In 1983, mathematician Hendrik Lenstra developed an algorithm to solve integer linear programming (ILP) problems, which involve finding the best integer solution to a set of linear inequalities. Lenstra represented the problem’s constraints as a convex shape called the convex body and searched for intersections with a lattice of grid points representing the integers. Over the years, researchers improved the algorithm, but progress was slow. In 2016, Oded Regev and Stephens-Davidowitz introduced a mathematical result that allowed researchers Timothee Reis and David Rothvoss to estimate the number of lattice points contained in an ILP covering radius, significantly speeding up the algorithm’s runtime. Although the algorithm has not been applied practically yet, its improvement is seen as a triumph in the intersection of math, computer science, and geometry. However, further improvements will require groundbreaking ideas.
https://www.quantamagazine.org/researchers-approach-new-speed-limit-for-seminal-problem-20240129/