TY - GEN
T1 - The closest pair problem under the hamming metric
AU - Min, Kerui
AU - Kao, Ming-Yang
AU - Zhu, Hong
PY - 2009/12/1
Y1 - 2009/12/1
N2 - Finding the closest pair among a given set of points under Hamming Metric is a fundamental problem with many applications. Let n be the number of points and D the dimensionality of all points. We show that for 0<D≤n 0.294, the problem, with the binary alphabet set, can be solved within time complexity , whereas for n 0.294<D≤n, it can be solved within time complexity . We also provide an alternative approach not involving algebraic matrix multiplication, which has the time complexity with small constant, and is effective for practical use. Moreover, for arbitrary large alphabet set, an algorithm with the time complexity is obtained for 0<D≤n 0.294, whereas the time complexity is for n 0.294<D≤n. In addition, the algorithms propose in this paper provides a solution to the open problem stated by Kao et al.
AB - Finding the closest pair among a given set of points under Hamming Metric is a fundamental problem with many applications. Let n be the number of points and D the dimensionality of all points. We show that for 0<D≤n 0.294, the problem, with the binary alphabet set, can be solved within time complexity , whereas for n 0.294<D≤n, it can be solved within time complexity . We also provide an alternative approach not involving algebraic matrix multiplication, which has the time complexity with small constant, and is effective for practical use. Moreover, for arbitrary large alphabet set, an algorithm with the time complexity is obtained for 0<D≤n 0.294, whereas the time complexity is for n 0.294<D≤n. In addition, the algorithms propose in this paper provides a solution to the open problem stated by Kao et al.
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U2 - 10.1007/978-3-642-02882-3_21
DO - 10.1007/978-3-642-02882-3_21
M3 - Conference contribution
AN - SCOPUS:76249117802
SN - 3642028810
SN - 9783642028816
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 205
EP - 214
BT - Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings
T2 - 15th Annual International Conference on Computing and Combinatorics, COCOON 2009
Y2 - 13 July 2009 through 15 July 2009
ER -