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Prefix graphs and their applications

Chaudhuri, Shiva and Hagerup, Torben

MPI-I-94-145. August 1994, 13 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

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.
References to related material:

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  AUTHOR = {Chaudhuri, Shiva and Hagerup, Torben},
  TITLE = {Prefix graphs and their applications},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-94-145},
  MONTH = {August},
  YEAR = {1994},
  ISSN = {0946-011X},