ER-Tree (Extended R*-Tree)

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1 1-9825/22/13(4) Journal of Software Vol13, No4 1, 1, 2, 1 1, 1 (, 2327) 2 (, 3127) xhzhou@ustceducn,,,,,,, 1, TP311 A,,,, Elias s Rivest,Cleary Arya Mount [1] O(2 d ) Arya Mount [1] Friedman,Bentley Finkel,, ( ) grid file [2] [2], [3],, 1,, 1 (Extended ),,, (69535) (994332) (1966 ),,,,,, (1963 ),,,,, (1974 ),,, (1943 ),,,, (1937 ),,,,

2 769,,,,,,, ,, Fig1 Feature space partition and structure M, m, (1) (2) m M (3), m M (4), (5), 12 M, m (1) M, (2) m, 112 C struct ERNODE { } int nhighlevel union{ } unextnode //, struct ERNODE*ptrChildNode[_MAX_INTERNAL_CAPACITY] FEATURE_DATA*ptrData[_MAX_LEAF_CAPACITY] int nnodecapacity int npointnum float fradius float fcentroid[_dimention] // // // // nhighlevel unextnode,, nnodecapacity fradius fcentroid

3 77 Journal of Software 22,13(4) 12,,,,,, [4,5],,,, (1), (2),,, (2), (3),,, 121, 1, 2, nhighlevel 1,,,,,,, 3, nhighlevel>1,,,,,, 122,,,,,, (1),,,, group1,group2 (2), 3,, M m 1,, (3), 2, M m 1,,, 13 SUN SPARCII(32M ) Sunos412 2D,3D,4D,5D,6D,7D,8D,9D,1D 5 2D,3D,4D,5D,6D,7D,8D,9D,1D 5, 131 2(a)~ 2(d) 5, M=3,, ( ),,,

4 771 1,,,,,,,, (a) Time of creation and (uniform distribution) (a) ( ) (c) Time of creation and (gaussian distribution) (c) ER-TREE R-TREE ( ) (b) Time of creation and (uniform distribution) (b) ( ) E (d) Time of creation and (gaussian distribution) (d) ( ) 132 K- Fig2 2, 3 (K-NN ), (PRK-NN), [5], 3 (1) K- 3(a)~ 3(f) M=3, 1- ( ),,,, K-NN K-NN (2) 1 1,ε Exact K-NN ( ),LeafNum ( ), 1, 2~3%

5 772 Journal of Software 22,13(4) Node Node Dimesion (a) Performance of K-NN retrieval on and (uniform distribution) (a) K-NN (c) Performance of PRK-NN retrieval on and (uniform distribution) (c) PRK-NN (e) Performance of K-NN retrieval on and (gaussian distribution) (e) K-NN Node (b) Performance of K-NN retrieval on and 5 Fig3 3 (uniform distribution) (b) K-NN (d) Performance of K-NN retrieval on and (gaussian distribution) (d) K-NN Table 1 Performance of approximate retrieval Dimesion (f) Performance of PRK-NN retrieval on and (gaussian distribution) (f) PRK-NN 1 Dimesion Uniform distribution Gaussion distribution Exact LeafNum ε Exact LeafNum ε ,,,

6 773 K-,,,,,,,, 1,,,, References [1] Sunil, A Nearest neighbor searching and applications [PhD Thesis] Computer Vision Laboratory, Center for Automation Research, University of Maryland, College Park, MD , 1995 [2] Hanan, S The Design and Analysis of Spatial Data Structures New York Addison-Wesley Publishing Company, Inc, 1989 [3] Beckmann, N, Kriegel, H-P, Schneider, R, et al The R*-tree an efficient and robust access method for points and rectangles In Clifford, J, King, R, eds Proceedings of the ACM SIGMOD International Conference on the Management of Data Denver, Colorado ACM Press, ~331 [4] Gong, Yu-chang, Wang, Wei-hong e-b+-tree an indexing organization optimized for DBMS supporting multi-users Journal of Software, 1996,7(5)314~32 (in Chinese) [5] Zhou, Xue-hai Research on image database system with content-based retrieval [PhD Thesis] Hefei University of Science and Technology of China, 1997 (in Chinese) [4], e-b+,1996,7(5)314~32 [5] [ ],1997 Research on Dynamic Indexing Structure for Multi-al Vectors ZHOU Xue-hai 1, LI Xi 1, XU Hai-yan 2, GONG Yu-chang 1, ZHAO Zhen-xi 1 1 (Department of Computer Science and Technology, University of Science and Technology of China, Hefei 2327,China) 2 (Department of Computer Science and Engineering, Zhejiang University, Hangzhou 3127, China) xhzhou@ustceducn Abstract Multi-al vectors indexing is one of the key technologies in multimedia database systems This paper focuses on the dynamic indexing structure based on the vector space An indexing structure is proposed which is efficient for medium and high dimensional vectors In the, the efficiency of retrieval could be improved by the ways of partition of the vector space with hyper-sphere and s re-insert technology introduced to enhance s capability to represent the data-sets features By introducing safe-inserted-node and safe-deleted-node concept into the structure, the performance of tree creation is reenforced The algorithms are also given for the creation of The empirical test results show that (1) the tree creation algorithm proposed is about 1 times faster than (2) the effectiveness of retrieval is highly improved Key words dynamic indexing structure similarity retrieval Received March 21, 2 accepted February 16, 21 Supported by the National Natural Science Foundation of China under Grant No69535 the Natural Science Foundation of Anhui Province of China under Grant No994332

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