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Prefix graphs and their applications

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44233

Chaudhuri,  Shiva
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44564

Hagerup,  Torben
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-94-145.pdf
(Any fulltext), 9MB

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Citation

Chaudhuri, S., & Hagerup, T.(1994). Prefix graphs and their applications (MPI-I-94-145). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B7A0-4
Abstract
The \Tstress{range product problem} is, for a given set $S$ equipped with an associative operator $\circ$, to preprocess a sequence $a_1,\ldots,a_n$ of elements from $S$ so as to enable efficient subsequent processing of queries of the form: Given a pair $(s,t)$ of integers with $1\le s\le t\le n$, return $a_s\circ a_{s+1}\circ\cdots\circ a_t$. The generic range product problem and special cases thereof, usually with $\circ$ computing the maximum of its arguments according to some linear order on $S$, have been extensively studied. We show that a large number of previous sequential and parallel algorithms for these problems can be unified and simplified by means of prefix graphs.