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A lower bound for set intersection queries

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45646

Uhrig,  Christian
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45250

Raman,  Rajeev
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Volltexte (frei zugänglich)

MPI-I-92-127.pdf
(beliebiger Volltext), 10MB

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Zitation

Mehlhorn, K., Uhrig, C., & Raman, R.(1992). A lower bound for set intersection queries (MPI-I-92-127). Saarbrücken: Max-Planck-Institut für Informatik.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0014-B706-D
Zusammenfassung
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.