Computational geometry: an introduction
Computational geometry: an introduction
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.)
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
Sorting and Element Distinctness on One-Way Turing Machines
Language and Automata Theory and Applications
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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We disprove a conjecture of López-Ortiz by showing that the Element Distinctness Problem for n numbers of size O(logn) can be solved in O(n2(logn)3/2(loglogn)1/2) steps by a nondeterministic one-tape Turing machine. Further we give a simplified algorithm for solving the problem for shorter numbers in time O(n2 log n) on a deterministic one-tape Turing machine and a new proof of the matching lower bound.