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<p><it>Abstract—</it>Let <math><tmath>$A$</tmath></math> be a sorted array of <math><tmath>$n$</tmath></math> numbers and <math><tmath>$B$</tmath></math> a sorted array of <math><tmath>$m$</tmath></math> numbers, both in nondecreasing order, with <math><tmath>$n \leq m$</tmath></math>. We consider the problem of determining, for each element <math><tmath>$A(j)$</tmath></math>, <math><tmath>$j$</tmath></math><math><tmath>$=$</tmath></math><math><tmath>$1$</tmath></math>, <math><tmath>$2$</tmath></math>, <math><tmath>$\cdots,$</tmath></math><math><tmath>$n$</tmath></math>, the unique element <math><tmath>$B(i)$</tmath></math>, <math><tmath>$0 \leq i \leq m$</tmath></math>, such that <math><tmath>$B(i)$</tmath></math><math><tmath>$\leq A(j)$</tmath></math><math><tmath>$< B(i+1)$</tmath></math> (with <math><tmath>$B(0) = - \infty$</tmath></math> and <math><tmath>$B(m+1) = +\infty$</tmath></math>). We present an efficient parallel algorithm for solving this problem in <math><tmath>$O(\log m)$</tmath></math> time using <math><tmath>$O\left({{n\;{\rm log}(m/n)}\over{{\rm log}\; m}}\right)$</tmath></math> 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>
Danny Z. Chen, "Efficient Parallel Binary Search on Sorted Arrays, with Applications", IEEE Transactions on Parallel & Distributed Systems, vol. 6, no. , pp. 440-445, April 1995, doi:10.1109/71.372799
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