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Researchers have found a faster way to do integer linear programming (quantamagazine.org)

498 points by pseudolus · 932 days ago · 191 comments on HN

Article summary

Researchers have made a significant breakthrough in integer linear programming (ILP) by developing a new algorithm that solves ILP problems in record time. ILP is a variant of linear programming that involves optimizing problems with whole-number amounts and is popular in applications such as production planning and airline crew scheduling. The new algorithm brings the runtime to (log n)O(n), which is considered almost the same as the runtime of the binary problem. This breakthrough has the potential to impact various fields that rely on ILP, including operations research and computer science.

Main themes

  • Integer Linear Programming
  • Linear Optimization
  • Operations Research
  • Computer Science
  • Algorithm Development
  • NP-Hard Problems

What commenters say

  • Linear programming is a powerful tool with many practical applications, including solving discrete optimization problems.
  • The term 'programming' in linear programming refers to scheduling and has nothing to do with computer programming.
  • Many problems in NP can be formulated as linear optimization, and some can be solved or well-approximated quickly using integer linear programming.
  • Despite being NP-hard, integer linear programming can be practical and solvable in many cases, especially with the development of new algorithms.
  • The distinction between continuous and integer linear optimization is important, with continuous linear optimization being in P and integer linear optimization being in NP.
  • Some commenters believe that industrial engineering and computer science should be combined into a single field, given the significant overlap between the two.
  • Others argue that computer science is already a broad field that encompasses many areas, including programming and optimization.
  • The development of new algorithms for integer linear programming has the potential to impact various fields, including operations research and computer science, and could lead to more efficient solutions for complex problems.