Lower bounds on the complexity of recognizing SAT by turing machines
Information Processing Letters
Optimal time-space trade-offs for non-comparison-based sorting
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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)
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It was conjectured in Borodin et al. [J. Comput. System Sci., 22 (1981), pp. 351--364] that to solve the element distinctness problem requires $TS = \Omega(n^2)$ on a comparison-based branching program using space $S$ and time $T$, which, if true, would be close to optimal since $TS = O((n \log n)^2)$ is achievable. Recently, Borodin et al. [SIAM J. Comput., 16 (1987), pp. 97--99] showed that $TS = \Omega (n^{3/2}(\log n)^{1/2})$. This paper presents a near-optimal tradeoff $TS = \Omega(n^{2-\epsilon(n)})$, where $\epsilon(n) = O(1/(\log n)^{1/2})$.