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S.K. Prasad, S.K. Das, C.C.Y. Chen, "Efficient EREW PRAM Algorithms for ParenthesesMatching," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 9, pp. 9951008, September, 1994.  
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@article{ 10.1109/71.308536, author = {S.K. Prasad and S.K. Das and C.C.Y. Chen}, title = {Efficient EREW PRAM Algorithms for ParenthesesMatching}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {5}, number = {9}, issn = {10459219}, year = {1994}, pages = {9951008}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.308536}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Efficient EREW PRAM Algorithms for ParenthesesMatching IS  9 SN  10459219 SP995 EP1008 EPD  9951008 A1  S.K. Prasad, A1  S.K. Das, A1  C.C.Y. Chen, PY  1994 KW  Index Termsparallel algorithms; parallel machines; randomaccess storage; computational complexity;pattern recognition; data structures; EREW PRAM algorithms; parenthesesmatching;polylogtime parallel algorithms; exclusiveread and exclusivewrite; parallelrandomaccess machine; PRAM model; time complexity; input string; working space;space complexity; timeoptimal algorithms; arrays; data structures VL  5 JA  IEEE Transactions on Parallel and Distributed Systems ER   
We present four polylogtime parallel algorithms for matching parentheses on anexclusiveread and exclusivewrite (EREW) parallel randomaccess machine (PRAM)model. These algorithms provide new insights into the parenthesesmatching problem.The first algorithm has a time complexity of O(log/sup 2/ n) employing O(n/(log n))processors for an input string containing n parentheses. Although this algorithm is notcostoptimal, it is extremely simple to implement. The remaining three algorithms, whichare based on a different approach, achieve O(log n) time complexity in each case, andrepresent successive improvements. The second algorithm requires O(n) processors andworking space, and it is comparable to the first algorithm in its ease of implementation.The third algorithm uses O(n/(log n)) processors and O(n log n) space. Thus, it iscostoptimal, but uses extra space compared to the standard stackbased sequentialalgorithm. The last algorithm reduces the space complexity to O(n) while maintaining thesame processor and time complexities. Compared to other existing timeoptimal algorithms for the parenthesesmatching problem that either employ extensive pipelining or use linked lists and comparable data structures, and employ sorting or a linked list ranking algorithm as subroutines, the last two algorithms have two distinct advantages. First, these algorithms employ arrays as their basic data structures, and second, they do not use any pipelining, sorting, or linked list ranking algorithms.
[1] R. Akker, H. Alblas, A. Nijholt, and P. Luttighuis, "An annotated bibliography on parallel parsing," Memoranda Informatica 8967, Dept. Comput. Sci., Univ. of Twente, the Netherlands, Dec. 1989.
[2] R. J. Anderson, E. W. Mayr, and M. K. Warmuth, "Parallel approximation algorithms for bin packing,"Inform. Computation, vol. 82, pp. 262277, Sept. 1989.
[3] F. Baccelli and T. Fleury, "On parsing arithmetic expressions in multiprocessing environment,"Acta Informatica. Berlin, Germany: SpringerVerlag, 1982, pp. 267310.
[4] I. BarOn and U. Vishkin, "Optimal generation of a computation tree form,"ACM Trans. Programming Lang. Syst., vol. 7, no. 2, pp. 659663, 1985.
[5] O. Berkman, B. Schieber, and U. Vishkin, "Some doubly logarithmic optimal parallel algorithms based on finding all nearest smaller values," Tech. Rep. UMIACSTR8879 CSTR2133, Dept. Comput. Sci., Univ. of Maryland, Oct. 1988.
[6] N. G. de Bruijn, D. E. Knuth, and S. O. Rice, "The average height of planted plane trees," in R. C. Reid Ed.,Graph Theory and Computing, Orlando, FL: Academic Press, 1972, pp. 1522.
[7] C.Y. Chen, "Efficient parallel algorithms and data structures related to trees," Ph.D. dissertation, Dept. Comput. Science, Univ. of North Texas, Denton, TX, Dec. 1991.
[8] C.Y. Chen and S. K. Das, "A costoptimal parallel algorithm for the parentheses matching problem on an EREW PRAM," inProc. 5th Int. Parallel Processing Symp., 1991, pp. 132137.
[9] C.Y. Chen and S. K. Das, "Breadthfirst traversal of trees and integer sorting in parallel,"Inform. Processing Lett., vol. 41, pp. 3949, Jan. 1992.
[10] R. Cole, "Parallel merge sort,"SIAM J. Comput., vol. 17, pp. 770785, 1988.
[11] R. Cole and U. Vishkin, "Deterministic coin tossing with applications to optimal list ranking,"Inform. Control, vol. 70, pp. 3253, 1986.
[12] R. Cole and U. Vishkin, "Approximate parallel scheduling, Part I: The basic technique with applications to optimal parallel list ranking in logarithmic time,"SIAM J. Comput., vol. 17, no. 1, pp. 128142, Feb. 1988.
[13] S. K. Das and C.Y. Chen, "Efficient parallel algorithms on interval graphs," inProc. Int. Conf. Parallel Architecture and Languages Europe (PARLE'92), Paris, France, June 1992,Lecture Notes in Computer Science 605. Berlin, Germany: SpringerVerlag, 1992, pp. 131143.
[14] [I4] S. K. Das, C.Y. Chen, G. Lewis, and S. Prasad, "Some fast parallel algorithms for parentheses matching," inProc. Int. Conf. Comput. Inform., 1991, pp. 443454.
[15] S. K. Das and G. Lewis, "A divideandconquer algorithm for parentheses matching," Tech. Rep. CRPDC915, Dept. Comput. Sci., Univ. North Texas, Denton, TX, June 1991.
[16] I. BarOn and U. Vishkin, "Optimal generation of a computation tree form,"ACM Trans. Programming Lang. Syst., vol. 7, no. 2, pp. 659663, 1985.
[17] N. Deo and S. Prasad, "Two EREW algorithms for parentheses matching," Tech. Rep. CSTR8918, Dept. Comput. Sci., Univ. of Central Florida, Orlando, Nov. 1989.
[18] N. Deo and S. Prasad, "Two EREW algorithms for parentheses matching," inProc. 5th Int. Parallel Processing Symp., 1991, pp. 126131.
[19] K. Diks and W. Rytter, "On optimal parallel computations for sequence of brackets,"Theoretical Comput. Sci., vol. 87, pp. 251262, Sept. 1991.
[20] A. Gibbons and W. Rytter,Efficient Parallel Algorithms. Cambridge, England: Cambridge University Press, 1988.
[21] T. Hagerup and H. Shen, "Improved nonconstructive sequential and parallel integer sorting,"Inform. Processing Lett., vol. 36, pp. 5763, 1990.
[22] M. A. Harrison,Introduction to Formal Language Theory. Reading, MA: AddisonWesley, 1978.
[23] O. H. Ibarra, T. Jiang, and B. Ravikumar, "Some subclasses of contextfree languages inNC1,"Inform. Processing Lett., vol. 29, pp. 111118, 1988.
[24] S. K. Kim, "Optimal parallel algorithms on sorted intervals," inProc. 27th Annual Allerton Conf. on Communication, Control, and Computing, 1989, pp. 766775.
[25] S. K. Kim, "Parallel algorithms for geometric intersection graphs," Tech. Rep. 900704, Ph.D. dissertation, Dept. Comput. Sci. and Eng., Univ. of Washington, 1990.
[26] R. E. Ladner and M. J. Fischer, "Parallel prefix computation,"J. ACM, vol. 27, no. 4, pp. 831838, Oct. 1980.
[27] C. Levcopoulos and O. Petersson, "Matching parentheses in parallel,"Discrete Applied Math., vol. 40, pp. 423431, Dec. 1992.
[28] G. Lewis and S. K. Das, "Fast parallel algorithms for parentheses matching," Dept. Comput. Sci., Univ. of North Texas, Denton, TX, in preparation, 1993.
[29] E. W. Mayr and R. Werchner, "Optimal routing of parentheses on the hypercube," inProc. 4th Ann. Symp. on Parallel Algorithms and Architectures, 1992, pp. 109117.
[30] S. Rajasekaran and S. Sen, "On parallel integer sorting,"ACTA Informatica, vol. 29, facs. 1, pp. 115, 1992.
[31] D. Sarkar and N. Deo, "Parallel algorithms for parentheses matching and generation of random balanced sequences of parentheses," inProc. 1st Int. Conf. Supercomputing, Athens, Greece,Lecture Notes in Computer Science 297. Berlin, Germany: SpringerVerlag, 1988, pp. 970984.
[32] Y. N. Srikant, "Parallel parsing of arithmetic expression,"IEEE Trans. Comput., vol. 39, pp. 130132, Jan. 1990.
[33] W. W. Tsang, T. W. Lam, and F. Chin, "An optimal EREW parallel algorithm for parentheses matching," inProc. Int. Conf. Parallel Processing, vol. 3, 1989, pp. 185192.
[34] R. A. Wagner and Y. Han, "Parallel algorithms for bucket sorting and the data dependent prefix problem," inProc. Int. Conf. Parallel Processing, 1986, pp. 924930.