<p><it>Abstract—</it>Let $<tmath>A</tmath>$ be a sorted array of $<tmath>n</tmath>$ numbers and $<tmath>B</tmath>$ a sorted array of $<tmath>m</tmath>$ numbers, both in nondecreasing order, with $<tmath>n \leq m</tmath>$. We consider the problem of determining, for each element $<tmath>A(j)</tmath>$, $<tmath>j</tmath>$$<tmath>=</tmath>$$<tmath>1</tmath>$, $<tmath>2</tmath>$, $<tmath>\cdots,</tmath>$$<tmath>n</tmath>$, the unique element $<tmath>B(i)</tmath>$, $<tmath>0 \leq i \leq m</tmath>$, such that $<tmath>B(i)</tmath>$$<tmath>\leq A(j)</tmath>$$<tmath>< B(i+1)</tmath>$ (with $<tmath>B(0) = - \infty</tmath>$ and $<tmath>B(m+1) = +\infty</tmath>$). We present an efficient parallel algorithm for solving this problem in $<tmath>O(\log m)</tmath>$ time using $<tmath>O\left({{n\;{\rm log}(m/n)}\over{{\rm log}\; m}}\right)</tmath>$ EREW PRAM processors. Our algorithm improves the previously known results on either the time or processor complexity, and enables us to solve several other problems optimally on the EREW PRAM.</p><p><it>Index Terms—</it>Binary search, computational geometry, merging, parallel algorithms, parallel random access machines, read conflicts, visibility.</p>