Abstract
We consider variations of the standard orthogonal range searching motivated by applications in database querying and VLSI layout processing. In a generic instance of such a problem, called a range-aggregate query problem we wish to preprocess a set S of geometric objects such that given a query orthogonal range q, a certain intersection or proximity query on the objects of S intersected by q can be answered efficiently. Efficient solutions are provided for point enclosure queries, 1-d interval intersection, 2-d orthogonal segment intersection and 1- and 2-d closest pair problems in this framework. Although range-aggregate queries have been widely investigated in the past for aggregation functions like average, count, min, max, sum etc. we consider geometric aggregation operations in this paper.
This research is supported in part by grants SR/S3/EECE/22/2004 and DST/INT/US/NSF-RPO-0155/04 from the Department of Science and Technology, Government of India.
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References
Agarwal, P.K., Erickson, J.: Geometric range searching and its relatives. In: Chazelle, B., Goodman, J.E., Pollack, R. (eds.) Advances in Discrete and Computational Geometry. Contemporary Mathematics, vol. 23, pp. 1–56. American Mathematical Society Press, Providence (1999)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications. Springer, Heidelberg (2000)
Balaban, I.J.: An optimal algorithm for finding segment intersections. In: Proceedings, 11th Annual ACM Symposium on Computational Geometry, pp. 211–219 (1995)
Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proceedings, ACM Symposium on Theory of Computing, pp. 135–142 (1984)
Govindarajan, S., Agarwal, P.K., Arge, L.: CRB-Tree: An efficient indexing scheme for Range Aggregate Queries. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds.) ICDT 2003. LNCS, vol. 2572, pp. 143–157. Springer, Heidelberg (2002)
Gray, J., Chaudhuri, S., Bosworth, A., Layman, A., Recichart, D., VenkatRao, M., Pellow, F., Pirahesh, H.: Data Cube: A relational aggregation operator generalizing Group-By, Cross-Tab, and Sub-Totals. Data Mining and Knowledge Discovery 1(1), 29–53 (1997)
Hong, S., Song, B., Lee, S.: Efficient execution of range-aggregate queries in data warehouse environments. In: Kunii, H.S., Jajodia, S., Sølvberg, A. (eds.) ER 2001. LNCS, vol. 2224, pp. 299–310. Springer, Heidelberg (2001)
Jampani, R., Thonangi, R., Gupta, P.: Overlaying multiple maps efficiently. In: Das, G., Gulati, V.P. (eds.) CIT 2004. LNCS, vol. 3356, pp. 263–272. Springer, Heidelberg (2004)
Mead, C.A., Conway, L.A.: Introduction to VLSI Systems. Addison Wesley, USA (1980)
McCreight, E.M.: Priority search trees. SIAM Journal of Computing 14(2), 257–276 (1985)
Shan, J., Zhang, D., Salzberg, B.: On spatial-range closest-pair query. In: Hadzilacos, T., Manolopoulos, Y., Roddick, J., Theodoridis, Y. (eds.) SSTD 2003. LNCS, vol. 2750, pp. 252–269. Springer, Heidelberg (2003)
Shekhar, S., Chawla, S.: Spatial Databases: A Tour. Prentice Hall, Englewood Cliffs (2002)
Sherwani, N.: Algorithms for VLSI Physical Design Automation. Kluwer Academic, Dordrecht (1998)
Smid, M.: Closest point problems in computational geometry. In: Sack, J., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 877–935. Elsevier, Amsterdam (2000)
Szymanski, T.G., van Wyk, C.J.: Layout analysis and verification. In: Preas, B., Lorenzetti, M. (eds.) Physical Design Automation of VLSI Systems, pp. 347–407. Benjamin/Cummins (1988)
Tao, Y., Papadias, D.: Range aggregate processing in spatial databases. IEEE Transactions on Knowledge and Data Engineering 16(12), 1555–1570 (2004)
Zhang, D., Tsotras, V.J.: Improving min/max aggregation over spatial objects. VLDB Journal 14(2), 170–181 (2005)
Zhang, D., Markowetz, A., Tsotras, V., Gunopulos, D., Seeger, B.: Efficient computation of temporal aggregates with range restrictions. In: Proceedings, Symposium on Principles of Database Systems (2001)
Zhang, D., Tsotras, V.J., Gunopulos, D.: Efficient aggregation over objects with extent. In: Proceedings, Symposium on Principles of Database Systems, pp. 121–132 (2002)
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Gupta, P. (2005). Algorithms for Range-Aggregate Query Problems Involving Geometric Aggregation Operations. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_89
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DOI: https://doi.org/10.1007/11602613_89
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