2005 Journal of Software (, ) A Spatial Index to Improve the Response Speed of WebGIS Servers

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1 /2005/16(05) Journal of Software Vol.16, No.5 WebGIS +,, (, ) A Spatial Index to Improve the Response Speed of WebGIS Servers YE Chang-Chun +, LUO Jin-Ping, ZHOU Xing-Ming (Institute of Computer Science and Technology, National University of Defense Technology, Changsha , China) + Corresponding author: Phn: , iamdouble@163.com, Received ; Accepted Ye CC, Luo JP, Zhou XM. A spatial index to improve the response speed of WebGIS servers. Journal of Software, 2005,16(5): DOI: /jos Abstract: WebGIS servers send digital maps to users. For each request-response round, the servers access map data in batches. The access has a feature called multiscale, that is, the map scales selected by users determine the map detail levels. The access method based on R-tree is not adaptive to the multiscale and batch feature. It has two problems: (1) the data records of features of the same level are not clustered in disks; (2) the granularity of data I/O is too small. So accessing map data for display is unefficient. This paper presents a novel spatial index called Multilevel R-tree, which can solve the two problems. The statistics from experiments show that for range queries, the access method based on multilevel R-tree is much more efficient than the one based on R-tree and can improve the response speed of WebGIS Servers. Key words: WebGIS service; spatial database; access method; spatial index; multilevel R-tree : WebGIS. /,.. R-tree, I/O,. R-tree.,, R-tree R-tree. R-tree WebGIS. : WebGIS ; ; ; ; R-tree : TP391 : A, WebGIS, Internet Web.WebGIS,,.,. /, WebGIS. : (1974 ),,,,, ; (1970 ),,,,,GIS ; (1938 ),,,,,,,.

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3 : WebGIS 821. (MBR,ptr),ptr ;MBR MBR.R-tree [1 4]..,.,,.,.,. m, m.. : m. (next,d,root),next,root d. Reactive R-tree [5,6].. ( m ) ; 2 m 1, 1.Reactive R-tree.m 1 1 ( m ).,.,..Reactive R-tree : ;,. [7]., ( ),. [8] 3D R-tree... f [ls,hs], s,. [ls,hs] f.,. 2 R-tree GIS. m. k (k=1,2,,m) k ; k k. 2.1 R-tree R-tree. n,, 1,2,,n. 1 m=3,n=4 R-tree.,N i (i=1,2,,7).r.,,.,n 1,N 2,N 4 ( ), ( ). R-tree m m (, m<n),. n m,. n i(i=1,2,,m 1) N 1 r r 1 2. ( N 2 N3 ),. m i r r r 3 4, m i. n m r N 1,. 4 N 5 r r r ( M). 7 8 r. R-tree, N 6 N 7., ( ) r r r r r r r r ; ( ) Fig.1 Multilevel R-tree 1 R-tree.,

4 822 Journal of Software 2005,16(5). MBR, C/M.,C..,. R-tree.,. R-tree, R-tree.. R-tree Reactive R-tree. :(1),.(2). R-tree,,,. 2.2 R-tree.. Q(w,s), I/O., I/O,., ( ): (1) nclusterminsize; (2) nclustermaxsize. (1).., I/O nclusterbestsize,, nclusterminsize<nclusterbestsize< nclustermaxsize. R-tree. nclustermaxsize ; nclusterminsize.,..,, ( ), I/O.,.,, I/O, I/O. [9],,. I/O. 3 R-tree R-tree R-tree.,R-tree. R-tree R-tree. Hilbert R-tree (multi-level Hilbert R-tree, MLHR).MLHR Hilbert R-tree [1,3], R-tree. C MLHR...,,., ;. Hilbert. Hilbert [1], MBR Hilbert Hilbert. MBR Hilbert Hilbert. LHV(largest Hilbert value).,,

5 : WebGIS 823 Hilbert LHV [1]., LHV LHV. 3.1 NewIndRec, nlevel. nlevel. InsertedLayerLeafSet(, ); InsertedLayerIntlNodeSet; nlevel HigherLeafSet; HigherIntlNodeSet Insert(NewIndRec,nLevel) :NewIndRec ;nlevel. : 1. [ ] nlevel., (4); 2. [ ] InsertedLayerLeafSet LHV, 1 LHV Hilbert. LHV Hilbert,. InsertedLeaf. 3. [ ] InsertedLeaf NewIndRec(, ),. if ( ){ if ( InsertedLeaf ){, nincrentrynum( ) ; } ; MBR LHV ; }else{ ( HigherIntlNodeSet ); InsertedLayerLeafSet NewIndRec IndRecSet; HandleOverflow(IndRecSet,InsertedLayerIntlNodeSet,HigherLeafSet) ; } 4. [ ] Leaf, ninitialentrynum( ), NewIndRec 1. Leaf InsertedLayerLeafSet. 5. [ ] nlevel InsertedLayerIntlNodeSet. InsertedLayerIntlNodeSet InsertedLayer LeafSet,, FartherSet.FartherSet N/M,.,N,M. 6. [ ] GrowUp(nLevel,FartherSet,HigherLeafSet) HandleOverflow(IndRecSet,InsertedLayerIntlNodeSet,HigherLeafSet) :IndRecSet. InsertedLayerLeafSet.InsertedLayerIntlNodeSet.HigherLeafSet

6 824 Journal of Software 2005,16(5). :, Root. : 1. IndRecSet Hilbert,, 1 nclusterbestsize,. NewLeafSet. 2. InsertedLayerIntlNodeSet NewLeafSet,, FartherSet.FartherSet N/M,.,N,M. 3. GrowUp(nLevel,FartherSet,HigherLeafSet) , I/O nclusterbestsize GrowUp(nLevel,IntlNodeSet,LeafSet) :nlevel.intlnodeset,., nlevel.leafset nlevel,. :, Root. : 5. LeafSet, IntlNodeSet NodeSet. 6. NodeSet, Hilbert, IndRecSet. 7. N IndRecSet, N/M, IntlNodeSet. 8. LeafSet, LeafSet (,LeafSet.) IntlNodeSet 1 ( Root), ; NodeSet = IntlNodeSet, ,. nclusterminsize.,,..,. 3.3 Q(w,s), R-tree :, ; ( ) I/O I/O., I/O I/O, I/O,..,,.,,.

7 : WebGIS Hilbert R-tree,Reactive R-tree Hilbert R-tree (MLHR). :, 3, 3, Mb, ,CPU 1.7G, 256M.,3. 1 I/O... I/O. Table 1 Average time used and statistics of disk I/O 1 I/O Access methods Total time used Time used by searches Time used by data Average granularity of Counts of by queries (ms) in the index (ms) I/O (ms) data I/O (bytes) data I/O Hilbert R-tree Reactive R-tree MLHR : MLHR. I/O. I/O., Queries/s I/O. MLHR,WebGIS I/O. I/O ( ) I/O Hilbert R-tree Reactive R-tree MLHR. I/O., Hilbert R-tree Fig.2 Query throughput 2 I/O,. Table 2 Time used by data I/O (ms) 2 I/O (ms) Access methods Maximal time used by Time used by accessing the each query whole map Hilbert R-tree Reactive R-tree MLHR WebGIS, ( ). ( ), R-tree., R-tree.,.,.,, R-tree.,,

8 826 Journal of Software 2005,16(5). 4.2 WebGIS, Q(w,s)., Hilbert R-tree Hilbert R-tree Reactive R-tree,. :(1) I/O, I/O,.(2),,.,, R-tree 100%., Hilbert R-tree Hilbert R-tree [3]. R-tree :(1).,.(2).,.,,. 5 /,WebGIS. R-tree I/O. R-tree,.. R-tree.WebGIS,. References: [1] Kamel I, Faloutsos C. Hilbert R-tree: An improved R-tree using fractals. In: Bocca JB, Jarke M, Zaniolo C, eds. Proc. of the 20th Int l Conf. of VLDB. Santiago: Morgan Kaufmann Publishers, [2] Guttman A. R-trees: A dynamic index structure for spatial searching. In: Yormark B, ed. Proc. of the Int l Conf. on Management of Data. Massachusetts: ACM Press, [3] Kamel I, Faloutsos C. On packing R-trees. In: Bhargava B, Finin T, Yesha Y, eds. Proc. of the 2nd Int l Conf. on Information and Knowledge Management. Washington, DC: ACM Press, [4] Beckmann N, Kriegel HP, Schneider R, Seeger B. The r*-tree: An efficient and robust access method for points and rectangles. ACM SIGMOD Record, 1990,19(2): [5] Oosterom PV. Reactive data structure for geographical information system [Ph.D. Thesis]. Leiden: University of Leiden, [6] Edward PFC, Kevin KWC. On multi scale display of geometric objects. Data and Knowledge Engineering, 2002,40(1): [7] Hörhammer M, Freeston M. Spatial indexing with a scale dimension. In: Güting RH, Papadias D, Lochovsky FH, eds. Proc. of the 6th Int l Symp. on Advances in Spatial Databases. Hong Kong: Springer-Verlag, [8] Zhou S, Christopher BJ. Design and implementation of multi-scale databases. In: Jensen CS, Schneider M, Seeger B, Tsotras VJ, eds. Proc. of the 7th Int l Symp. on Advances in Spatial and Temporal Databases. London: Springer-Verlag, [9] Ye CC, Zhou XM. A method for organizing map dataset to support multi-scale. Chinese Journal of Computers, 2004,27(7): (in Chinese with English abstract). : [9],..,2004,27(7):