Shortest Vector Problem
The Shortest Vector Problem (SVP) is a fundamental challenge in computational geometry and lattice theory. It involves finding the shortest non-zero vector in a lattice, which is a discrete set of points in space formed by linear combinations of basis vectors. This problem is significant in various fields, including cryptography, where it underpins the security of certain encryption schemes.
SVP is known to be NP-hard, meaning that no efficient algorithm is currently known to solve it in all cases. Researchers study SVP to understand its complexity and to develop approximate solutions, which can be useful in applications like cryptographic systems and integer programming.