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.
“The basis on which good repute in any highly organized industrial community ultimately rests is pecuniary strength; and the means of showing pecuniary strength, and so of gaining or retaining a good name, are leisure and a conspicuous consumption of goods.”
—Thorstein Veblen (1857–1929)
“Only in the problem play is there any real drama, because drama is no mere setting up of the camera to nature: it is the presentation in parable of the conflict between Man’s will and his environment: in a word, of problem.”
—George Bernard Shaw (1856–1950)