Paired Pointset Traversal

In the Paired Pointset Traversal problem we ask whether, 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 Fr´echet 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.

• Type: Conference
• Year: 2004
• Where: ISAAC
• Authors: Peter Hui, Marcus Schaefer
• Keywords: ISAAC 2004, Pointset Traversal, Pointset Traversal Problem, Self-avoiding Polygonal Arcs