Approximation schemes for NP-hard geometric optimization problems: a survey

  title={Approximation schemes for NP-hard geometric optimization problems: a survey},
  author={Sanjeev Arora},
  journal={Math. Program.},
NP-hard geometric optimization problems arise in many disciplines. Perhaps the most famous one is the traveling salesman problem (TSP): given n nodes in<2 (more generally, in<d), find the minimum length path that visits each node exactly once. If distance is computed using the Euclidean norm (distance between nodes (x1, y1) and (x2, y2) is ((x1−x2)+(y1−y2))) then the problem is called Euclidean TSP. More generally the distance could be defined using other norms, such as `p norms for any p > 1… CONTINUE READING
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