Abstract
Relaxation and approximation techniques have been proposed as approaches for improving the quality of query results, in terms of completeness and accuracy, in environments where the user may not be able to specify the query in a complete and exact way, since data are quite heterogeneous or she may not know all the characteristics of data at hand. This problem, mainly addressed for relational and XML data, is nowadays quite relevant also for geo-spatial data, due to their increasing usage in highly critical decisional processes. Among geo-spatial queries, those based on spatial and more precisely topological relations are currently used in an increasing number of applications. As far as we know, no approach has been proposed so far for relaxing queries based on topological predicates when they return an empty or insufficient answer, in order to improve result quality and user satisfaction. In this paper, we consider this problem and we present a general relaxation strategy for, possibly multi-domain, topological selection and join queries. Two specific semantics are also provided: the first applies the minimum amount of relaxation in order to get an acceptable answer; the second relaxes the given query of a certain fixed amount, depending on the considered topological predicate. Index-based processing algorithms, for efficiently executing relaxed queries based on the proposed semantics, are also presented and a specific topological similarity function, to be used for relaxation purposes, is proposed. Experimental results show that the overhead given by query relaxation is acceptable.
Similar content being viewed by others
Notes
See Table 1 for the exact meaning of topological relations.
PG Lig stands for the polygon representing Liguria—see Fig. 1.
We assume that the feature type Pr (Province) has a property called region representing the administrative region a province belongs to.
As we will see later, there is no need to define compatibility rules for entries of different types since the algorithms we are going to present only compute topological similarity intervals between entries of the same type.
PG Lig stands for the polygon representing Liguria—see Fig. 1.
Notice that, when taking as input the objects corresponding to the MBRs, INR can be interpreted as a sort of relaxed evaluation.
For join, we obtained even better results, since computing join using sequential scans is very inefficient; thus, for space constraints, we have not reported these results in this paper.
We exclude also touch since its relaxation with v no_dj = 0.5 includes disjoint.
We consider in instead of equal, differently from what has been done for selection, since equal in this case is a too strong selective relation, thus it is not suitable to highlight the differences between the proposed techniques.
References
Beckmann N et al (1990) The R*-Tree: an efficient and robust access method for points and rectangles. In: Proc. of SIGMOD, pp 322–331
Belussi A et al (2006) Towards similarity-based topological query languages. In: LNCS 4254: Proc. of EDBT workshops, pp 675–686
Belussi A, Brovelli MA, Negri M, Pelagatti G, Sansò F (2006) Dealing with multiple accuracy levels in spatial databases with continuous update. In: Proc. of the 7th int. symp. on spatial accuracy assessment in natural resources and environmental sciences, pp 203–212
Belussi A, Catania B, Podestà P (2007) Using qualitative information in query processing over multiresolution maps. In: Spatial data on the Web: modeling and management. Springer, Berlin, pp 159–186
Belussi A, Catania B, Podestà P (2009) Relaxing topological selection operators: an index-based approach. In: Proc. of the Italian symp. SEBD, pp 185–196
Belussi A, Catania B, Podestà P (2009) Towards relaxed topological operators. Technical report, University of Genoa, Italy
Beyer KS, Golstein J, Ramakrishnan R, Shaft U (1999) When is “nearest neighbor” meaningful? In: LNCS 1540: Proc. of EDBT, pp 217–235
Börzsönyi S, Kossmann D, Stocker K (2001) The skyline operator. In: Proc of ICDE, pp 421–430
Clementini E, di Felice P, van Oosterom P (1993) A small set of formal topological relationships suitable for end-user interaction. In: LNCS 692: Proc. of SSD, pp 277–295
Corral A, Manolopoulos Y, Theodoridis Y, Vassilakopoulos M (2000) Closest pair queries in spatial databases. In: Proc. of SIGMOD, pp 189–200
Egenhofer MJ, Franzosa RD (1995) On the equivalence of topological relations. Int J Geogr Inf Syst 9(2):133–152
Guo X, Ishikawa Y, Gao Y (2010) Direction-based spatial skylines. In: MobiDE, pp 73–80
Guttman A (1984) R-trees: a dynamic index structure for spatial searching. In: Proc. of SIGMOD, pp 47–57
Hjaltason GR, Samet H (1999) Distance browsing in spatial databases. ACM Trans Database Syst 24(2):256–318
Hsueh Y-L, Zimmermann R, Yang MH (2005) Approximate continuous k nearest neighbor queries for continuous moving objects with pre-defined paths. In: Proc. of ER workshops, pp 270–279
Kadlag A, Wanjari AV, Freire J, Haritsa JR (2004) Supporting exploratory queries in databases. In: Proc. of DASFAA, pp 594–605
Koudas N, Srivastava D (2005) Approximate joins: concepts and techniques. In: VLDB tutorial
Koudas N, Li C, Tung AKH, Vernica R (2006) Relaxing join and selection queries. In: Proc. of VLDB, pp 199–210
Ilyas IF, Beskales G, Soliman MA (2008) A survey of top-k query processing techniques in relational database systems. ACM Comput Surv 40(4):11:1–11
Jacox EH, Samet H (2007) Spatial join techniques. ACM Trans Database Syst 33(1):7:1–7
Jhingran A (2006) Enterprise information mash-ups: integrating information, simply. In: Proc. of VLDB, pp 3–4
Lee D (2002) Query relaxation for XML model. PhD thesis, University of California
Li L, Wang H, Li J, Gao H (2009) Efficient algorithms for skyline top-k keyword queries on XML streams. In: Proc. of DASFAA, pp 283–287
Mishra C, Koudas N (2009) Interactive query refinement. In: Proc. of EDBT, pp 862–873
OGC (2010) OpenGIS implementation spec. for geographic information—simple features access—part 1: common architecture. OGC Inc
Papadias D et al (1995) Topological relations in the world of minimum bounding rectangles: a study with R-Trees. SIGMOD Rec 24(2):92–103
Papadias D, Arkoumanis D (2002) Approximate processing of multiway spatial joins in very large databases. In: Proc. of EDBT, pp 179–196
Papadias D, Tao Y, Fu G, Seeger B (2005) Progressive skyline computation in data-base systems. ACM Trans Database Syst 30(1):41–82
Rigaux P, Scholl M, Voisard A (2002) Spatial databases: with application to GIS. Morgan Kaufmann, San Francisco
Roussopoulos N, Kelley S, Vincent F (1995) Nearest neighbor queries. In: Proc. of SIGMOD, pp 71–79
Shan J, Zhang D, Salzberg B (2003) On spatial-range closest-pair query. In: Proc. of SSTD, pp 252–269
Sharifzadeh M, Shahabi C (2006) The spatial skyline queries. In: Proc. of VLDB, pp 751–762
Sharifzadeh E, Shahabi C, Kazemi L (2009) Processing spatial skyline queries in both vector spaces and spatial network databases. ACM Trans Database Syst 34(3):14:1–14
Son W, Lee M-W, Ahn HK, Hwang S-W (2009) Spatial skyline queries: an efficient geometric algorithm. In: Proc. of SSTD, pp 247–264
Tian Y, Lee KCK, Lee W-C (2009) Finding skyline paths in road networks. In: Proc. of ACM GIS, pp 444–447
Xia T et al (2005) On computing top-t most influential spatial sites. In: Proc. of VLDB, pp 946–957
Yiu ML et al (2007) Top-k spatial preference queries. In: Proc. of ICDE, pp 1076–1085
Zhou X, Gaugaz J, Balke W-T, Nejdl W (2007) Query relaxation using malleable schemas. In: Proc. of SIGMOD, pp 545–556
Zhu M et al (2005) Top-k spatial joins. IEEE Trans Knowl Data Eng 17(4):567–579
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix A: An example of topological similarity function
Appendix B: Compatibility tables
Table 7 summarizes selection compatibility rules for leaf and intermediate entries, for objects of any dimension. The first column of the table contains the relation θ satisfied by e a .r and O.r; the second column points out the dimension of O.r, since both c() and co() may change when MBRs degenerates to points (in very particular cases, MBR can also degenerate to a vertical or horizontal line; for sake of readability we did not report these cases in the tables); the fourth and the fifth columns contain c(θ, dim(ft), dim(O)) and co(θ, dim(ft), dim(O)), respectively, for any pair of object dimension (dim(ft), dim(O)), pointed out in the third column.
Compatibility rules for join operator are shown in Table 8. With respect to Table 7, the second column points out the dimension of (d(e a .r), d(e b .r)), since both ci() and co() may change when MBRs degenerates to points.
For sake of readability in table heading we replace dim() with d(). The notation\({\cal T}_{x,y}\) has been introduced in Section 3. Empty compatibility sets always correspond tosituations in which MBRs of non object entries degenerate to points or point objectsare compared.
Appendix C: Query processing algorithm for relaxed selection operator based on BF semantics
Rights and permissions
About this article
Cite this article
Belussi, A., Catania, B. & Podestà, P. Topological operators: a relaxed query processing approach. Geoinformatica 16, 67–110 (2012). https://doi.org/10.1007/s10707-011-0124-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10707-011-0124-9