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#### Prefix graphs and their applications

##### MPS-Authors

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##### Fulltext (public)

MPI-I-94-145.pdf

(Any fulltext), 9MB

##### Supplementary Material (public)

There is no public supplementary material available

##### 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.