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External Memory Three-Sided Range Reporting and Top-k Queries with Sublogarithmic Updates

Author Gerth Stølting Brodal



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Gerth Stølting Brodal

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Gerth Stølting Brodal. External Memory Three-Sided Range Reporting and Top-k Queries with Sublogarithmic Updates. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 23:1-23:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.STACS.2016.23

Abstract

An external memory data structure is presented for maintaining a dynamic set of N two-dimensional points under the insertion and deletion of points, and supporting unsorted 3-sided range reporting queries and top-k queries, where top-k queries report the k points with highest y-value within a given x-range. For any constant 0 < epsilon <= 1/2, a data structure is constructed that supports updates in amortized O(1/(epsilon * B^{1-epsilon}) * log_B(N)) IOs and queries in amortized O(1/epsilon * log_B(N+K/B)) IOs, where B is the external memory block size, and K is the size of the output to the query (for top-k queries K is the minimum of k and the number of points in the query interval). The data structure uses linear space. The update bound is a significant factor B^{1-epsilon} improvement over the previous best update bounds for these two query problems, while staying within the same query and space bounds.
Keywords
  • External memory
  • priority search tree
  • 3-sided range reporting
  • top-k queries

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