Abstract
Distribution-sensitive data structures attempt to exploit patterns in query distributions in order to allow many sequences of queries execute faster than in traditional data structures. In this paper, we survey the history of such data structures, outline open problems in the area, and offer some new results.
Research supported in part by NSERC. Dedicated to Ian Munro.
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
Knuth, D.: Optimum binary search trees. Acta Informatica 1, 14–25 (1971)
Mehlhorn, K.: Nearly optimal binary search trees. Acta Inf. 5, 287–295 (1975)
Mehlhorn, K.: A best possible bound for the weighted path length of binary search trees. SIAM J. Comput. 6(2), 235–239 (1977)
Bayer, P.: Improved bounds on the cost of optimal and balanced binary search trees. Master’s thesis, MIT (1975)
Fredman, M.L.: Two applications of a probabilistic search technique: Sorting x + y and building balanced search trees. In: STOC, pp. 240–244 (1975)
Shannon, C.: A mathematical theory of communication. Bell Systems Technical Journal 27, 379–423, 623–565 (1948)
Iacono, J.: Key-independent optimality. Algorithmica 42(1), 3–10 (2005)
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. Journal of the ACM 32(3), 652–686 (1985)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28(2), 202–208 (1985)
Iacono, J.: Improved upper bounds for pairing heaps. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 32–45. Springer, Heidelberg (2000)
Bose, P., Douïeb, K., Langerman, S.: Dynamic optimality for skip lists and B-trees. In: SODA 2008: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1106–1114 (2008)
Iacono, J., Langerman, S.: Queaps. Algorithmica 42(1), 49–56 (2005)
Iacono, J.: Distribution Sensitive Data Structures. PhD thesis, Rutgers, The State University of New Jersey (2001)
Bădoiu, M., Cole, R., Demaine, E.D., Iacono, J.: A unified access bound on comparison-based dynamic dictionaries. Theoretical Computer Science 382(2), 86–96 (2007)
Cole, R.: On the dynamic finger conjecture for splay trees. Part II: The proof. SIAM Journal on Computing 30(1), 44–85 (2000)
Cole, R., Mishra, B., Schmidt, J., Siegel, A.: On the dynamic finger conjecture for splay trees. Part I: Splay Sorting logn-Block Sequences. SIAM Journal on Computing 30(1), 1–43 (2000)
Tarjan, R.: Sequential access in splay trees takes linear time. Combinatorica 5, 367–378 (1985)
Bose, P., Douïeb, K., Dujmović, V., Howat, J.: Layered working-set trees. Algorithmica 63(1), 476–489 (2012)
Derryberry, J.C.: Adapative Binary Search Trees. PhD thesis, Carnegie Mellon University (2009)
Derryberry, J.C., Sleator, D.D.: Skip-splay: Toward achieving the unified bound in the BST model. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 194–205. Springer, Heidelberg (2009)
Bose, P., Douïeb, K., Dujmović, V., Fagerberg, R.: An o(log log n)-competitive binary search tree with optimal worst-case access times. In: Kaplan, H. (ed.) SWAT 2010. LNCS, vol. 6139, pp. 38–49. Springer, Heidelberg (2010)
Demaine, E.D., Harmon, D., Iacono, J., Pǎtraşcu, M.: Dynamic optimality—almost. SIAM Journal on Computing 37(1), 240–251 (2007)
Wang, C.C., Derryberry, J., Sleator, D.D.: O(loglogn)-competitive dynamic binary search trees. In: SODA 2006: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 374–383 (2006)
Andersson, A.A., Thorup, M.: Dynamic ordered sets with exponential search trees. Journal of the ACM 54(3) (2007)
Brodal, G.S., Lagogiannis, G., Makris, C., Tsakalidis, A., Tsichlas, K.: Optimal finger search trees in the pointer machine. Journal of Computer and System Sciences 67(2), 381–418 (2003)
Dietz, P.F., Raman, R.: A constant update time finger search tree. Information Processing Letters 52(3), 147–154 (1994)
Pugh, W.: Skip lists: a probabilistic alternative to balanced trees. Communications of the ACM 33(6), 668–676 (1990)
Kaporis, A.C., Makris, C., Sioutas, S., Tsakalidis, A., Tsichlas, K., Zaroliagis, C.: Improved bounds for finger search on a RAM. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 325–336. Springer, Heidelberg (2003)
Bent, S.W., Sleator, D.D., Tarjan, R.E.: Biased search trees. SIAM Journal on Computing 14, 545–568 (1985)
Seidel, R., Aragon, C.R.: Randomized search trees. Algorithmica 16(4/5), 464–497 (1996)
Bagchi, A., Buchsbaum, A.L., Goodrich, M.T.: Biased skip lists. Algorithmica 42, 31–48 (2005)
Johnson, D.B.: A priority queue in which initialization and queue operations take O(loglogD) time. Theory of Computing Systems 15(1), 295–309 (1981)
Elmasry, A.: A priority queue with the working-set property. International Journal of Foundations of Computer Science 17(6), 1455–1465 (2006)
Wilber, R.: Lower bounds for accessing binary search trees with rotations. SIAM Journal on Computing 18(1), 56–67 (1989)
Brodal, G.S., Makris, C., Sioutas, S., Tsakalidis, A., Tsichlas, K.: Optimal solutions for the temporal precedence problem. Algorithmica 33(4), 494–510 (2002)
Belazzougui, D., Kaporis, A., Spirakis, P.: Random input helps searching predecessors. arXiv:1104.4353 (2011)
Demaine, E.D., Iacono, J., Langerman, S.: Proximate point searching. Computational Geometry: Theory and Applications 28(1), 29–40 (2004)
Arya, S., Malamatos, T., Mount, D.M., Wong, K.C.: Optimal expected-case planar point location. SIAM Journal on Computing 37(2), 584–610 (2007)
Colette, S., Dujmović, V., Iacono, J., Langerman, S., Morin, P.: Distribution-sensitive point location in convex subdivisions. In: SODA 2008: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 912–921 (2008)
Iacono, J.: A static optimality transformation with applications to planar point location. arXiv:1104.5597 (2011)
Iacono, J., Langerman, S.: Proximate planar point location. In: SoCG 2003: Proceedings of the 19th Annual ACM Symposium on Computational Geometry, pp. 220–226 (2003)
Derryberry, J., Sheehy, D., Woo, M., Sleator, D.D.: Achieving spatial adaptivity while finding approximate nearest neighbors. In: CCCG 2008: Proceedings of the 20th Annual Canadian Conference on Computational Geometry, pp. 163–166 (2008)
Dujmović, V., Howat, J., Morin, P.: Biased range trees. In: SODA 2009: Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 486–495 (2009)
Afshani, P., Barbay, J., Chan, T.M.: Instance-optimal geometric algorithms. In: FOCS 2009: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, pp. 129–138 (2009)
Elmasry, A., Farzan, A., Iacono, J.: A unifying property for distribution-sensitive priority queues. In: Iliopoulos, C.S., Smyth, W.F. (eds.) IWOCA 2011. LNCS, vol. 7056, pp. 209–222. Springer, Heidelberg (2011)
Adelson-Velskii, G., Landis, E.: An algorithm for the organization of information. Soviet Math. Doklady 3, 1259–1263 (1962)
Willard, D.E.: Log-logarithmic worst-case range queries are possible in space Θ(N). Information Processing Letters 17(2), 81–84 (1983)
Beame, P., Fich, F.E.: Optimal bounds for the predecessor problem and related problems. Journal of Computer and System Sciences 65(1), 38–72 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bose, P., Howat, J., Morin, P. (2013). A History of Distribution-Sensitive Data Structures. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds) Space-Efficient Data Structures, Streams, and Algorithms. Lecture Notes in Computer Science, vol 8066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40273-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-40273-9_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40272-2
Online ISBN: 978-3-642-40273-9
eBook Packages: Computer ScienceComputer Science (R0)