SIAM Journal on Computing
On the general motion-planning problem with two degrees of freedom
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Efficient collision detection for moving polyhedra
Proceedings of the eleventh annual symposium on Computational geometry
New Lower Bounds for Convex Hull Problems in Odd Dimensions
SIAM Journal on Computing
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem
Journal of the ACM (JACM)
Collision detection for deforming necklaces
Proceedings of the eighteenth annual symposium on Computational geometry
Efficient maintenance and self-collision testing for Kinematic Chains
Proceedings of the eighteenth annual symposium on Computational geometry
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Towards polynomial lower bounds for dynamic problems
Proceedings of the forty-second ACM symposium on Theory of computing
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We examine a computational geometric problem concerning the structure of polymers. We model a polymer as a polygonal chain in three dimensions. Each edge splits the polymer into two subchains, and a dihedral rotation rotates one of these subchains rigidly about the edge. The problem is to determine, given a chain, an edge, and an angle of rotation, if the motion can be performed without causing the chain to self-intersect. An Ω (nlogn) lower bound on the time complexity of this problem is known.We prove that preprocessing a chain of n edges and answering n dihedral rotation queries is 3SUM-hard, giving strong evidence that Ω (n2) preprocessing is required to achieve sublinear query time in the worst case. For dynamic queries, which also modify the chain if the requested dihedral rotation is feasible, we show that answering n queries is by itself 3SUM-hard, suggesting that sublinear query time is impossible after any amount of preprocessing.