Balanced Quadtree Research Articles

A dynamic balanced quadtree for real-time streaming data

With the advent of big data, industries and individuals generate a large amount of stream data through various intelligent devices. Stream data arrive gradually over time, unlike historical data. This causes an increasingly unbalanced tree because of the unpredictable data density when an index method such as the classical quadtree is used. To solve this problem, this paper formally defines the quadtree imbalance problem caused by constant stream data density, defines a more reasonable measure to evaluate the balance of a quadtree, and proposes a dynamic balanced quadtree (DB-quadtree) for real-time stream data. Experiments on one synthetic dataset and three real datasets show that the method can improve the balance of the tree.

A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete

A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility.

All-quad meshing without cleanup

We present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.

Robust All-quad Meshing of Domains with Connected Regions

In this paper, we present a new algorithm for all-quad meshing of non-convex domains, with connected regions. Our method starts with a strongly balanced quadtree. In contrast to snapping the grid points onto the geometric boundaries, we move points a slight distance away from the common boundaries. Then we intersect the moved grid with the geometry. This allows us to avoid creating any flat quads, and we are able to handle two-sided regions and more complex topologies than prior methods. The algorithm is provably correct, robust, and cleanup-free; meaning we have angle and edge length bounds, without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is also more predictable than prior art.

Development of Cloud P2P OLAP system based on balanced quadtree

To make use of the recent distributed OLAP environment, researches on P2P (Peer-to-Peer) OLAP with the dynamic hybrid tree (DHT) and Grid OLAP are actively proposed. In addition, OLAP query execution costs many minutes by its enormous data and OLAP query properties. To adapt OLAP systems to the cloud computing environment, P2P OLAP has problems on executing multi-dimensional range queries because of P2P properties. In this paper, the central management Cloud P2P OLAP is proposed to provide an efficient cloud computing environment which query results are able to be reused with the time-series properties by various users. The Cloud P2P OLAP is grafted onto hierarchical hybrid P2P for fast query results and multi-dimensional range query, so that the index loads are distributed and the performance is improved.

PARALLEL CONSTRUCTION OF QUADTREES AND QUALITY TRIANGULATIONS

We describe efficient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtree-based finite element meshes. Our algorithms take time O(log n) for point set input and O(log n log k) time for planar straight-line graphs, using O(n+k/log n) processors, where n measures input size and k output size.

Algorithms for Coloring Quadtrees

We describe simple linear time algorithms for coloring the squares of balanced and unbalanced quadtrees so that no two adjacent squares are given the same color. If squares sharing sides are defined as adjacent, we color balanced quadtrees with three colors, and unbalanced quadtrees with four colors; these results are both tight, as some quadtrees require this many colors. If squares sharing corners are defined as adjacent, we color balanced or unbalanced quadtrees with six colors; for some quadtrees, at least five colors are required.

Nearly Balanced Quad List Quad Tree -A Data Structure for VLSI Layout Systems

In the past ten years, many researchers have focused attention on developing better data structures for storing graphical information. Among the proposed data structures, the quad tree data structure provides a good way to organize objects on a 2-D plane. Region searches proceed at logarithmic speeds a desirable characteristic, but no previously proposed VLSI quad tree data structure distributed objects to subdivide the spatial area. This has been a major drawback for operations such as tree searching and window query. In this paper, we present a new division method to reconstruct those quad trees including the multiple storage quad tree (MSQT) and the quad list quad tree (QLQT) into nearly balanced quad tree data structures. Nearly balanced quad trees based on our new spatial division method are constructed by dynamically translating unbalanced multiple storage quad trees or unbalanced quad list quad trees into balanced structures. All benefits of the original quad tree data structures are completely retained. In addition, this method is simple and balanced quad trees memory require less than the original quad trees. Experimental results illustrate that the improvement in region queries of the presented nearly balanced quad trees to both of the QLQT and the MSQT is better than the improvement of the QLQT to the MSQT.

Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees

Given a file of N records each of which has k keys, the worst-case analysis for the region and partial region queries in multidimensional binary search trees and balanced quad trees are presented. It is shown that the search algorithms proposed in [1, 3] run in time O(k·N 1?1/k) for region queries in both tree structures. For partial region queries with s keys specified, the search algorithms run at most in time O(s·N 1?1/k ) in both structures.