The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.01 - Jan.-Feb. (2013 vol.10)
pp: 226-229
Aleksandar Poleksic , Dept. of Comput. Sci., Univ. of Northern Iowa, Cedar Falls, IA, USA
ABSTRACT
The Largest Common Point-set (LCP) and the Pattern Matching (PM) problems have received much attention in the fields of pattern matching, computer vision and computational biology. Perhaps, the most important application of these problems is the protein structural alignment, which seeks to find a superposition of a pair of input proteins that maximizes a given protein structure similarity metric. Although it has been shown that LCP and PM are both tractable problems, the running times of existing algorithms are high-degree polynomials. Here, we present novel methods for finding approximate and exact threshold-LCP and threshold-PM for r-separated sets, in general, and protein 3D structures, in particular. Improved running times of our methods are achieved by building upon several different, previously published techniques.
INDEX TERMS
Proteins, Approximation algorithms, Approximation methods, Pattern matching, Computational biology, Bioinformatics, Polynomials,structural alignment, Pattern matching, protein structure
CITATION
Aleksandar Poleksic, "Improved Algorithms for Matching r-Separated Sets with Applications to Protein Structure Alignment", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.10, no. 1, pp. 226-229, Jan.-Feb. 2013, doi:10.1109/TCBB.2012.135
REFERENCES
[1] T. Akutsu, H. Tamaki, and T. Tokuyama, “Distribution of Distances and Triangles in a Point Set and Algorithms for Computing the Largest Common Point Sets,” Discrete Computational Geometry, vol. 20, pp. 307-331, 1998.
[2] Y. Hecker and R. Bolle, “On Geometric Hashing and the Generalized Hough Transform,” IEEE Trans System, Man, and Cybernetics, vol. 24, no. 9, pp. 1328-1338, Sept. 1994.
[3] S. Irani and P. Raghavan, “Combinatorial and Experimental Results for Randomized Point Matching Algorithms,” Computational Geometry, vol. 12, pp. 17-31, 1999.
[4] Y. Lamdan and H.J. Wolfson, “Geometric Hashing: A General and Efficient Model-Based Recognition Scheme,” Proc. Second Int'l Conf. Computer Vision, pp. 238-249, 1988.
[5] C.F. Olson, “Efficient Pose Clustering Using a Randomized Algorithm,” Int'l J. Computer Vision, vol. 23, pp. 131-147, 1997.
[6] S.B. Needleman and C.D. Wunsch, “A General Method Applicable to the Search for Similarities in the Amino Acid Sequence of Two Proteins,” J. Molecular Biology, vol. 48, pp. 443-453, 1970.
[7] T. Akutsu, “Protein Structure Alignment Using Dynamic Programming and Iterative Improvement,” IEICE Trans. Information Systems, vol. E79-D, no. 12, pp. 1629-1636, 1995.
[8] A. Poleksic, “Algorithms for Optimal Protein Structure Alignment,” Bioinformatics, vol. 25, pp. 2751-2756, 2009.
[9] A. Poleksic, “Optimizing a Widely Used Protein Structure Alignment Measure in Expected Polynomial Time,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 8, no. 6, pp. 1716-1720, Nov./Dec. 2011.
[10] A. Poleksic, “On Complexity of Protein Structure Alignment Problem under Distance Constraint,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 9, no. 2, pp. 511-516, Mar./Apr. 2012.
[11] S.C. Li and Y.K. Ng, “On Protein Structure Alignment under Distance Constraint,” Theoretical Computer Science, vol. 412, pp. 4187-4199, 2011.
[12] C. Ambühl, S. Chakraborty, and B. Gärtner, “Computing Largest Common Point Sets under Approximate Congruence,” Proc. Ann. European Symp. Algorithms, pp. 52-63, 2000.
[13] H. Alt, K. Mehlhorn, H. Wagener, and E. Welzl, “Congruence, Similarity, and Symmetries of Geometric Objects,” Discrete Computational Geometry, vol. 3, pp. 237-256, 1988.
[14] V. Choi and N. Goyal, “A Combinatorial Shape Matching Algorithm for Rigid Protein Docking,” Proc. Ann. Symp. Combinatorial Pattern Matching (CPM), pp. 285-296, 2004.
[15] P. Indyk, R. Motwani, and S. Venkatasubramanian, “Geometric Matching under Noise: Combinatorial Bounds and Algorithms,” Proc. 10th Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 457-465, 1999.
[16] S. Micali and V.V. Vazirani, “An $O(\sqrt{\vert V\Vert E \vert})$ Algorithm for Finding Maximum Matching in General Graphs,” Proc. 21st IEEE Symp. Foundations of Computer Science, pp. 17-27, 1980.
39 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool