Abstract
We present a practical implementation of the first adaptive data structure for orthogonal range queries in 2D [Arroyuelo et al., ISAAC 2009]. The structure is static, requires only linear space for its representation, and can even be made implicit. The running time for a query is \(O(\lg k\lg n + \min(k,m)\lg n + m)\), where k is the number of non-crossing monotonic chains in which we can partition the set of points, and m is the size of the output. The space consumption of our implementation is 2n + o(n) words. The experimental results show that this structure is competitive with the state of the art. We also present an alternative construction algorithm for our structure, which in practice outperforms the original proposal by orders of magnitude.
This work was supported in part by NSERC Canada, the Canada Research Chairs Programme, the Go-Bell and David R. Cheriton Scholarships Program, and an Ontario Graduate Scholarship.
An Erratum for this chapter can be found at http://dx.doi.org/10.1007/978-3-642-16321-0_42
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cgal, Computational Geometry Algorithms Library, http://www.cgal.org
Arroyuelo, D., Claude, F., Dorrigiv, R., Durocher, S., He, M., López-Ortiz, A., Munro, J.I., Nicholson, P.K., Salinger, A., Skala, M.: Untangled monotonic chains and adaptive range search, http://www.recoded.cl/docs/untangling.pdf
Arroyuelo, D., Claude, F., Dorrigiv, R., Durocher, S., He, M., López-Ortiz, A., Munro, J.I., Nicholson, P.K., Salinger, A., Skala, M.: Untangled monotonic chains and adaptive range search. In: 20th International Symposium on Algorithms and Computation (ISAAC), pp. 203–212 (2009)
Bar Yehuda, R., Fogel, S.: Partitioning a sequence into few monotone subsequences. Acta Informatica 35(5), 421–440 (1998)
Barbay, J., López-Ortiz, A., Lu, T., Salinger, A.: An experimental investigation of set intersection algorithms for text searching. J. Exp. Algorithmics 14 ,3.7–3.24 (2009)
Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975)
Chazelle, B., Guibas, L.J.: Fractional Cascading: I. A Data Structuring Technique. Algorithmica 1(2), 133–162 (1986)
Di Stefano, G., Krause, S., Lübbecke, M.E., Zimmermann, U.T.: On minimum k-modal partitions of permutations. Journal of Discrete Algorithms 6(3), 381–392 (2008)
van Emde Boas, P.: Preserving order in a forest in less than logarithmic time. In: 16th Annual Symposium on Foundations of Computer Science (FOCS), pp. 75–84 (1975)
Fomin, F.V., Kratsch, D., Novelli, J.C.: Approximating minimum cocolorings. Information Processing Letters 84(5), 285–290 (2002)
Guttman, A.: R-trees: a dynamic index structure for spatial searching. In: 1984 ACM SIGMOD international conference on Management of data (SIGMOD), pp. 47–57. ACM, New York (1984)
Kanth, K.V.R., Singh, A.K.: Optimal dynamic range searching in non-replicating index structures. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 257–276. Springer, Heidelberg (1998)
Lueker, G.S.: A data structure for orthogonal range queries. In: 19th Annual Symposium on Foundations of Computer Science (SFCS), pp. 28–34. IEEE Computer Society, Washington (1978)
Supowit, K.J.: Decomposing a set of points into chains, with applications to permutation and circle graphs. Information Processing Letters 21(5), 249–252 (1985)
Yang, B., Chen, J., Lu, E., Zheng, S.: Design and Performance Evaluation of Sequence Partition Algorithms. Journal of Computer Science and Technology 23(5), 711–718 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Claude, F., Munro, J.I., Nicholson, P.K. (2010). Range Queries over Untangled Chains. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-16321-0_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16320-3
Online ISBN: 978-3-642-16321-0
eBook Packages: Computer ScienceComputer Science (R0)