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

Gerth Stølting Brodal

Technical Report, 1509.08240, arXiv.org, 16 pages, September 2015.

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 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<ε≤ 1/2, a data structure is constructed that supports updates in amortized O(1/(ε B1-ε)logB N) IOs and queries in amortized O(1/(ε)logB 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 B1-ε improvement over the previous best update bounds for the two query problems, while staying within the same query and space bounds.

Online version

arxiv1509.08240.pdf (201 Kb)

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BIBTEX entry

@techreport{arxiv1509.08240,
  author = "Gerth St{\o}lting Brodal",
  institution = "arXiv.org",
  month = "September",
  number = "1509.08240",
  pages = "16",
  title = "External Memory Three-Sided Range Reporting and Top-$k$ Queries with Sublogarithmic Updates",
  year = "2015"
}