MPI-INF/SWS Research Reports 1991-2021

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Prefix graphs and their applications

Chaudhuri, Shiva and Hagerup, Torben

August 1994, 13 pages.

Status: available - back from printing

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.

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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},