Data structures and network algorithms
Data structures and network algorithms
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Computing homotopic shortest paths in the plane
Journal of Algorithms
On map-matching vehicle tracking data
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Fréchet Distance Based Approach for Searching Online Handwritten Documents
ICDAR '07 Proceedings of the Ninth International Conference on Document Analysis and Recognition - Volume 01
Computing the Fréchet distance between simple polygons
Computational Geometry: Theory and Applications
Detecting Commuting Patterns by Clustering Subtrajectories
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Can We Compute the Similarity between Surfaces?
Discrete & Computational Geometry
Constrained free space diagrams: a tool for trajectory analysis
International Journal of Geographical Information Science
Convergence, stability, and discrete approximation of Laplace spectra
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The frechet distance revisited and extended
Proceedings of the twenty-seventh annual symposium on Computational geometry
Computing the Fréchet distance between folded polygons
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Partial matching between surfaces using fréchet distance
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
The fréchet distance revisited and extended
ACM Transactions on Algorithms (TALG)
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We show that it is NP-hard to decide the FrÉchet distance between (i) non-intersecting polygons with holes embedded in the plane, (ii) 2d terrains, and (iii) self-intersecting simple polygons in 2d, which can be unfolded in 3d. The only previously known NP-hardness result for 2d surfaces was based on self-intersecting polygons with an unfolding in 4d. In contrast to this old result, our NP-hardness reductions are substantially simpler. As a positive result we show that the Fréchet distance between polygons with one hole can be computed in polynomial time.