Abstract
We present the first uniquely represented data structure for an external memory model of computation, a B-tree analogue called a B-treap. Uniquely represented data structures represent each logical state with a unique machine state. Such data structures are strongly history-independent; they reveal no information about the historical sequence of operations that led to the current logical state. For example, a uniquely represented file-system would support the deletion of a file in a way that, in a strong information-theoretic sense, provably removes all evidence that the file ever existed. Like the B-tree, the B-treap has depth \(O(\log_{\ensuremath{B}} n)\), uses linear space with high probability, where \({\ensuremath{B}}\) is the block transfer size of the external memory, and supports efficient one-dimensional range queries.
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References
Acar, U.A., Blelloch, G.E., Harper, R., Vittes, J.L., Woo, S.L.M.: Dynamizing static algorithms, with applications to dynamic trees and history independence. In: 15th annual ACM-SIAM Symposium on Discrete Algorithms, pp. 531–540 (2004)
Andersson, A., Ottmann, T.: New tight bounds on uniquely represented dictionaries. SIAM Journal of Computing 24(5), 1091–1103 (1995)
Bayer, R., McCreight, E.M.: Organization and maintenance of large ordered indices. Acta Informatica 1, 173–189 (1972)
Blelloch, G.E., Golovin, D.: Strongly history-independent hashing with applications. In: 48th Annual IEEE Symposium on Foundations of Computer Science, pp. 272–282 (2007)
Blelloch, G.E., Golovin, D., Vassilevska, V.: Uniquely represented data structures for computational geometry. In: Gudmundsson, J. (ed.) SWAT 2008. LNCS, vol. 5124, pp. 17–28. Springer, Heidelberg (2008)
Buchbinder, N., Petrank, E.: Lower and upper bounds on obtaining history independence. Information and Computation 204(2), 291–337 (2006)
Fagin, R., Nievergelt, J., Pippenger, N., Strong, H.R.: Extendible hashing—a fast access method for dynamic files. ACM Trans. Database Syst. 4(3), 315–344 (1979)
Golovin, D.: Uniquely Represented Data Structures with Applications to Privacy. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, Tech. Report CMU-CS-08-135 (2008)
Hartline, J.D., Hong, E.S., Mohr, A.E., Pentney, W.R., Rocke, E.: Characterizing history independent data structures. Algorithmica 42(1), 57–74 (2005)
Micciancio, D.: Oblivious data structures: applications to cryptography. In: STOC 1997: Proceedings of the twenty-ninth annual ACM Symposium on Theory of Computing, pp. 456–464. ACM Press, New York (1997)
Naor, M., Segev, G., Wieder, U.: History-independent cuckoo hashing. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 631–642. Springer, Heidelberg (2008)
Naor, M., Teague, V.: Anti-persistence: history independent data structures. In: STOC 2001: Proceedings of the thirty-third annual ACM Symposium on Theory of Computing, pp. 492–501. ACM Press, New York (2001)
Östlin, A., Pagh, R.: Uniform hashing in constant time and linear space. In: STOC 2003: Proceedings of the thirty-fifth annual ACM Symposium on Theory of Computing, pp. 622–628. ACM Press, New York (2003)
Seidel, R., Aragon, C.R.: Randomized search trees. Algorithmica 16(4/5), 464–497 (1996)
Snyder, L.: On uniquely representable data structures. In: FOCS 1977: IEEE Symposium on Foundations of Computer Science, pp. 142–146. IEEE Computer Society Press, Los Alamitos (1977)
Sundar, R., Tarjan, R.E.: Unique binary search tree representations and equality-testing of sets and sequences. In: STOC 1990: Proceedings of the twenty-second annual ACM Symposium on Theory of Computing, pp. 18–25. ACM Press, New York (1990)
Vitter, J.S.: Algorithms and data structures for external memory. Foundations and Trends in Theoretical Computer Science 2(4), 305–474 (2006)
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Golovin, D. (2009). B-Treaps: A Uniquely Represented Alternative to B-Trees. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02927-1_41
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DOI: https://doi.org/10.1007/978-3-642-02927-1_41
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