在過去幾年，無線通訊科技、行動式服務系統及全球定位系統在快速的發展下越
來越重要。由於行動式服務越來越熱門，空間資料庫管理也成為一個重要的應
用。其中一個在空間資料庫中最重要的主題為反向最近鄰居查詢。反向最近鄰居
查詢目的為找出哪些資料物件將查詢點當作最近鄰居。反向最近鄰居查詢和最近
鄰居查訊不同，反向最近鄰居查詢的答案會得到零個到無限多個資料物件，且得
到的答案不一定為最近鄰居查詢的答案。因此，反向最近鄰居查詢及最近鄰居查
詢之間不存在對稱性。反向最近鄰居查詢的問題不僅可以被應用在全球行動通訊
系統，甚至是一些商業策略中。反向最近鄰居查詢的研究一開始著重在歐幾里得
空間中。接者在歐幾里得空間中，動態資料的反向最近鄰居查詢研究也取得不錯
的成果。在過去幾年，研究開始被著重在實際道路的空間中。在實際道路中，我
們通常將物件分成兩種型態：查詢型態及資料型態。過去的研究中，凡諾伊圖曾
被使用來解決反向最近鄰居查詢的問題。凡諾伊圖成功的減少查詢時間，但凡諾
伊圖在使用動態資料時仍有缺點，凡諾伊圖無法在物件移動的情況下有效率的查
詢答案。OpinitialBN-RNN 演算法是用來處理反向最近鄰居查詢在動態資料及實
際道路中的問題。這個演算法使用一個被稱為multi-way tree 的資料結構在資
料物件會移動的情況下有效的解決反向最近鄰居查詢的問題。然而當資料中的查
詢點在實際道路中移動時，OpinitialBN-RNN 演算法會使用太多的時間去重建
multi-way tree。因此，我們提出一個演算法來解決這個問題，改善當查詢點移
動時的執行效率。我們的演算法在查詢點移動後會旋轉原本的multi-way tree。
接著在查詢點移動後根據查詢點的新位置從終端節點縮減或擴增multi-way
tree。我們不會重建整個multi-way tree。從我們的實驗結果來看我們的方法
比起OpinitialBN-RNN 演算法在查詢點移動時有更好的效率。特別是當查詢點擁
有區域性我們的方法比OpinitialBN-RNN 演算法好。

In recent years, the wireless communication technologies, mobile system, and
Global Positioning System (GPS) are more important and develop quickly. Due to
the mobile services are becoming more popularity, the spatial database management
are also becoming more important. One of the important research in the spatial
database system is the Reverse Nearest Neighbor query (RNN query). The RNN
query means that "The query object will nd what objects regard oneself as their
nearest neighbor." The RNN query is di erent from the Nearest Neighbor query (NN
query), it will nd zero to in nite of results, and the RNN query results could not be
the NN query results. Therefore, there is no symmetry between RNN query and NN
query. The RNN query research can be applied on Global System for Mobile Com-
munications (GSM), even business strategies. The beginning of RNN query research
has focused on Euclidean space. Then, the RNN research has gotten good e cency
on dynamic dataset in Euclidean space. In recent years, RNN research has focused on
the road network database. On the road network, we usually divide objects into two
types : query type and data type. There are some algorithms using Voronoi diagram
to solve the RNN problem in road networks. Those algorithms aim to reduce time
to compute the answers. But they have drawback on dynamic dataset. They do
not work e cently when the objects move. The OpinitialBN-RNN algorithm is an
algorithm to deal with the RNN query problem in dynamic dataset in road networks.
The algorithm uses a structure named mutli-way tree to solve the movement of data
objects of RNN query problem e cently. However, when the query object moves to a
new location in road networks, the OpinitialBN-RNN algorithm has to take long time
to reconstruct the multi-way tree. Therefore, in this thesis, we propose an incremental
approach to solve the problem and improve the performance when the query object
moves. Our algorithm will rotate the original multi-way tree when the query object
moves. Then we will shrink/extend the multi-way tree from the terminal nodes ac-
cording to the new location of the query object after we rotate the original multi-way
tree. We do not reconstruct the multi-way tree. From the simulation results, we show
that our algorithm is more e cient than the OpinitialBN-RNN algorithm when the
query object moves. Especially, when the movement of the query object has strong
locality, our algorithm outperforms the OpinitialBN-RNN algorithm.

論文審定書………………..……………………………………………………..i
謝辭…………………………………………...………………………………….i
論文檢索…………………………………………...………………………….. iii
中文摘要…………………………………….…………………………….……iv
英文摘要………………………………….……..………………………………v
LIST OF FIGURES………………………..………………..………………....viii
LIST OF TABLES……………………………..……………………………….xi
1. Introduction……..…………………………………………………………1
1.1 The Basic Concept of RNN Query….…………………………………..1
1.2 The RNN Query in Road Networks.……………………...…………….3
1.3 The Related Work of the RNN Query in Road Networks.………...……5
1.4 Motivation.……………………………………………………...………6
1.5 Organization of the Thesis.…………………………………...…………7
2. A Survey of Algorithms for Reverse Nearest Neighbor Queries . 9
2.1 Visible Reverse Nearest Neighbor Query in Spatial Database……..…..9
2.2 The IGERN Algorithms of RNN Problems.……………....…….……..10
2.3 Voronoi-Base Reverse Nearest Neighbor Querise in Road
Networks..……………..…………………………………………...14
2.3.1 Network Voronoi Diagram……….……..……………..15
2.3.2 Reverse Nearest Neighbor Queries.……..………….……16
2.4 The OpInitialBN-RNN Algorithm of Bichromatic RNN Problem in
Road Networks..……..……………………………………………18
2.4.1 The PMR Quad-tree and the Multi-way Tree in Road
Networks ……………………………………………………...18
2.4.2 Optimize Algorithm OpInitialBN-RNN……………………...20
2.4.3 Continuous Reverse Nearest Neighbor Monitoring.………….23
3. An Incremental Approach……………………………………………….26
3.1 Data Structure………………………………………………………….26
3.2 Algorithm……………………………………………………………...30
3.2.1 The Initial Step…………………………………………………30
3.2.2 The Incremental Step…………………………………………...34
3.2.2.1 Case 1: The Moving Case of Data Objects ………….35
3.2.2.2 Case 2: The Moving Case of the Query Object………36
3.2.2.3 Case 3: The Moving Case of Both Data Objects and
the Query Object……………………………………43
3.3 A Comparison…………………………………………………………..49
4. Performance………………………………………………………………51
4.1 The Performance Model……………………………………………….51
4.2 Experiment Results…………………………………………………….51
5. Conclusion………………………………………………………………...58
5.1 Summary……………………………………………………………….58
5.2 Future Work…………………………………………………………....59
BIBLIOGRAPHY……………………………………………………………..60

[1] M. A. Cheema, W. Zhang, X. Lin, Y. Zhang, and X. Li, “Continuous Reverse k Nearest Neighbors Queries in Euclidean Space and in Spatial Networks,” The International Journal on Very Large Data Bases, Vol. 21, No. 1, pp. 617–627, Feb. 2012.
[2] H. J. Cho and C. W. Chung, “An Efficient and Scalable Approach to CNN Queries in a Road Network,” Proc. of the 31st Int. Conf. on Very Large Data Bases, pp. 865–876, 2005.
[3] Y. Gao, B. Zheng, G. Chen, W. C. Lee, K. C. K. Lee, and Q. Li, “Visible Reverse k-Nearest Neighbor Query Processing in Spatial Databases,” IEEE Transactions on Knowledge and Data Engineering, Vol. 21, No. 9, pp. 1314–1327, Sept. 2009.
[4] P. Ghaemi, K. Shahabi, J. P. Wilson, and F. Banaei-Kashani, “Continuous Maximal Reverse Nearest Neighbor Query on Spatial Networks,” Proc. of the 20th Int. Conf. on Advances in Geographic Information Systems, pp. 61–70, 2012.
[5] L. Guohui, L. Yanhong, L. Jianjun, L. Shu, and Y. Fumin, “Continuous Reverse k Nearest Neighbor Monitoring on Moving Objects in Road Networks,” Information Systems, Vol. 35, No. 8, pp. 860–883, Dec. 2010.
[6] E. G. Hoel and H. Samet, “Efficient Processing of Spatial Queries in Line Segment Databases,” Proc. of the 2nd Int. Symp. on Advances in Spatial Databases, pp. 235–256, 1991.
[7] J. M. Kang, M. F. Mokbel, S. Shekhar, T. Xia, and D. Zhang, “Incremental and General Evaluation of Reverse Nearest Neighbors,” IEEE Transactions on Knowledge and Data Engineering, Vol. 22, No. 7, pp. 983–999, July 2010.
[8] F. Korn and S. Muthukrishnan, “Inuence Sets Based on Reverse Nearest Neighbor Queries,” ACM SIGMOD Record, Vol. 29, No. 2, pp. 201–212, June 2000.
[9] K. Mouratidis, M. L. Yiu, D. Papadias, and N. Mamoulis, “Continuous Nearest Neighbor Monitoring in Road Networks,” Proc. of the 32nd Int. Conf. on Very Large Data Bases, pp. 43–54, 2006.
[10] M. Safar, D. Ibrahimi, and D. Taniar, “Voronoi-Based Reverse Nearest Neighbor Query Processing on Spatial Networks,” Multimedia Systems, Vol. 15, No. 5, pp. 295–308, Oct. 2009.
[11] M. Safar and A. A. Saleh, “Pine Based RNN Queries in Road Networks,” Proc. of the 7th Edition of the Series of Brazilian Symposium on Geoinformatics, pp. 356–367, 2005.
[12] I. Stanoi, D. Agrawal, and A. Abbadi, “Reverse Nearest Neighbor Queries for Dynamic Databases,” ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery, pp. 44–53, 2000.
[13] H. L. Sun, C. Jiang, J. L. Liu, and L. Sun, “Continuous Reverse Nearest Neighbor Queries on Moving Objects in Road Networks,” Proc. of the 9th Int. Conf. on Web-Age Information Management, pp. 238–245, 2008.
[14] D. Taniar, M. Safar, Q. T. Tran, W. Rahayu, and J. H. Park, “Spatial Network RNN Queries in GIS,” The Computer Journal, Vol. 54, No. 4, pp. 617–627, Sept. 2011.
[15] Y. Tao, D. Papadias, and X. Lian, “Reverse kNN Search in Arbitrary Dimensionality,” Proc. of the 13th Int. Conf. on Very Large Data Bases, Vol. 30, pp. 744–755, 2004.
[16] Y. Tao, M. L. Yiu, and N. Mamoulis, “Reverse Nearest Neighbor Search in Metric Spaces,” IEEE Transactions on Knowledge and Data Engineering, Vol. 18, No. 9, pp. 1239–1252, Sept. 2006.
[17] Q. T. Tran, D. Taniar, and M. Safar, “Bichromatic Reverse Nearest-Neighbor Search in Mobile Systems,” Systems Journal, Vol. 4, No. 2, pp. 230–242, June 2010.
[18] T. Wan, K. Zeitouni, and X. Meng, “An Olap System for Network-Constrained Moving Objects,” Proc. of the 2007 ACM Symposium on Applied Computing, pp. 13–18, 2007.
[19] W. Wu, F. Yang, C. Y. Chan, and K. L. Tan, “Continuous Reverse k-Nearest-Neighbor Monitoring,” Proc. of the 9th Int. Conf. on Mobile Data Management, pp. 132–139, 2008.
[20] T. Xia and D. Zhang, “Continuous Reverse Nearest Neighbor Monitoring,” Proc. of the 22nd Int. Conf. on Data Engineering, pp. 77–77, 2006.
[21] C. Yang and K. Lin, “An Index Structure for Efficient Reverse Nearest Neighbor Queries,” Proc. 17th Int. Conf. on Data Engineering, pp. 485–492, 2001.
[22] M. L. Yiu, D. Papadias, N. Mamoulis, and Y. Tao, ”Reverse Nearest Neighbors in Large Graphs,” IEEE Transactions on Knowledge and Data Engineering, Vol. 18, No. 4, pp. 540–553, April 2006.