Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Two time-space tradeoffs for element distinctness
Theoretical Computer Science
The complexity of matrix transposition on one-tape off-line Turing machines
Theoretical Computer Science
New lower bounds for element distinctness on a one-tape Turing machine
Information Processing Letters
The element distinctness problem on one-tape Turing machines
Information Processing Letters
Communication complexity
Bounds for the element distinctness problem on one-tape Turing machines
Information Processing Letters
Optimal Algorithms for Sorting on Single-tape Turing Machines
Proceedings of the IFIP 12th World Computer Congress on Algorithms, Software, Architecture - Information Processing '92, Volume 1 - Volume I
Quantum Algorithms for Element Distinctness
SIAM Journal on Computing
The problem of space invariance for sequential machines
Information and Computation
Sorting and Element Distinctness on One-Way Turing Machines
Language and Automata Theory and Applications
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We investigate off-line Turing machines equipped with a two-way input-tape and one work-tape. It is shown that the Element Distinctness Problem (EDP) for m binary strings of length l = O(m/log2m) can be solved in time O(m3/2l1/2) and space O(m1/2l1/2) on a nondeterministic machine. This is faster than the best sorting algorithm on the computational model and optimal if time and space are considered simultaneously. For deterministic machines we give an optimal algorithm that can sort m binary strings consisting of l bits each in O(m3/2l) steps, provided that l = O(m1/4). By modifying the solution we obtain the time bound O(m3/2l) and the space bound O(m1/2l2) for the EDP.