Abstract
Consider laying out a fixed-topology binary tree of N nodes into external memory with block size B so as to minimize the worst-case number of block memory transfers required to traverse a path from the root to a node of depth D. We prove that the optimal number of memory transfers is
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Acknowledgements
This research was initiated during the Seminar on Cache-Oblivious and Cache-Aware Algorithms held at Schloss Dagstuhl in July 2004. We thank Jeff Erickson and J. Ian Munro for many helpful discussions during that seminar. We also thank Paulo Ferragina for early discussions on this problem.
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Work of E.D.D. is supported in part by NSF grants CCF-0430849, OISE-0334653 and MADALGO—Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation.
Research of J.I. is partially supported by NSF grants CCF-0430849, OISE-0334653, CCF-1018370, and an Alfred P. Sloan fellowship.
S.L. is Directeur de recherches du F.R.S.-FNRS.
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Demaine, E.D., Iacono, J. & Langerman, S. Worst-Case Optimal Tree Layout in External Memory. Algorithmica 72, 369–378 (2015). https://doi.org/10.1007/s00453-013-9856-2
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DOI: https://doi.org/10.1007/s00453-013-9856-2