Shortest Vector Problem (SVP)
In SVP, a basis of a vector space V and a norm N (often L2) are given for a lattice L and one must find the shortest non-zero vector in V, as measured by N, in L. In other words, the algorithm should output a non-zero vector v such that .
In the -approximation version, one must find a non-zero lattice vector of length at most .
Read more about this topic: Lattice Problem
Famous quotes containing the words shortest and/or problem:
“The shortest route is not the most direct one, but rather the one where the most favorable winds swell our sails:Mthat is the lesson that seafarers teach. Not to abide by this lesson is to be obstinate: here, firmness of character is tainted with stupidity.”
—Friedrich Nietzsche (18441900)
“What had really caused the womens movement was the additional years of human life. At the turn of the century womens life expectancy was forty-six; now it was nearly eighty. Our groping sense that we couldnt live all those years in terms of motherhood alone was the problem that had no name. Realizing that it was not some freakish personal fault but our common problem as women had enabled us to take the first steps to change our lives.”
—Betty Friedan (20th century)