Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
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
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
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
The problem of space invariance for sequential machines
Information and Computation
Element distinctness and sorting on one-tape off-line turing machines
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
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For nondeterministic Turing machines with one work-tape and one-way input a lower time bound Ω(m2茂戮驴) on sorting mstrings of length 茂戮驴 each is shown, which matches the upper bound. For the related Element Distinctness Problem with input of the same format we prove the upper bound O(m2) if 茂戮驴 = O(m/logm), showing this problem to be easier than sorting. The bound O(m2) also holds for deterministic machines if 茂戮驴 = c+ logmwith constant c. For this problem Szepietowski has shown the bound 茂戮驴(m2logm) on deterministic Turing machines without input tape.