Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Approximate matching of polygonal shapes (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Measuring the resemblance of polygonal curves
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Matching Polygonal Curves with Respect to the Fréchet Distance
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Simplifying 3D polygonal chains under the discrete Fréchet distance
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
A polynomial time solution for protein chain pair simplification under the discrete fréchet distance
ISBRA'12 Proceedings of the 8th international conference on Bioinformatics Research and Applications
Protein Chain Pair Simplification under the Discrete Fréchet Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Aligning and comparing two polygonal chains in 3D space is an important problem in many areas of research, like in protein structure alignment. A lot of research has been done in the past on this problem, using RMSD as the distance measure. Recently, the discrete Fréchet distance has been applied to align and simplify protein backbones (geometrically, 3D polygonal chains) by Jiang et al., with insightful new results found. On the other hand, as a protein backbone can have as many as 500-600 vertices, even if a pair of chains are nicely aligned, as long as they are not identical, it is still difficult for humans to visualize their similarity and difference. In 2008, a problem called CPS-3F was proposed to simplify a pair of 3D chains simultaneously under the discrete Fréchet distance. However, it is still open whether CPS-3F is NP-complete or not. In this paper, we first present a new practical method to align a pair of protein backbones, improving the previous method by Jiang et al. Finally, we present a greedy-and-backtrack method, using the new alignment method as a subroutine, to handle the CPS-3F problem. We also prove two simple lemmas, giving some evidence to why our new method works well. Some preliminary empirical results using some proteins from the Protein Data Bank (PDB), with comparisons to the previous method, are presented.