Numerical analysis: mathematics of scientific computing (2nd ed)
Numerical analysis: mathematics of scientific computing (2nd ed)
Complexity and real computation
Complexity and real computation
Journal of Symbolic Computation - Special issue: validated numerical methods and computer algebra
Handbook of discrete and computational geometry
Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Computable analysis: an introduction
Computable analysis: an introduction
Counterexamples to the uniformity conjecture
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
An O(n2log n) time algorithm for computing shortest paths amidst growing discs in the plane
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
A polynomial-time approximation algorithm for a geometric dispersion problem
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Computing shortest paths amid pseudodisks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Shortest path in a multiply-connected domain having curved boundaries
Computer-Aided Design
Computing shortest paths among curved obstacles in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
On soft predicates in subdivision motion planning
Proceedings of the twenty-ninth annual symposium on Computational geometry
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An open question in Exact Geometric Computation is whether there re 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 re collection of n discs.This problem can be solved in O (n 2 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 Turing-computability 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 single-exponential time upper bound when the input numbers are rational.Our result ppears to be the first example of non-algebraic combinatorial problem which is shown computable. It is also rare example of transcendental number theory yielding positive computational results.