Shortest Basis Problem
Many problems become easier if the input basis consists of short vectors. An algorithm that solves the Shortest Basis Problem (SBP) must, given a lattice basis, output an equivalent basis such that the length of the longest vector in is as short as possible.
The approximation version problem consist of finding a basis whose longest vector is at most times longer than the longest vector in the shortest basis.
Read more about this topic: Lattice Problem
Famous quotes containing the words shortest, basis and/or problem:
“Jesus wept.”
—Bible: New Testament John, 11:35.
The shortest verse in the Bible; refers to Jesus’ grief at the death of Lazarus, whom he raised from the dead after four days.
“Protoplasm, simple or nucleated, is the formal basis of all life. It is the clay of the potter: which, bake it and paint it as he will, remains clay, separated by artifice, and not by nature from the commonest brick or sun-dried clod.”
—Thomas Henry Huxley (1825–1895)
“[How] the young . . . can grow from the primitive to the civilized, from emotional anarchy to the disciplined freedom of maturity without losing the joy of spontaneity and the peace of self-honesty is a problem of education that no school and no culture have ever solved.”
—Leontine Young (20th century)