):  
Andrii Dashkevych
Keyword(s):  
Hash Table ◽  
Computational Approach ◽  
Spatial Processing ◽  
Spatial Relationships ◽  
Two Dimensional ◽  
Regular Grid ◽  
Hash Tables ◽  
Processing Task ◽  
Point Set ◽  
Intersection Points

The paper presents an approach to solving problems of spatial processing on sets of points on a plane. The presented method consists in plotting regions of an arbitrary geometric shape near given points of the set on a regular grid and determining the intersection points of the regions using spatial hash tables to improve the efficiency of operations. The proposed approach is implemented in the form of software for determining the spatial relationships between points as a sequence of operations with discretized sets and allows visualization of research results. Figs.: 2. Refs.: 13. Keywords: spatial processing task; point set; plane; regular grid; spatial hash table.

Statistical measures of two dimensional point set uniformity

2012 ◽  
Vol 56 (6) ◽  
pp. 2159-2181 ◽  
Author(s):  
Meng Sang Ong ◽  
Ye Chow Kuang ◽  
Melanie Po-Leen Ooi
Keyword(s):  
Two Dimensional ◽  
Statistical Measures ◽  
Point Set

A Simulated Annealing-Based Approach to Three Dimensional Component Packing

1994 ◽  
Author(s):  
Simon Szykman ◽  
Jonathan Cagan
Keyword(s):  
Simulated Annealing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Computational Approach ◽  
Vlsi Circuits ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Layout Problem ◽  
Component Layout ◽  
General Component

Abstract This paper introduces a computational approach to three dimensional component layout that employs simulated annealing to generate optimal solutions. Simulated annealing has been used extensively for two dimensional layout of VLSI circuits; this research extends techniques developed for two dimensional layout optimization to three dimensional problems which are more representative of mechanical engineering applications. In many of these applications, miniaturization trends increase the need to achieve higher packing density and fit components into smaller containers. This research addresses the three dimensional packing problem, which is a subset of the general component layout problem, as a framework in which to solve general layout problems.

scholarly journals The Maximum Displacement for Linear Probing Hashing

2013 ◽  
Vol 22 (3) ◽  
pp. 455-476
Author(s):  
NICLAS PETERSSON
Keyword(s):  
Probabilistic Model ◽  
Hash Table ◽  
Critical Value ◽  
Hash Tables ◽  
Maximum Displacement ◽  
Asymptotic Nature ◽  
Process Convergence

In this paper we study the maximum displacement for linear probing hashing. We use the standard probabilistic model together with the insertion policy known as First-Come-(First-Served). The results are of asymptotic nature and focus on dense hash tables. That is, the number of occupied cellsnand the size of the hash tablemtend to infinity with ration/m→ 1. We present distributions and moments for the size of the maximum displacement, as well as for the number of items with displacement larger than some critical value. This is done via process convergence of the (appropriately normalized) length of the largest block of consecutive occupied cells, when the total number of occupied cellsnvaries.

scholarly journals Semi-Infinite Paths of the Two-Dimensional Radial Spanning Tree

2013 ◽  
Vol 45 (4) ◽  
pp. 895-916 ◽  
Author(s):  
François Baccelli ◽  
David Coupier ◽  
Viet Chi Tran
Keyword(s):  
Point Process ◽  
Infinite Number ◽  
Spanning Tree ◽  
Poisson Point Process ◽  
Two Dimensional ◽  
Infinite Path ◽  
Intersection Points

We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite paths and the sphere with radius r grows sublinearly with r. Then we prove that in each (deterministic) direction there exists, with probability 1, a unique semi-infinite path, framed by an infinite number of other semi-infinite paths of close asymptotic directions. The set of (random) directions in which there is more than one semi-infinite path is dense in [0, 2π). It corresponds to possible asymptotic directions of competition interfaces. We show that the RST can be decomposed into at most five infinite subtrees directly connected to the root. The interfaces separating these subtrees are studied and simulations are provided.

scholarly journals HD-Tree: An Efficient High-Dimensional Virtual Index Structure Using a Half Decomposition Strategy

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 338
Author(s):  
Ting Huang ◽  
Zhengping Weng ◽  
Gang Liu ◽  
Zhenwen He
Keyword(s):  
Hash Table ◽  
Index Structure ◽  
High Dimensional ◽  
Sequential Search ◽  
Storage Space ◽  
Hash Tables ◽  
Time Performance ◽  
Indexing Method ◽  
Point Data ◽  
Better Than

To manage multidimensional point data more efficiently, this paper presents an improvement, called HD-tree, of a previous indexing method, called D-tree. Both structures combine quadtree-like partitioning (using integer shift operations without storing internal nodes, but only leaves) and hash tables (for searching for the nodes stored). However, the HD-tree follows a brand-new decomposition strategy, which is called half decomposition strategy. This improvement avoids the generation of nodes containing only a small amount of data and the sequential search of the hash table, so that it can save storage space while having faster I/O and better time performance when building the tree and querying data. The results demonstrate convincingly that the time and space performance of HD-tree is better than that of D-tree regardless of uniform or uneven data, which are less affected by data distribution.

scholarly journals Chemistry of cysteine assembly on Au(100): electrochemistry, in situ STM and molecular modeling

Nanoscale ◽  
2019 ◽  
Vol 11 (37) ◽  
pp. 17235-17251
Author(s):  
Christian Engelbrekt ◽  
Renat R. Nazmutdinov ◽  
Tamara T. Zinkicheva ◽  
Dmitrii V. Glukhov ◽  
Jiawei Yan ◽  
...  
Keyword(s):  
Molecular Modeling ◽  
Single Crystal ◽  
Computational Approach ◽  
Two Dimensional ◽  
In Situ Stm ◽  
Molecular Forces

Unique two-dimensional super-structures form when cysteine self-assembles on single-crystal Au(100) due to inter-molecular forces and adsorption energetics, addressed through a comprehensive experimental and quantum computational approach.

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