隨著無線通訊和行動計算技術的進步，移動物體(moving object)的應用也已經在各個領域興起，如交通偵測、行動商務、導航系統、地理資訊系統等等)。移動物體的特色就是物體會連續地改變它們的位置。因為資料庫要常常更新，所以傳統的空間資料庫無法有效的運用來儲存這些移動物體。因此，對移動物體建立索引去有效地回答有關移動物體的預測查詢(predictive query)就很重要了。在對於預測現在和未來的空間時間資料庫(spatio-temporal database)中，Parametric Spatial Access Methods 這類的方法是被應用的最廣泛的，因為它只需要很少的記憶體空間去儲存那些含有參數的矩形，而且它仍有好的效能，因此它被廣泛的採用。這一類的方法包含TPR-tree， TPR*-tree， Bx-tree，和Bxr-tree。在這些方法中，Bxr-tree 先利用查詢範圍的擴張(the expansion of the query region)來改進了TPR-tree 的CPU 效能，再加上利用區塊範圍的擴張(the expansion of data block)來改進Bx-tree 的I/O 效能。然而，Bxr-tree 的查詢處理是粗略的，使得它花費大量CPU 和I/O 時間去檢查用不到的資料。因此，在這篇論文中，我們提供了一個新的資料結構和一個新的查詢處理方法，叫做可調式擴張的索引方式(AEI)，去改進Bxr-tree 的缺點。在我們方法中，我們讓每個區塊存有八個方向的最大和最小速率，而非原本Bxr-tree 方法中四個方向的最大速率。基於這個資料結構，查詢範圍可以在八個方向分別擴張，而非Bxr-tree 方法中僅四個方向的同時擴張一次。此外，在我們的AEI 方法中，區塊範圍可以根據它朝著查詢範圍的方向去做擴張，而非原本在Bx
r-tree 方法中擴張四個方向。如此一來，因為AEI 考慮
了八個方向的最小速度，所以AEI 的查詢處理會檢查較少的資料區塊。再者，在AEI 中，物件根據它們的方向被分進四個群組中，而Bxr-tree 方法沒有這麼做。在AEI 的查詢處理中，只有那些往查詢範圍移動的物件會被檢查。因此，我們比起Bxr-tree 減少了很多檢索的資料區塊以及I/O 的運算數。從我們的模擬結果顯示出，在平均檢索的資料區塊以及I/O 的運算次數，我們的可調式擴張索引的
查詢處理方式遠比Bxr-tree 來得有效率。

With the development of wireless communications and mobile computing technologies, the applications of moving objects have been developed in many topics, for example, traffic monitoring, mobile E-Commerce, Navigation System, and Geographic Information System. The feature of the moving objects is that objects change their locations continuously. Conventional spatial databases can not support to
store the moving objects efficiently, because the databases must be updated frequently. Therefore, it is important to index moving objects for efficiently answering queries about moving objects. Among the spatial indexing methods for predicting current and future data, the approach of parametric spatial access methods has been applied largely, since it needs little memory space to preserve parametric rectangles, and it still provides good performance, so it is adopted generally. The methods of this approach include the TPR-tree, the TPR*-tree, the Bx-tree, and the Bxr-tree. Among those methods, the Bxr-tree improves CPU performance of TPR-tree by expanding query region first, and improves I/O performance of the
Bxr-tree by expanding the data blocks additionally. However, the query process of the B$^x_r$-tree is too rough such that it costs too much CPU and I/O time to check the useless data. Therefore, in this thesis, we propose a new data structure and a new query processing method named Adjustable Expanded Index (AEI), to improve the disadvantages of the Bxr-tree. In our method, we let each block records the maximum and minimum speeds of each of eight directions, instead of only the maximum speed of each of four directions in the Bxr-tree method. Based on the data structure, the query region can be expanded in each of eight directions individually, instead of being expanded in each of four directions once in the Bxr-tree method. Moreover, in our AEI method, the data blocks can be expanded
according to the direction toward the query region, instead of being expanded in four directions in the Bxr-tree method. In this way, the query process of AEI checks less number of data blocks because it considers the minimum speed of each of eight directions. Furthermore, the objects are divided into four groups in AEI according to their directions,
while the Bxr-tree method does not. Only the objects moving to query region will be checked in the query process of AEI. Therefore, we can reduce more number of retrieved data blocks and the number of I/O operations in our method than the Bxr-tree. From our simulation, we show that the query process of the AEI method is more efficient than that of the Bxr-tree in term of the average numbers of retrieved data blocks and I/O operations.

TABLE OF CONTENTS
Page
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Spatio-temporal Databases . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Categories of Spatio-Temporal Databases . . . . . . . . . . . . . . . . 2
1.2.1 Indexing the Past . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Indexing the Current and Future Positions . . . . . . . . . . . 3
1.3 Future Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2. A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Indexing the Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.1 The STR-tree . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.2 SETI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Indexing the Current and Future Positions . . . . . . . . . . . . . . . 18
2.2.1 PMR-quadtree . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 TPR-tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 TPR*-tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.4 Bx-tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.5 Bxr-tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Indexing Positions from Past to Future . . . . . . . . . . . . . . . . . 22
ii
Page
3. An Adjustable Expanded Index . . . . . . . . . . . . . . . . . . . . . 23
3.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 The Insertion Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Query Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 A Query Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1 Performance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

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