Integer programming is a technique used in computations for scheduling, combinatorial, and optimization problems that require variables to take integer values. Last year, Victor Reis and his advisor Thomas Rothvoss proved a new upper bound on the time to solve integer programs, building on previous work by Daniel Dadush. The algorithm they analyzed provides an efficient solution to either/or problems, such as the traveling-salesperson problem. While the new result represents a theoretical advancement in solving integer linear programs, practical challenges remain. Heuristics are commonly used for large-scale industrial problems due to their efficiency, while algorithms like Reis and Rothvoss’s may have limited practical implementation due to memory and computational constraints.
https://cacm.acm.org/news/faster-integer-programming/