Optimal parallel generation of a computation tree form
ACM Transactions on Programming Languages and Systems (TOPLAS) - Lecture notes in computer science Vol. 174
Deterministic coin tossing with applications to optimal parallel list ranking
Information and Control
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Some subclasses of context-free languages in NC1
Information Processing Letters
SIAM Journal on Computing
Parallel approximation algorithms for bin packing
Information and Computation
Proceedings of the 1st International Conference on Supercomputing
Parallel Parsing of Arithmetic Expressions
IEEE Transactions on Computers
Improved nonconservative sequential and parallel integer sorting
Information Processing Letters
On optimal parallel computations for sequences of brackets
Theoretical Computer Science
Breadth-first traversal of trees and integer sorting in parallel
Information Processing Letters
Acta Informatica
Optimal routing of parentheses on the hypercube
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Efficient parallel algorithms and data structures related to trees
Efficient parallel algorithms and data structures related to trees
Matching parentheses in parallel
Discrete Applied Mathematics - Special issue: graphs in electrical engineering, discrete algorithms and complexity
Journal of the ACM (JACM)
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Some Fast Parallel Algorithms for Parentheses Matching
ICCI '91 Proceedings of the International Conference on Computing and Information: Advances in Computing and Information
Efficient Parallel Algorithms on Interval Graphs
PARLE '92 Proceedings of the 4th International PARLE Conference on Parallel Architectures and Languages Europe
Parallel algorithms for geometric intersection graphs
Parallel algorithms for geometric intersection graphs
A new Parallel Algorithm for the Parentheses-Matching Problem
PAS '97 Proceedings of the 2nd AIZU International Symposium on Parallel Algorithms / Architecture Synthesis
Formal Translation Directed by Parallel LLP Parsing
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Efficient Parallel Tree Reductions on Distributed Memory Environments
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
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We present four polylog-time parallel algorithms for matching parentheses on anexclusive-read and exclusive-write (EREW) parallel random-access machine (PRAM)model. These algorithms provide new insights into the parentheses-matching 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 notcost-optimal, 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 iscost-optimal, but uses extra space compared to the standard stack-based sequentialalgorithm. The last algorithm reduces the space complexity to O(n) while maintaining thesame processor and time complexities. Compared to other existing time-optimal algorithms for the parentheses-matching 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.