Determinism versus non-determinism for linear time RAMs (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Optimal time-space trade-offs for non-comparison-based sorting
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Determinism versus nondeterminism for linear time RAMs with memory restrictions
Journal of Computer and System Sciences - STOC 1999
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Improved upper bounds for time-space trade-offs for selection
Nordic Journal of Computing
Quantum time-space tradeoffs for sorting
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Navigation piles with applications to sorting, priority queues, and priority deques
Nordic Journal of Computing
Multi-pass geometric algorithms
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Regression analysis for massive datasets
Data & Knowledge Engineering
Tests and variables selection on regression analysis for massive datasets
Data & Knowledge Engineering
Comparison-based time-space lower bounds for selection
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Comparison-based time-space lower bounds for selection
ACM Transactions on Algorithms (TALG)
Quantum and classical communication-space tradeoffs from rectangle bounds
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem.Beame has shown a lower bound of $\Omega(n^2)$ for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of $O(n^2\log n)$ due to Frederickson. Since then, no progress has been made towards tightening this gap.The main contribution of this paper is a comparison based sorting algorithm which closes the gap by meeting the lower bound of Beame. The time-space product $O(n^2)$ upper bound holds for the full range of space bounds between $\log n$ and $n/\log n$. Hence in this range our algorithm is optimal for comparison based models as well as for the very powerful general models considered by Beame.