We show that the position of an input point in the Euclideand-dimensional space with respect to a given set of hyperplanes can be determined efficiently by linear decision trees. As an application, we prove that many concrete problems whose recognition versions are NP-complete, like the traveling salesman problem, many other shortest path problems, and integer programming, have polynomial-time upper bounds in the linear decision tree model of computation.

/pdf/a-polynomial-time-linear-decision-tree-for-the-traveling-15xfg2nuxr.pdf

Martin Kolinek

Papers

A polynomial-time linear decision tree for the traveling salesman problem and other NP-complete problems