Abstract
Data collected from real world are often imprecise. A few algorithms were proposed recently to compute the convex hull of maximum area when the axis-aligned squares model is used to represent imprecise input data. If squares are non-overlapping and of different sizes, the time complexity of the best known algorithm is O(n 7). If squares are allowed to overlap but have the same size, the time complexity of the best known algorithm is O(n 5). In this paper, we improve both bounds by a quadratic factor, i.e., to O(n 5) and O(n 3), respectively.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beresford, A.R., Stajano, F.: Location Privacy in Pervasive Computing. IEEE Pervasive Computing 2(1), 46–55 (2003)
Akl, S.G., Toussaint, G.T.: Efficient convex hull algorithms for pattern recognition applications. In: Int. Joint Conf. on Pattern Recognition, pp. 483–487 (1978)
Bhattacharya, B.K., El-Gindy, H.: A new linear convex hull algorithm for simple polygons. IEEE Trans. Inform. Theory 30, 85–88 (1984)
Bőhm, C., Kriegel, H.: Determining the convex hull in large multidimensional databases. In: Kambayashi, Y., Winiwarter, W., Arikawa, M. (eds.) DaWaK 2001. LNCS, vol. 2114, pp. 298–306. Springer, Heidelberg (2001)
Taubman, D.: High Performance Scalable Image Compression. IEEE Transactions on Image Processing 9, 1158–1170 (2000)
Freeman, H., Shapira, R.: Determining the minimum-area encasing rectangle for an arbitrary closed curve. Communications of the ACM 18(7), 409–413 (1975)
Graham, R.L.: An efficient algorithm for determining the convex hull of a finite planar set. Information Processing Letters 26, 132–133 (1972)
Graham, R.L., Yao, F.F.: Finding the convex hull of a simple polygon. J. Algorithms 4, 324–331 (1984)
Lee, D.T.: On finding the convex huff of a simple polygon. Internat. J. Comput. Inform. Sci. 12, 87–98 (1983)
Löffler, M., van Kreveld, M.: Largest and Smallest Convex Hulls for Imprecise Points. Algorithmica 56(2), 235–269 (2010)
Melkman, A.: On-Line Construction of the Convex Hull of a Simple Polyline. Information Processing Letters 25, 11–12 (1987)
Pfoser, D., Jensen, C.S.: Capturing the uncertainty of moving-objects representations. In: Proceedings of the 6th International Symposium on Advances in Spatial Databases, pp. 111–132 (1999)
Cheng, R., Kalashnikov, D.V., Prabhakar, S.: Querying Imprecise Data in Moving Object. IEEE Transactions on Environments, Knowledge and Data Engineering 16(9), 1112–1127 (2004)
Sistla, P.A., Wolfson, O., Chamberlain, S., Dao, S.: Querying the uncertain position of moving objects. In: Etzion, O., Jajodia, S., Sripada, S. (eds.) Dagstuhl Seminar 1997. LNCS, vol. 1399, pp. 310–337. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Daescu, O., Ju, W., Luo, J., Zhu, B. (2011). Largest Area Convex Hull of Axis-Aligned Squares Based on Imprecise Data. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-22685-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22684-7
Online ISBN: 978-3-642-22685-4
eBook Packages: Computer ScienceComputer Science (R0)