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Efficient Parallel Binary Search on Sorted Arrays, with Applications
April 1995 (vol. 6 no. 4)
pp. 440-445

Abstract—Let $A$ be a sorted array of $n$ numbers and $B$ a sorted array of $m$ numbers, both in nondecreasing order, with $n \leq m$. We consider the problem of determining, for each element $A(j)$, $j$$=$$1$, $2$, $\cdots,$$n$, the unique element $B(i)$, $0 \leq i \leq m$, such that $B(i)$$\leq A(j)$$< B(i+1)$ (with $B(0) = - \infty$ and $B(m+1) = +\infty$). We present an efficient parallel algorithm for solving this problem in $O(\log m)$ time using $O\left({{n\;{\rm log}(m/n)}\over{{\rm log}\; m}}\right)$ 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.

Index Terms—Binary search, computational geometry, merging, parallel algorithms, parallel random access machines, read conflicts, visibility.

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Danny Z. Chen, "Efficient Parallel Binary Search on Sorted Arrays, with Applications," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 4, pp. 440-445, April 1995, doi:10.1109/71.372799
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