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 answer is doing.”
—English proverb, collected in George Herbert, Jacula Prudentum (1651)
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)