Abstract
In the Paired Pointset Traversal problem we ask if, given two sets A = {a 1, ..., a n } and B = {b 1, ..., b n } in the plane, there is an ordering π of the points such that both a π(1), ..., a π(n) and b π(1), ..., b π(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.
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© 2004 Springer-Verlag Berlin Heidelberg
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Hui, P., Schaefer, M. (2004). Paired Pointset Traversal. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_47
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DOI: https://doi.org/10.1007/978-3-540-30551-4_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24131-7
Online ISBN: 978-3-540-30551-4
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