Abstract
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.
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Communicated by Victor Klee
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Kolinek, M. A polynomial-time linear decision tree for the traveling salesman problem and other NP-complete problems. Discrete Comput Geom 2, 37–48 (1987). https://doi.org/10.1007/BF02187869
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DOI: https://doi.org/10.1007/BF02187869