• Spatial Information Research
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• v.19 no.4
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• pp.45-54
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• 2011

In this paper, we propose a hybrid index structure, called the SQMR-tree(Spatial Quad MR-tree) that can process spatial data efficiently by combining advantages of the MR-tree and the SQR-tree. The MR-tree is an extended R-tree using a mapping tree to access directly to leaf nodes of the R-tree and the SQR-tree is a combination of the SQ-tree(Spatial Quad-tree) which is an extended Quad-tree to process spatial objects with non-zero area and the R-tree which actually stores spatial objects and are associated with each leaf node of the SQ-tree. The SQMR-tree consists of the SQR-tree as the base structure and the mapping trees associated with each R-tree of the SQR-tree. Therefore, because spatial objects are distributedly inserted into several R-trees and only R-trees intersected with the query area are accessed to process spatial queries like the SQR-tree, the query processing cost of the SQMR-tree can be reduced. Moreover, the search performance of the SQMR-tree is improved by using the mapping trees to access directly to leaf nodes of the R-tree without tree traversal like the MR-tree. Finally, we proved superiority of the SQMR-tree through experiments.

• Proceedings of the Korea Information Processing Society Conference
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• 2009.11a
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• pp.771-772
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• 2009

최근 대표적인 공간 인덱스 구조인 R-tree를 기반으로 KD-tree나 Quad-tree와 같은 공간 분할 특성을 이용하여 인덱싱 성능을 향상시키기 위한 연구가 활발하다. 본 논문에서는 기존에 제시된 R-tree 기반 인덱스 구조인 SQR-tree와 PMR-tree의 특성을 결합하여 대용량 공간 데이타를 보다 효율적으로 처리하는 인덱스 구조인 MSQR-tree(Mapping-based SQR-tree)를 제시한다. SQR-tree는 Quad-tree를 확장한 SQ-tree와 각 SQ-tree 리프 노드마다 실제로 공간 객체를 저장하는 R-tree가 연계되어 있는 인덱스 구조이고, PMR-tree는 R-tree에 R-tree 리프 노드를 직접 접근할 수 있는 매핑 트리를 적용한 인덱스 구조이다. 본 논문에서 제시하는 MSQR-tree는 SQR-tree를 기본 구조로 가지고 R-tree마다 매핑 트리가 적용된 구조를 갖는다. 따라서, MSQR-tree에서는 SQR-tree와 같이 질의가 여러 R-tree에서 분산 처리되고, PMR-tree와 같이 매핑 트리를 통해 R-tree 리프 노드를 빠르게 접근할 수 있다. 마지막으로 성능 실험을 통해 MSQR-tree의 우수성을 입증하였다.

• Spatial Information Research
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• v.18 no.4
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• pp.109-120
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• 2010

Recently, due to rapid increasement of spatial data collected from various geosensors in u-GIS environments, the importance of spatial index for efficient search of large spatial data is rising gradually. Especially, researches based R-Tree to improve search performance of spatial data have been actively performed. These previous researches focus on reducing overlaps between nodes or the height of the R -Tree. However, these can not solve an unnecessary node access problem efficiently occurred in tree traversal. In this paper, we propose a MR-Tree(Mapping-based R-Tree) to solve this problem and to support efficient search of large spatial data. The MR-Tree can improve search performance by using a mapping tree for direct access to leaf nodes of the R-Tree without tree traversal. The mapping tree is composed with MBRs and pointers of R-Tree leaf nodes associating each partition which is made by splitting data area repeatedly along dimensions. Especially, the MR-Tree can be adopted in various variations of the R-Tree easily without a modification of the R-Tree structure. In addition, because the mapping tree is constructed in main memory, search time can be greatly reduced. Finally, we proved superiority of MR-Tree performance through experiments.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04a
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• pp.749-751
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• 2003

R-Tree는 일반적으로 트리 노드의 크기를 디스크 페이지의 크기와 같게 함으로써 I/O 성능에 최적이 되도록 구현한다. 최근에는 CPU 캐시 성능을 최적화하는 R-Tree의 변형이 개발되었다. 이는 노드의 크기를 캐시 라인 크기의 수 배로 하고 MBR에 저장되는 키를 압축하여 노드 하나에 더 많은 엔트리를 저장함으로써 가능하였다. 그러나, 디스크 최적 R-Tree와 CPU 캐시 최적 R-Tree의 노드 크기 사이에는 수십-수백 바이트와 수-수십 킬로바이트라는 큰 차이가 있으므로, 디스크 최적 R-Tree는 캐시 성능이 나쁘고, CPU 캐시 최적 H-Tree는 나쁜 디스크 성능을 보이는 문제점을 가지고 있다. 이 논문에서는 CPU 캐시와 디스크에 모두 최적인 R-Tree. TR-Tree를 제안한다. 먼저, 디스크 페이지 안에 들어가는 페이지 내부 트리의 높이와 단말, 중간 노드의 크기를 결정하는 방법을 제시한다. 그리고, 이틀 이용하여 TR-Tree의 검색 연산에 필요한 캐시 미스 수를 최소화였고. TR-Tree의 검색 성능을 최적화하였다. 또한, 디스크 I/O 성능을 최적화하기 위해 메모리 노드들을 디스크 페이지에 잘 맞게 배치하였다. 여기에서 구현한 TR-Tree는 디스크 최적 R-Tree보다 삽입 연산에서 6에서 28배 정도 빨랐으며, 검색 연산에서는 1.28배에서 2배의 성능 향상을 보였다.

• Journal of Korea Spatial Information System Society
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• v.6 no.1 s.11
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• pp.19-29
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• 2004

Recently, studies have been performed to improve the cache performance of the R-Tree in main memory. A general mothed to improve the cache performance of the R-Tree is to reduce size of an entry so that a node can store more entries and fanout of it can increase. However, this method generally requites additional process to reduce information of entries and do not support incremental updates. In addition, the cache miss always occurs on moving between a parent node and a child node. To solve these problems efficiently, this paper proposes and evaluates the PR-Tree that is an extended R-Tree indexing method using prefetching in main memory. The PR-Tree can produce a wider node to optimize prefetching without additional modifications on the R-Tree. Moreover, the PR-Tree reduces cache miss rates that occur in moving between a parent node and a child node. In our simulation, the search performance, the update performance, and the node split performance of the PR-Tree improve up to 38%. 30%, and 67% respectively, compared with the original R-Tree.

• Journal of KIISE
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• v.41 no.10
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• pp.792-798
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• 2014

In spatial databases, R-tree is one of the most widely used indexing structures and many variants have been proposed for its performance improvement. Among these variants, Hilbert R-tree is a representative method using Hilbert curve to process large amounts of data without high cost split techniques to construct the R-tree. This Hilbert R-tree, however, is hardly applicable to large-scale applications in practice mainly due to high pre-processing costs and slow bulk-load time. To overcome the limitations of Hilbert R-tree, we propose a novel approach for parallelizing Hilbert mapping and thus accelerating bulk-loading of Hilbert R-tree on GPU memory. Hilbert R-tree based on GPU improves bulk-loading performance by applying the inversed-cell method and exploiting parallelism for packing the R-tree structure. Our experimental results show that the proposed scheme is up to 45 times faster compared to the traditional CPU-based bulk-loading schemes.

• Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
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• 2008.10a
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• pp.82-89
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• 2008

최근, GIS 분야에서 RFID와 GPS 센서 같은 위치 및 공간 데이타를 포함하는 다양한 GeoSensor의 활용으로 수집되는 공간 데이타가 크게 증가하면서, 대용량 공간 데이타의 빠른 처리를 위한 공간 인덱스의 중요성이 높아지고 있다. 특히, 대표적인 공간 인덱스인 R-Tree를 기반으로 검색 성능을 높이기 위한 연구가 활발히 진행되고 있다. 그러나, 기존 연구는 R-Tree에서 노드의 MBR 간의 겹침이나 트리 높이를 어느 정도 줄임으로써 다소 검색 성능을 향상시켰지만, 트리 검색에서 발생하는 불필요한 노드 접근 비용 문제를 효율적으로 해결하지 못하고 있다. 본 논문에서는 이러한 문제를 해결하고 R-Tree에서 대용량 공간 데이타의 빠른 검색을 제공하는 인덱스인 HR-Tree(Hash based R-Tree)를 제시한다. HR-Tree는 트리 검색 없이 R-Tree 리프 노드를 직접 접근할 수 있는 해시 테이블을 이용함으로써 R-Tree의 검색 성능을 높인다. 해시 테이블은 데이타 영역을 차원에 따라 반복적으로 분할한 Partition과 대응되는 R-Tree 리프 노드의 MBR과 포인터들로 구성된다. 각 Partition은 생성 과정에서 고유의 식별 코드를 갖기 때문에 Partition 코드가 주어지면 해시 테이블에서 해당 레코드를 쉽게 접근할 수 있다. 또한, HR-Tree는 R-Tree구조의 변경없이 다양한 R-Tree 변형 구조에 쉽게 적용할 수 있는 장점이 있다. 마지막으로 실험을 통하여 HR-Tree의 우수성을 입증하였다.

• Journal of KIISE
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• v.42 no.4
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• pp.522-529
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• 2015

Ever since the R-tree was proposed to index multi-dimensional data, many efforts have been made to improve its query performances. One common trend to improve query performance is to parallelize query processing with the use of multi-core architectures. To this end, a GPU-base R-tree has been recently proposed. However, even though a GPU-based R-tree can exhibit an improvement in query performance, it is limited in its ability to handle large volumes of data because GPUs have limited physical memory. To address this problem, we propose MGR-tree (Multi-GPU R-tree), which can manage large volumes of data by dividing nodes into multiple GPUs. Our experiments show that MGR-tree is up to 9.1 times faster than a sequential search on a GPU and up to 1.6 times faster than a conventional GPU-based R-tree.

• The KIPS Transactions:PartD
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• v.13D no.4 s.107
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• pp.463-476
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• 2006

R-trees have been traditionally optimized for the I/O performance with the disk page as the tree node. Recently, researchers have proposed cache-conscious variations of R-trees optimized for the CPU cache performance in main memory environments, where the node size is several cache lines wide and more entries are packed in a node by compressing MBR keys. However, because there is a big difference between the node sizes of two types of R-trees, disk-optimized R-trees show poor cache performance while cache-optimized R-trees exhibit poor disk performance. In this paper, we propose a cache and disk optimized R-tree, called the PR-tree (Prefetching R-tree). For the cache performance, the node size of the PR-tree is wider than a cache line, and the prefetch instruction is used to reduce the number of cache misses. For the I/O performance, the nodes of the PR-tree are fitted into one disk page. We represent the detailed analysis of cache misses for range queries, and enumerate all the reasonable in-page leaf and nonleaf node sizes, and heights of in-page trees to figure out tree parameters for best cache and I/O performance. The PR-tree that we propose achieves better cache performance than the disk-optimized R-tree: a factor of 3.5-15.1 improvement for one-by-one insertions, 6.5-15.1 improvement for deletions, 1.3-1.9 improvement for range queries, and 2.7-9.7 improvement for k-nearest neighbor queries. All experimental results do not show notable declines of the I/O performance.

• The KIPS Transactions:PartD
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• v.8D no.5
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• pp.507-512
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• 2001

Feature-based similarity has become an important research issue in multimedia database systems. The features of multimedia data are useful for discriminating between multimedia objects. the performance of conventional multidimensional data structures tends to deteriorate as the number of dimensions of feature vectors increase. The $R^{*}-Tree$ is the most successful variant of the R-Tree. In this paper, we propose a SOM-based $R^{*}-Tree$ as a new indexing method for high-dimensional feature vectors. The SOM-based $R^{*}-Tree$ combines SOM and $R^{*}-Tree$ to achieve search performance more scalable to high-dimensionalties. Self-Organizingf Maps (SOMs) provide mapping from high-dimensional feature vectors onto a two-dimensional space. The map is called a topological feature map, and preserves the mutual relationships (similarity) in the feature spaces of input data, clustering mutually similar feature vectors in neighboring nodes. Each node of the topological feature map holds a codebook vector. We experimentally compare the retrieval time cost of a SOM-based $R^{*}-Tree$ with of an SOM and $R^{*}-Tree$ using color feature vectors extracted from 40,000 images. The results show that the SOM-based $R^{*}-Tree$ outperform both the SOM and $R^{*}-Tree$ due to reduction of the number of nodes to build $R^{*}-Tree$ and retrieval time cost.