Abstract
We present a linear-space data structure that maintains a dynamic set of n points with coordinates of real numbers on the plane to support orthogonal range counting, as well as insertions and deletions, in \(O((\frac{\lg n}{\lg\lg n})^2)\) time. This provides faster support for updates than previous results with the same bounds on space cost and query time. We also obtain two other new results by considering the same problem for points on a U×U grid, and by designing the first succinct data structures for a dynamic integer sequence to support range counting.
This work was supported by NSERC and the Canada Research Chairs program.
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
Arge, L., Vitter, J.S.: Optimal external memory interval management. SIAM J. Comput. 32(6), 1488–1508 (2003)
Bentley, J.L.: Multidimensional divide-and-conquer. Commun. ACM 23(4), 214–229 (1980)
Bose, P., He, M., Maheshwari, A., Morin, P.: Succinct orthogonal range search structures on a grid with applications to text indexing. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 98–109. Springer, Heidelberg (2009)
Chazelle, B.: A functional approach to data structures and its use in multidimensional searching. SIAM Journal on Computing 17(3), 427–462 (1988)
Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Compressing and indexing labeled trees, with applications. Journal of the ACM 57(1) (2009)
Ferragina, P., Manzini, G., Mäkinen, V., Navarro, G.: Compressed representations of sequences and full-text indexes. ACM Transactions on Algorithms 3(2) (2007)
González, R., Navarro, G.: Rank/select on dynamic compressed sequences and applications. Theoretical Computer Science 410(43), 4414–4422 (2009)
He, M., Munro, J.I.: Succinct representations of dynamic strings. In: SPIRE, pp. 334–346 (2010)
He, M., Munro, J.I.: Succinct representations of dynamic strings. CoRR abs/1005.4652 (2010)
Jacobson, G.: Space-efficient static trees and graphs. In: FOCS, pp. 549–554 (1989)
JáJá, J., Mortensen, C.W., Shi, Q.: Space-efficient and fast algorithms for multidimensional dominance reporting and counting. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 558–568. Springer, Heidelberg (2004)
Nekrich, Y.: Orthogonal range searching in linear and almost-linear space. Computational Geometry: Theory and Applications 42(4), 342–351 (2009)
Pǎtraşcu, M.: Lower bounds for 2-dimensional range counting. In: STOC, pp. 40–46 (2007)
Raman, R., Raman, V., Rao, S.S.: Succinct dynamic data structures. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, pp. 426–437. Springer, Heidelberg (2001)
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
He, M., Munro, J.I. (2011). Space Efficient Data Structures for Dynamic Orthogonal Range Counting. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_42
Download citation
DOI: https://doi.org/10.1007/978-3-642-22300-6_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22299-3
Online ISBN: 978-3-642-22300-6
eBook Packages: Computer ScienceComputer Science (R0)