Abstract
We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the operations: insert; delete; test membership; and predecessor. The performance of our data structure is within an O(logw)-factor of optimal. Here w ≤ n is the width of the partial-order—a natural obstacle in searching a partial order.
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
Ben-Asher, Y., Farchi, E., Newman, I.: Optimal search in trees. SIAM J. Comput. 28(6), 2090–2102 (1999)
Carmo, R., Donadelli, J., Kohayakawa, Y., Laber, E.S.: Searching in random partially ordered sets. Theor. Comput. Sci. 321(1), 41–57 (2004)
Mozes, S., Onak, K., Weimann, O.: Finding an optimal tree searching strategy in linear time. In: SODA 2008: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1096–1105. Society for Industrial and Applied Mathematics, Philadelphia (2008)
Onak, K., Parys, P.: Generalization of binary search: Searching in trees and forest-like partial orders. In: FOCS 2006: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 379–388. IEEE Computer Society, Washington, DC, USA (2006)
Dereniowski, D.: Edge ranking and searching in partial orders. Discrete Appl. Math. 156(13), 2493–2500 (2008)
Jacobs, T., Cicalese, F., Laber, E.S., Molinaro, M.: On the complexity of searching in trees: Average-case minimization. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 527–539. Springer, Heidelberg (2010)
Laber, E., Molinaro, M.: An approximation algorithm for binary searching in trees. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 459–471. Springer, Heidelberg (2008)
Daskalakis, C., Karp, R.M., Mossel, E., Riesenfeld, S., Verbin, E.: Sorting and selection in posets. In: SODA 2009: Proceedings of the Nineteenth Annual ACM-SIAM SODA, pp. 392–401. SIAM, Philadelphia (2009)
Daskalakis, C., Karp, R.M., Mossel, E., Riesenfeld, S., Verbin, E.: Sorting and selection in posets. CoRR abs/0707.1532 (2007)
Heeringa, B., Iordan, M.C., Theran, L.: Searching in dynamic tree-like partial orders. CoRR abs/1010.1316 (2010)
Laber, E., Nogueira, L.T.: Fast searching in trees. Electronic Notes in Discrete Mathematics 7, 1–4 (2001)
Meir, A., Moon, J.W.: On the altitude of nodes in random trees. Canadian Journal of Mathematics 30, 997–1015 (1978)
Bergeron, F., Flajolet, P., Salvy, B.: Varieties of increasing trees. In: Raoult, J.-C. (ed.) CAAP 1992. LNCS, vol. 581, pp. 24–48. Springer, Heidelberg (1992)
Drmota, M.: The height of increasing trees. Annals of Combinatorics 12, 373–402 (2009), doi:10.1007/s00026-009-0009-x
Grimmett, G.R.: Random labelled trees and their branching networks. J. Austral. Math. Soc. Ser. A 30(2), 229–237 (1980/1981)
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
Heeringa, B., Iordan, M.C., Theran, L. (2011). Searching in Dynamic Tree-Like Partial Orders. 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_43
Download citation
DOI: https://doi.org/10.1007/978-3-642-22300-6_43
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)