Towards optimal parallel bucket sorting
Information and Computation
An optimally efficient selection algorithm
Information Processing Letters
Sorting in c log n parallel steps
Combinatorica
Optimal and sublogarithmic time randomized parallel sorting algorithms
SIAM Journal on Computing
A complexity theory of efficient parallel algorithms
Theoretical Computer Science - Special issue: Fifteenth international colloquium on automata, languages and programming, Tampere, Finland, July 1988
Improved nonconservative sequential and parallel integer sorting
Information Processing Letters
Improved deterministic parallel integer sorting
Information and Computation
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Acta Informatica
Surpassing the information theoretic bound with fusion trees
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Lower bounds for union-split-find related problems on random access machines
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A reliable randomized algorithm for the closest-pair problem
Journal of Algorithms
Improved parallel integer sorting without concurrent writing
Information and Computation
Improved bounds for integer sorting in the EREW PRAM model
Journal of Parallel and Distributed Computing
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Parallel integer sorting is more efficient than parallel comparison sorting on exclusive write PRAMs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Faster deterministic sorting and priority queues in linear space
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Conservative Algorithms for Parallel and Sequential Integer Sorting
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Priority Queues: Small, Monotone and Trans-dichotomous
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Faster deterministic sorting and searching in linear space
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Deterministic sorting in O(nlog log n) time and linear space
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Deterministic sorting in O(nlog logn) time and linear space
Journal of Algorithms
Dynamic ordered sets with exponential search trees
Journal of the ACM (JACM)
Voronoi diagrams in n · 2o(√lg lg n) time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Equivalence between priority queues and sorting
Journal of the ACM (JACM)
More efficient parallel integer sorting
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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We present a fast deterministic algorithm for integer sorting in linear space. Our algorithm sorts n integers in the range {0, 1, 2, ..., m-1} in linear space in O (n log log n log log log n) time. When log m log 2+ε n, ε0, we can further achieve O (n log log n) time. This improves the O (n (log log n)2) time bound given in M. Thorup (1998) in "Proc. 1998 ACM-SIAM Symp. on Discrete Algorithms (SODA'98)," pp. 550-555). This result is obtained by combining our new technique with that of Thorup's. Signature sorting (A. Andersson, T. Hagerup, S. Nilsson, and R. Raman, 1995, in "Proc. 1995 Symposium on Theory of Computing," pp. 427-436), A. Andersson's result (1996, in "Proc. 1996 IEEE Symp. on Foundations of Computer Science," pp. 135-141), R. Raman's result (1996, Lecture Notes in Computer Science, Vol. 1136, pp. 121-137, Springer-Verlag Berlin/New York), and our previous result (Y. Han and X. Shen, 1999, in "Proc. 1999 Tenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'99)," Baltimore, MD, January, pp. 419-428) are also used for the design of our algorithms. We provide an approach and techniques which are totally different from previous approaches and techniques for the problem. As a consequence our technique can be extended to apply to nonconservative sorting and parallel sorting. Our nonconservative sorting algorithm sorts n integers in {0, 1, ..., m-1} in time O (n (log log n)2/(log k+log log log n)) using word length k log(m+n), where k log n. Our EREW parallel algorithm sorts n integers in {0, 1, ..., m-1} in O ((log n)2) time and O (n (log log n)2/log log log n) operations provided log m=&Ohgr; ((log n)2). Copyright 2001 Academic Press.