Abstract
A data structure is presented for the Mergeable Dictionary abstract data type, which supports the operations Predecessor-Search, Split, and Merge on a collection of disjoint sets of totally ordered data. While in a typical mergeable dictionary (e.g. 2-4 Trees), the Merge operation can only be performed on sets that span disjoint intervals in keyspace, the structure here has no such limitation. A data structure which can handle arbitrary Merge operations in O(log n) amortized time in the absence of Split operations was presented by Brown and Tarjan [2]. A data structure which can handle both Split and Merge operations in \({\mathcal O}({\rm log^2}_n)\) amortized time was presented by Farach and Thorup [4]. In contrast, our data structure supports all operations, including Split and Merge, in \({\mathcal O}({\rm log}_n)\) amortized time, thus showing that interleaved Merge operations can be supported at no additional cost vis-à-vis disjoint Merge operations.
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References
Bagchi, A., Buchsbaum, A.L., Goodrich, M.T.: Biased skip lists. Algorithmica 42(1), 31–48 (2005)
Brown, M.R., Tarjan, R.E.: A fast merging algorithm. J. ACM 26(2), 211–226 (1979)
Demaine, E.D., López-Ortiz, A., Munro, J.I.: Adaptive set intersections, unions, and differences. In: Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 743–752 (2000)
Farach, M., Thorup, M.: String matching in lempel-ziv compressed strings. Algorithmica 20(4), 388–404 (1998)
Georgiadis, L., Kaplan, H., Shafrir, N., Tarjan, R.E., Werneck, R.F.F.: Data structures for mergeable trees. In: CoRR, abs/0711.1682 (2007)
Georgiadis, L., Tarjan, R.E., Werneck, R.F.F.: Design of data structures for mergeable trees. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 394–403. ACM Press, New York (2006)
Iacono, J., Özkan, Ö.: Mergeable Dictionaries. In: CoRR, abs/1002.4248 (2010)
Lai, K.J.: Complexity of union-split-find problems. Master’s thesis, Massachusetts Institute of Technology, Erik Demaine, Adviser (2008)
Pugh, W.: Skip lists: A probabilistic alternative to balanced trees. Communications of the ACM 33(6), 668–676 (1990)
Tarjan, R.E.: Amortized computational complexity. SIAM Journal on Algebraic Discrete Methods 6(2), 306–318 (1985)
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Iacono, J., Özkan, Ö. (2010). Mergeable Dictionaries. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_15
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DOI: https://doi.org/10.1007/978-3-642-14165-2_15
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