現實生活中的應用，例如地理位置服務和地理資訊系統服務，物體資料的空間查詢會隨著時間大量地產生。因此，時空資料庫日漸發展，以空間資料庫或時間資料庫，來處理這些空間查詢與物體資料。我們是針對在空間資料庫中執行空間查詢，用以擷取現今時間上的靜止與移動物體資料。然而，我們很難用一個總順序性來儲存會隨著時間改變幾何屬性、大量且具複雜結構的物體資料。以空間索引為基礎的空間擷取方法能夠有效地組織、盡量地儲存空間物體資料的鄰近關係，進而減少磁碟存取次數，減少空間查詢時所需時間。因此，在此博士論文中，以九分區域樹(NA-tree)為空間索引，第一，我們提出一種對靜止物體作空間聯結的NA-Tree Join方法。NA-Tree Join方法是使用空間交集序號對的表格，在兩個不同的NA-Tree內，判斷交集不為空區域的候選葉節點，直接擷取物體資料作距離比對，獲得交集不為空區域的成對物體資料。第二，我們提出一種基於NA-Tree特徵位元組之連續性範圍查詢內移動物體的NABP方法。NABP方法是使用相應NA-Tree空間索引之特徵位元組，快速地判斷出範圍查詢與移動物體的關係，尋找範圍查詢內的移動物體。NABP方法只需搜尋NA-tree下的單一分支，就可以找到範圍查詢的區域，不同於利用R-Tree的空間索引之查詢方法，不同節點侷限的範圍會有重疊情形。當範圍查詢數目增加且超載於單一區域負載率時，NABP方法只需漸進地使用特徵位元組更新影響的範圍查詢，不同於利用Cell空間索引之查詢方法，必需重建整個索引。在範圍查詢更新頻率多的情況，NABP方法比利用Cell空間索引之查詢方法所需較少的時間。在移動物體更新頻率多的情況，NABP方法比利用R-Tree的空間索引之查詢方法所需較少的時間。基於Hilbert曲線良好的叢聚性質，我們提出一種以單一最近鄰居查詢之ONHC方法為基礎的所有最近鄰居查詢之ANHC方法。我們使用Hilbert曲線將空間劃分成不同階層的區塊，產生四位元數方向順序位組來儲存區塊的方位。使用與查詢區塊有關的四位元數，在方向順序位組的位置來判斷其方位，進而計算出相鄰區塊的四位元數，經位數轉換來獲得相鄰區塊在Hilbert曲線內的十分位數。我們直接擷取這些相鄰區塊中的物體資料作距離比對，以獲得最近鄰居。在回答單一最近鄰居查詢時，ONHC方法比使用Peano曲線與Hilbert曲線間轉換的CCSF方法所需較少的時間。在回答所有鄰居查詢時，ANHC方法比利用R-Tree的空間索引之查詢方法所需較少的時間。

With the large number of spatial queries for spatial data objects changing with time in many applications, e.g., the location based services and geographic information systems, spatio-temporal databases have been developed to manipulate them in spatial or temporal databases. We focus on queries for stationary and moving objects in the spatial database in the present. However, there is no total ordering for the large volume and complicated objects which may change their geometries with time. A spatial access method based on the spatial index structure attempts to preserve the spatial proximity as much as possible. Then, the number of disk access which takes the response time is reduced during the query processing. Therefore, in this dissertation, based on the NA-tree, first, we propose the NA-tree join method over the stationary objects. Our NA-tree join simply uses the correlation table to directly obtain candidate leaf nodes based on two NA-trees which have non-empty overlaps. Moreover, our NA-tree join accesses objects once from those candidate leaf nodes and returns pairs of objects which have non-empty overlaps. Second, we propose the NABP method for the continuous range queries over the moving objects. Our NABP method uses the bit-patterns of regions in the NA-tree to check the relation between the range queries and moving objects. Our NABP method searches only one path in the NA-tree for the range query, instead of more than one path in the R*-tree-based method which has the overlapping problem. When the number of range queries increases with time, our NABP method incrementally updates the affected range queries by bit-patterns checking, instead of rebuilding the index like the cell-based method. From the experimental results, we have shown that our NABP method needs less time than the cell-based method for range queries update and less time than the R*-tree-based method for moving objects update. Based on the Hilbert curve with the good clustering property, we propose the ANHC method to answer the all-nearest-neighbors query by our ONHC method. Our ONHC method is used to answer the one-nearest-neighbor query over the stationary objects. We generate direction sequences to store the orientations of the query block in the Hilbert curve of different orders. By using quaternary numbers and direction sequences of the query block, we obtain the relative locations of the neighboring blocks and compute their quaternary numbers. Then, we directly access the neighboring blocks by their sequence numbers which is the transformation of the quaternary numbers from base four to ten. The nearest neighbor can be obtained by distance comparisons in these blocks. From the experimental results, we have shown that our ONHC and ANHC methods need less time than CCSF method for the one-nearest-neighbor query and the method based on R*-trees for the all-nearest-neighbors query, respectively.

LIST OF FIGURES --iv
LIST OF TABLES --viii
1. Introduction --1
1.1 Spatio-Temporal Database --2
1.2 Spatial Database --3
1.3 Spatial Access Methods --5
1.4 Sptial Join --6
1.5 Continuous Range Query --9
1.6 All-Nearest-Neighbors Query --12
1.7 Motivations and Contributions --14
1.7.1 Spatial Join Based on NA-Trees --14
1.7.2 An NA-Tree-Bit-Patterns-based Method for Continuous Range Queries over Moving Objects --15
1.7.3 All-Nearest-Neighbors Finding Based on the Hilbert Curve --16
1.8 Organization of Dissertation --19
2. A Survey of Spatial Access Methods --21
2.1 The R-Tree-based Method for the Spatial Join --21
2.2 Methods for Continuous Range Queries --22
2.2.1 The Cell-based Method --22
2.2.2 The R*-Tree-based Method --23
2.3 Methods for the All-Nearest-Neighbors Query --24
2.3.1 The R-Tree-based Method --25
2.3.2 The Hilbert-Curve-based Method --26
2.4 The NA-Tree (Nine-Area Tree) --27
3. Spatial Join Based on NA-Trees --33
3.1 The NA-tree Join --34
3.1.1 A Correlation Pair --34
3.1.2 NA-Trees of the Same Height --39
3.1.3 NA-Trees of Different Heights --40
3.2 Performance --41
3.2.1 The System Model --41
3.2.2 Simulation Results --43
3.3 Summary --43
4. An NA-Tree-Bit-Patterns-based Method for Continuous Range Queries over Moving Objects --46
4.1 The NABP Method --47
4.1.1 The Bit-Pattern of the Region in the NA-Tree --47
4.1.2 Continuous Query Processing --50
4.1.3 A Range Query Update --53
4.1.4 A Moving Object Update --62
4.1.5 An Example --63
4.2 Performance --66
4.2.1 The System Model --66
4.2.2 Simulation Results --68
4.3 Summary --72
5. All-Nearest-Neighbor Finding Based on the Hilbert Curve --73
5.1 All-Nearest-Neighbors Finding --74
5.1.1 Orientations and Direction Sequences --74
5.1.2 Quaternary Numbers, Orders, and Direction Sequences --75
5.1.3 The ONHC Method --79
5.1.4 The ANHC Method --87
5.2 Performance --92
5.2.1 The System Model --93
5.2.2 Simulation Results --96
5.3 Summary --104
6. Conclusions --105
6.1 Summary --105
6.2 The Future Research Direction --108
BIBLOGRAPHY --110

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