A note on the unsolvability of the weighted region shortest path problem

作者:De Carufel Jean Lou*; Grimm Carsten; Maheshwari Anil; Owen Megan; Smid Michiel
来源:Computational Geometry-Theory and Applications, 2014, 47(7): 724-727.
DOI:10.1016/j.comgeo.2014.02.004

摘要

Let S be a subdivision of the plane into polygonal regions, where each region has an associated positive weight. The weighted region shortest path problem is to determine a shortest path in S between two points s, t is an element of R-2, where the distances are measured according to the weighted Euclidean metric-the length of a path is defined to be the weighted sum of (Euclidean) lengths of the sub-paths within each region. We show that this problem cannot be solved in the Algebraic Computation Model over the Rational Numbers (ACMQ). In the ACMQ, one can compute exactly any number that can be obtained from the rationals Q by applying a finite number of operations from +, -, x, divided by, (k)root, for any integer k %26gt;= 2. Our proof uses Galois theory and is based on Bajaj%26apos;s technique.

  • 出版日期2014-8