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COMPGEOM
2005
ACM

Shortest path amidst disc obstacles is computable

10 years 6 months ago
Shortest path amidst disc obstacles is computable
An open question in Exact Geometric Computation is whether there are transcendental computations that can be made “geometrically exact”. Perhaps the simplest such problem in computational geometry is that of computing the shortest obstacle-avoiding path between two points p, q in the plane, where the obstacles are a collection of n discs. This problem can be solved in O(n2 log n) time in the Real RAM model, but nothing was known about its computability in the standard (Turing) model of computation. We first show the Turingcomputability of this problem, provided the radii of the discs are rationally related. We make the usual assumption that the numerical input data are real algebraic numbers. By appealing to effective bounds from transcendental number theory, we further show a single-exponential time upper bound when the input numbers are rational. Our result appears to be the first example of a non-algebraic combinatorial problem which is shown computable. It is also a rare ex...
Ee-Chien Chang, Sung Woo Choi, DoYong Kwon, Hyungj
Added 13 Oct 2010
Updated 13 Oct 2010
Type Conference
Year 2005
Where COMPGEOM
Authors Ee-Chien Chang, Sung Woo Choi, DoYong Kwon, Hyungju Park, Chee-Keng Yap
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