On minimal Hamming compatible distances
1 (Data Scientist) Facebook, Inc. Menlo
2 King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics PO Box 5046, Dhahran 31261, Saudi Arabia.
Accepted: 26 May 2014
A Hamming compatible metric is an integer-valued metric on the words of a finite alphabet which agrees with the usual Hamming distance for words of equal length. We define a new Hamming compatible metric and show this metric is minimal in the class of all “well-behaved” Hamming compatible metrics. This gives a negative answer to a question stated by Echi in his paper [O. Echi, Appl. Math. Sci. (Ruse) 3 (2009) 813–824.].
Mathematics Subject Classification: 54E35 / 68R01
Key words: Edit distance / Hamming distance / metric space
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