Optimal shortest path queries in a simple polygon
Journal of Computer and System Sciences
A new data structure for shortest path queries in a simple polygon
Information Processing Letters
On the Difficulty of Embedding Planar Graphs with Inaccuracies
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Computing the Fréchet distance between simple polygons in polynomial time
Proceedings of the twenty-second annual symposium on Computational geometry
Exact algorithms for partial curve matching via the Fréchet distance
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Can We Compute the Similarity between Surfaces?
Discrete & Computational Geometry
Fréchet distance of surfaces: some simple hard cases
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Computing the Fréchet distance between folded polygons
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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Computing the Fréchet distance for surfaces is a surprisingly hard problem. We introduce a partial variant of the Fréchet distance problem, which for given surfaces P and Q asks to compute a surface R⊆Q with minimum Fréchet distance to P. Like the Fréchet distance, the partial Fréchet distance is NP-hard to compute between terrains and also between polygons with holes. We restrict P, Q, and R to be coplanar simple polygons. For this restricted class of surfaces, we develop a polynomial time algorithm to compute the partial Fréchet distance and show that such an R⊆Q can be computed in polynomial time as well. This is the first algorithm to address a partial Fréchet distance problem for surfaces and extends Buchin et al.'s algorithm for computing the Fréchet distance between simple polygons.