MPI-INF/SWS Research Reports 1991-2021

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A lower bound for set intersection queries

Mehlhorn, Kurt and Uhrig, Christian and Raman, Rajeev

April 1992, 14 pages.

Status: available - back from printing

We consider the following {\em set intersection reporting\/} problem. We have a collection of initially empty sets and would like to process an intermixed sequence of $n$ updates (insertions into and deletions from individual sets) and $q$ queries (reporting the intersection of two sets). We cast this problem in the {\em arithmetic\/} model of computation of Fredman and Yao and show that any algorithm that fits in this model must take $\Omega(q + n \sqrt{q})$ to process a sequence of $n$ updates and $q$ queries, ignoring factors that are polynomial in $\log n$. By adapting an algorithm due to Yellin we can show that this bound is tight in this model of computation, again to within a polynomial in $\log n$ factor.

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  AUTHOR = {Mehlhorn, Kurt and Uhrig, Christian and Raman, Rajeev},
  TITLE = {A lower bound for set intersection queries},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-92-127},
  MONTH = {April},
  YEAR = {1992},
  ISSN = {0946-011X},