Sentence:  The general behavior of lattice reduction algorithms is far from being well understood....We explain how a mixed methodology has already proved fruitful for small dimensions "p", corresponding to the variety of <WSD>Euclidean algorithms</WSD> ("p" = 1) and to the Gauss algorithm ("p" = 2). 
Meaning of the word marked with <WSD> tags:  "Specifically", a method, based on a division algorithm, for finding the greatest common divisor (gcd) of two given integers; any of certain variations or generalisations of said method.