Scientists have made a breakthrough in the field of intellectual linear programming (TsLP), a key tool in operations research. This new method can greatly accelerate the solution of various problems, from production planning to air travel planning. Santosh Vempla, a scientist specializing in computer sciences at the Georgia Technological Institute, highlights the significance of TsLP.
Recently, Victor Flight from the Institute of Advanced Studies and Thomas Rotsessus from the University of Washington presented their research on TsLP, which has significantly sped up the problem-solving process. Their work was recognized as the best article at a conference on computer science fundamentals in 2023.
The method of TsLP involves converting the problem into a set of linear equations that satisfy certain inequalities. While specific equations vary based on the task, the main structure of TsLP remains constant, allowing researchers to apply a single approach across different problems.
In 1983, mathematician Hendrick Lenstra proposed the first algorithm for solving the general problem of TsLP. He used a geometric approach, transforming the underlying inequalities into a convex form such as a polygon. The problem was then solved by finding the intersection between this form and a set of integers.
Flight and Rotsessus built upon this approach, employing geometric tools to narrow down the possible solutions. This led to the development of a faster algorithm for solving TsLP, significantly improving the overall execution time to (log n) o (n), where n represents the number of variables.
Daniel Dadush from the National Research Institute of CWI in the Netherlands, who contributed to the algorithm used by Flight and Rotsessus to measure the execution time of TsLP, describes this achievement as “a triumph at the junction of mathematics, computer science, and geometry.”
Although the new algorithm has not yet been applied to practical problems due to the need for major updates in existing software, it represents a theoretical breakthrough with fundamental applications, according to Rotsessus. Researchers are continuing to work on enhancing the computational efficiency of TsLP, striving for optimal execution time. Vempala emphasizes that further progress will require a fundamentally new idea.