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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.