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Small Candidate Set for Translational Pattern Search

Authors Ziyun Huang, Qilong Feng, Jianxin Wang, Jinhui Xu

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Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Theory of computation
Keywords
  • Bipartite matching
  • Alignment
  • Discretization
  • Approximate algorithm

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Abstract

In this paper, we study the following pattern search problem: Given a pair of point sets A and B in fixed dimensional space R^d, with |B| = n, |A| = m and n >= m, the pattern search problem is to find the translations T’s of A such that each of the identified translations induces a matching between T(A) and a subset B' of B with cost no more than some given threshold, where the cost is defined as the minimum bipartite matching cost of T(A) and B'. We present a novel algorithm to produce a small set of candidate translations for the pattern search problem. For any B' subseteq B with |B'| = |A|, there exists at least one translation T in the candidate set such that the minimum bipartite matching cost between T(A) and B' is no larger than (1+epsilon) times the minimum bipartite matching cost between A and B' under any translation (i.e., the optimal translational matching cost). We also show that there exists an alternative solution to this problem, which constructs a candidate set of size O(n log^2 n) in O(n log^2 n) time with high probability of success. As a by-product of our construction, we obtain a weak epsilon-net for hypercube ranges, which significantly improves the construction time and the size of the candidate set. Our technique can be applied to a number of applications, including the translational pattern matching problem.

Cite As Get BibTex

Ziyun Huang, Qilong Feng, Jianxin Wang, and Jinhui Xu. Small Candidate Set for Translational Pattern Search. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ISAAC.2019.26

Author Details

Ziyun Huang
  • Department of Computer Science and Software Engineering, Penn State Erie, The Behrend College, Erie, PA, USA
Qilong Feng
  • School of Computer Science and Engineering, Central South University, P.R. China
Jianxin Wang
  • School of Computer Science and Engineering, Central South University, P.R. China
Jinhui Xu
  • Department of Computer Science and Engineering, State University of New York at Buffalo, USA

Funding

The research of the first and last authors was supported in part by NSF through grant CCF-1716400. The research of the last author was also supported by NSF through grant IIS-1910492. The research of the second and third authors was supported in part by NSFC through grants 61872450, 61828205, and 61672536.

References

  1. Helmut Alt and Leonidas J Guibas. Discrete geometric shapes: Matching, interpolation, and approximation. In Handbook of computational geometry, pages 121-153. Elsevier, 2000. Google Scholar
  2. Boris Aronov, Esther Ezra, and Micha Sharir. Small-Size $$1eps-Nets for Axis-Parallel Rectangles and Boxes. SIAM Journal on Computing, 39(7):3248-3282, 2010. Google Scholar
  3. Sunil Arya, Theocharis Malamatos, and David M Mount. Space-time tradeoffs for approximate nearest neighbor searching. Journal of the ACM (JACM), 57(1):1, 2009. Google Scholar
  4. Rinat Ben-Avraham, Matthias Henze, Rafel Jaume, Balázs Keszegh, Orit E Raz, Micha Sharir, and Igor Tubis. Minimum partial-matching and Hausdorff RMS-distance under translation: combinatorics and algorithms. In European Symposium on Algorithms, pages 100-111. Springer, 2014. Google Scholar
  5. Sergio Cabello, Panos Giannopoulos, and Christian Knauer. On the parameterized complexity of d-dimensional point set pattern matching. In International Workshop on Parameterized and Exact Computation, pages 175-183. Springer, 2006. Google Scholar
  6. Paul B Callahan and S Rao Kosaraju. A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. Journal of the ACM, 42(1):67-90, 1995. Google Scholar
  7. Danny Z Chen, Ziyun Huang, Yangwei Liu, and Jinhui Xu. On Clustering Induced Voronoi Diagrams. SIAM Journal on Computing, 46(6):1679-1711, 2017. Google Scholar
  8. Kenneth L Clarkson and Kasturi Varadarajan. Improved approximation algorithms for geometric set cover. Discrete & Computational Geometry, 37(1):43-58, 2007. Google Scholar
  9. Hu Ding, Ronald Berezney, and Jinhui Xu. k-prototype learning for 3d rigid structures. In Advances in Neural Information Processing Systems, pages 2589-2597, 2013. Google Scholar
  10. Hu Ding, Branislav Stojkovic, Ronald Berezney, and Jinhui Xu. Gauging association patterns of chromosome territories via chromatic median. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1296-1303, 2013. Google Scholar
  11. Hu Ding and Jinhui Xu. FPTAS for minimizing earth mover’s distance under rigid transformations. In European Symposium on Algorithms, pages 397-408. Springer, 2013. Google Scholar
  12. Esther Ezra. A note about weak ε-nets for axis-parallel boxes in d-space. Information Processing Letters, 110(18-19):835-840, 2010. Google Scholar
  13. Martin Gavrilov, Piotr Indyk, Rajeev Motwani, and Suresh Venkatasubramanian. Combinatorial and experimental methods for approximate point pattern matching. Algorithmica, 38(1):59-90, 2004. Google Scholar
  14. Michael T Goodrich, Joseph SB Mitchell, and Mark W Orletsky. Practical methods for approximate geometric pattern matching under rigid motions:(preliminary version). In Proceedings of the tenth annual symposium on Computational geometry, pages 103-112. ACM, 1994. Google Scholar
  15. Sariel Har-Peled. A replacement for Voronoi diagrams of near linear size. In Proceedings 42nd IEEE Symposium on Foundations of Computer Science, pages 94-103. IEEE, 2001. Google Scholar
  16. David Haussler and Emo Welzl. ε-nets and simplex range queries. Discrete & Computational Geometry, 2(2):127-151, 1987. Google Scholar
  17. Matthias Henze, Rafel Jaume, and Balázs Keszegh. On the complexity of the partial least-squares matching Voronoi diagram. In Proc. 29th European Workshop on Computational Geometry, pages 193-196, 2013. Google Scholar
  18. Daniel P Huttenlocher, Klara Kedem, and Micha Sharir. The upper envelope of Voronoi surfaces and its applications. Discrete & Computational Geometry, 9(3):267-291, 1993. Google Scholar
  19. Janardhan Kulkarni and Sathish Govindarajan. New ε-net constructions. In Proceedings of the 22nd Annual Canadian Conference on Computational Geometry, Winnipeg, Manitoba, Canada, pages 159-162. Citeseer, 2010. Google Scholar
  20. Jiří Matoušek, Raimund Seidel, and Emo Welzl. How to net a lot with little: Small ε-nets for disks and halfspaces. In Proceedings of the sixth annual symposium on Computational geometry, pages 16-22. ACM, 1990. Google Scholar
  21. Günter Rote. Partial least-squares point matching under translations. In Proc. 26th European Workshop on Computational Geometry, pages 249-251. Citeseer, 2010. Google Scholar
  22. Nitasha Sehgal, Andrew J Fritz, Jaromira Vecerova, Hu Ding, Zihe Chen, Branislav Stojkovic, Sambit Bhattacharya, Jinhui Xu, and Ronald Berezney. Large-scale probabilistic 3D organization of human chromosome territories. Human molecular genetics, 25(3):419-436, 2015. Google Scholar
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