Abstract
Let \(w \in {\mathbb {N}}\) and \(U = \{0, 1, \dots , 2^w-1\}\) be a bounded universe of w-bit integers. We present a dynamic data structure for predecessor searching in U. Our structure needs \(O(\log \log \varDelta )\) time for queries and \(O(\log \log \varDelta )\) expected time for updates, where \(\varDelta \) is the difference between the query element and its nearest neighbor in the structure. Our data structure requires linear space. This improves a result by Bose et al. [CGTA, 46(2), pp. 181–189].
The structure can be applied for answering approximate nearest neighbor queries in low dimensions and for dominance queries on a grid.
Supported in part by DFG project MU/3501-1.
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.
Similar content being viewed by others
References
Belazzougui, D., Boldi, P., Vigna, S.: Dynamic Z-fast tries. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 159–172. Springer, Heidelberg (2010). doi:10.1007/978-3-642-16321-0_15
Belazzougui, D., Boldi, P., Vigna, S.: Predecessor search with distance-sensitive query time (2012). arXiv:1209.5441
Bose, P., Douïeb, K., Dujmovic, V., Howat, J., Morin, P.: Fast local searches and updates in bounded universes. Comput. Geom. Theory Appl. 46(2), 181–189 (2013)
Chan, T.M.: Closest-point problems simplified on the RAM. In: Proc. 13th Annu. ACM-SIAM Sympos. Discrete Algorithms (SODA), pp. 472–473 (2002)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms, 3rd edn. MIT Press (2009)
Demaine, E.D., Harmon, D., Iacono, J., Pǎtraşcu, M.: Dynamic optimality – almost. SIAM J. Comput. 37(1), 240–251 (2007)
Demaine, E.D., Heide, F.M., Pagh, R., Pǎtraşcu, M.: De dictionariis dynamicis pauco spatio utentibus. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 349–361. Springer, Heidelberg (2006). doi:10.1007/11682462_34
Ehrhardt, M.: An In-Depth Analysis of Data Structures Derived from van-Emde-Boas-Trees. Master’s thesis, Freie Universität Berlin (2015) http://www.mi.fu-berlin.de/inf/groups/ag-ti/theses/download/Ehrhardt15.pdf
van Emde Boas, P., Kaas, R., Zijlstra, E.: Design and implementation of an efficient priority queue. Math. Systems Theory 10(2), 99–127 (1976)
van Emde Boas, P.: Preserving order in a forest in less than logarithmic time and linear space. Inform. Process. Lett. 6(3), 80–82 (1977)
Har-Peled, S.: Geometric approximation algorithms, Mathematical Surveys and Monographs, vol. 173. American Mathematical Society (2011)
Knuth, D.E.: The art of computer programming. Sorting and searching, vol. 3, 2nd edn. Addison-Wesley (1998)
Overmars, M.H.: Efficient data structures for range searching on a grid. J. Algorithms 9(2), 254–275 (1988)
Preparata, F.P., Shamos, M.I.: Computational geometry. An introduction. Springer Verlag (1985)
Pǎtraşcu, M.: vEB space: Method 4 (2010). http://infoweekly.blogspot.de/2010/09/veb-space-method-4.html
Ružić, M.: Making deterministic signatures quickly. ACM Transactions on Algorithms 5(3), 26:1–26:26 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Ehrhardt, M., Mulzer, W. (2017). Delta-Fast Tries: Local Searches in Bounded Universes with Linear Space. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_31
Download citation
DOI: https://doi.org/10.1007/978-3-319-62127-2_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62126-5
Online ISBN: 978-3-319-62127-2
eBook Packages: Computer ScienceComputer Science (R0)