This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
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.

[1] S. G. Akl and H. Meijer,“Parallel binary search,”IEEE Trans. Parallel Distrib. Syst., vol. 1, pp. 247–250, 1990.
[2] M.J. Atallah,R. Cole,, and M.T. Goodrich,“Cascading divide-and-conquer: A technique for designing parallelalgorithms,” SIAM J. Computing, vol. 18, no. 3, pp. 499-532, 1989.
[3] P. Bertolazzi, S. Salza, and C. Guerra,“A parallel algorithm for the visibility problem from a point,”J. Parallel Distrib. Computing, vol. 9, pp. 11–14, 1990.
[4] G. Bilardi and A. Nicolau,“Adaptive bitonic sorting: An optimal parallel algorithm for shared-memory machines,”SIAM J. Comput., vol. 18, pp. 216–228, 1989.
[5] R.P. Brent, "The Parallel Evaluation of General Arithmetic Expressions," J. ACM, vol. 21, pp. 201-206, 1974.
[6] D. Z. Chen,“Efficient parallel binary search on sorted arrays,”Tech. Rep. 1009, Dept. Comput. Sci., Purdue University, W. Lafayette, IN, Aug. 1990.
[7] R. Cole, "Parallel Merge Sort," SIAM J. Computing, vol. 17, pp. 770-785, 1988.
[8] T. Hagerup and C. Rub,"Optimal merging and sorting on the EREW PRAM," Information Processing Letters, vol. 33, pp. 181-185, 1989.
[9] C. P. Kruskal, L. Rudolph, and M. Snir,“The power of parallel prefix,”IEEE Trans. Comput., vol. C-34, pp. 965–968, 1985.
[10] R.E. Ladner and M.J. Fischer, "Parallel Prefix Computation," J. ACM, vol. 27, no. 4, pp. 831-838, Oct. 1980.
[11] S. D. Lang and N. Deo,“Recursive batched binary searching of sequential files,”Comput. J., to be published.
[12] H. Meijer and S. Akl,“Parallel binary search with delayed read conflicts,”Int. J. High Speed Computing, vol. 2, no. 1, pp. 17–21, 1990.
[13] W. Paul, U. Vishkin, and H. Wagener,“Parallel dictionaries on 2-3 trees,”Tech. Rep. 70, Courant Inst., New YorkUniv., 1983.

Citation:
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
Usage of this product signifies your acceptance of the Terms of Use.