Computational geometry: an introduction
Computational geometry: an introduction
Measuring the resemblance of polygonal curves
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Computing crossing numbers in quadratic time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the red/blue spanning tree problem
Theoretical Computer Science
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In the Paired Pointset Traversal problem we ask if, given two sets A = {a1, ..., an} and B = {b1, ..., bn} in the plane, there is an ordering π of the points such that both aπ(1), ..., aπ(n) and bπ(1), ..., bπ(n) are self-avoiding polygonal arcs? We show that Paired Pointset Traversal is NP-complete This has consequences for the complexity of computing the Fréchet distance of two-dimensional surfaces We also show that the problem can be solved in polynomial time if the points in A and B are in convex position, and derive some combinatorial estimates on lct(A,B), the length of a longest common traversal of A and B.