Revisiting the Parameterized Complexity of Maximum-Duo Preservation String Mapping

Authors Christian Komusiewicz, Mateus de Oliveira Oliveira, Meirav Zehavi



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Christian Komusiewicz
Mateus de Oliveira Oliveira
Meirav Zehavi

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Christian Komusiewicz, Mateus de Oliveira Oliveira, and Meirav Zehavi. Revisiting the Parameterized Complexity of Maximum-Duo Preservation String Mapping. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CPM.2017.11

Abstract

In the Maximum-Duo Preservation String Mapping (Max-Duo PSM) problem, the input consists of two related strings A and B of length n and a nonnegative integer k. The objective is to determine whether there exists a mapping m from the set of positions of A to the set of positions of B that maps only to positions with the same character and preserves at least k duos, which are pairs of adjacent positions. We develop a randomized algorithm that solves Max-Duo PSM in time 4^k * n^{O(1)}, and a deterministic algorithm that solves this problem in time 6.855^k * n^{O(1)}. The previous best known (deterministic) algorithm for this problem has running time (8e)^{2k+o(k)} * n^{O(1)} [Beretta et al., Theor. Comput. Sci. 2016]. We also show that Max-Duo PSM admits a problem kernel of size O(k^3), improving upon the previous best known problem kernel of size O(k^6).
Keywords
  • comparative genomics
  • parameterized complexity
  • kernelization

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References

  1. Stefano Beretta, Mauro Castelli, and Riccardo Dondi. Corrigendum to “Parameterized tractability of the maximum-duo preservation string mapping problem” [Theoret. Comput. Sci. 646 (2016) 16–25]. Theor. Comput. Sci., 653:108-110, 2016. URL: http://dx.doi.org/10.1016/j.tcs.2016.09.015.
  2. Stefano Beretta, Mauro Castelli, and Riccardo Dondi. Parameterized tractability of the maximum-duo preservation string mapping problem. Theor. Comput. Sci., 646:16-25, 2016. URL: http://dx.doi.org/10.1016/j.tcs.2016.07.011.
  3. Andreas Björklund. Determinant sums for undirected Hamiltonicity. SIAM J. Comput., 43(1):280-299, 2014. URL: http://dx.doi.org/10.1137/110839229.
  4. Andreas Björklund, Thore Husfeldt, Petteri Kaski, and Mikko Koivisto. Narrow sieves for parameterized paths and packings. J. Comput. Syst. Sci., 87:119-139, 2017. http://arxiv.org/abs/1007.1161, URL: http://dx.doi.org/10.1016/J.JCSS.2017.03.003.
  5. Nicolas Boria, Gianpiero Cabodi, Paolo Camurati, Marco Palena, Paolo Pasini, and Stefano Quer. A 7/2-approximation algorithm for the maximum duo-preservation string mapping problem. In Roberto Grossi and Moshe Lewenstein, editors, Proceedings of the 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016), volume 54 of LIPIcs, pages 11:1-11:8. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.CPM.2016.11.
  6. Nicolas Boria, Adam Kurpisz, Samuli Leppänen, and Monaldo Mastrolilli. Improved approximation for the maximum duo-preservation string mapping problem. In Daniel G. Brown and Burkhard Morgenstern, editors, Proceedings of the 14th International Workshop on Algorithms in Bioinformatics (WABI 2014), volume 8701 of LNCS, pages 14-25. Springer, 2014. URL: http://dx.doi.org/10.1007/978-3-662-44753-6_2.
  7. Brian Brubach. Further improvement in approximating the maximum duo-preservation string mapping problem. In Martin C. Frith and Christian Nørgaard Storm Pedersen, editors, Proceedings of the 16th International Workshop on Algorithms in Bioinformatics (WABI 2016), volume 9838 of LNCS, pages 52-64. Springer, 2016. URL: http://dx.doi.org/10.1007/978-3-319-43681-4_5.
  8. Laurent Bulteau, Guillaume Fertin, Christian Komusiewicz, and Irena Rusu. A fixed-parameter algorithm for minimum common string partition with few duplications. In Aaron E. Darling and Jens Stoye, editors, Proceedings of the 13th International Workshop on Algorithms in Bioinformatics (WABI 2013), volume 8126 of LNCS, pages 244-258. Springer, 2013. URL: http://dx.doi.org/10.1007/978-3-642-40453-5_19.
  9. Laurent Bulteau and Christian Komusiewicz. Minimum common string partition parameterized by partition size is fixed-parameter tractable. In Chandra Chekuri, editor, Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2014), pages 102-121. SIAM, 2014. URL: http://dx.doi.org/10.1137/1.9781611973402.8.
  10. Wenbin Chen, Zhengzhang Chen, Nagiza F. Samatova, Lingxi Peng, Jianxiong Wang, and Maobin Tang. Solving the maximum duo-preservation string mapping problem with linear programming. Theor. Comput. Sci., 530:1-11, 2014. URL: http://dx.doi.org/10.1016/j.tcs.2014.02.017.
  11. Xin Chen, Jie Zheng, Zheng Fu, Peng Nan, Yang Zhong, Stefano Lonardi, and Tao Jiang. Assignment of orthologous genes via genome rearrangement. IEEE/ACM Trans. Comput. Biol. Bioinform., 2(4):302-315, 2005. URL: http://dx.doi.org/10.1109/TCBB.2005.48.
  12. Graham Cormode and S. Muthukrishnan. The string edit distance matching problem with moves. ACM Trans. Algorithms, 3(1):2:1-2:19, 2007. URL: http://dx.doi.org/10.1145/1219944.1219947.
  13. Maxime Crochemore, Christophe Hancart, and Thierry Lecroq. Algorithms on strings. Cambridge University Press, 2007. URL: http://dx.doi.org/10.1017/CBO9780511546853.
  14. Marek Cygan, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. URL: http://dx.doi.org/10.1007/978-3-319-21275-3.
  15. Peter Damaschke. Minimum common string partition parameterized. In Keith A. Crandall and Jens Lagergren, editors, Proceedings of the 8th International Workshop on Algorithms in Bioinformatics (WABI 2008), volume 5251 of LNCS, pages 87-98. Springer, 2008. URL: http://dx.doi.org/10.1007/978-3-540-87361-7_8.
  16. Richard A. DeMillo and Richard J. Lipton. A probabilistic remark on algebraic program testing. Inf. Process. Lett., 7(4):193-195, 1978. URL: http://dx.doi.org/10.1016/0020-0190(78)90067-4.
  17. Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, 2013. URL: http://dx.doi.org/10.1007/978-1-4471-5559-1.
  18. Bartłomiej Dudek, Paweł Gawrychowski, and Piotr Ostropolski-Nalewaja. A family of approximation algorithms for the maximum duo-preservation string mapping problem. In Juha Kärkkäinen, Jakub Radoszewski, and Wojciech Rytter, editors, Proceedings of the 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017), volume 78 of LIPIcs, pages 10:1-10:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. http://arxiv.org/abs/1702.02405, URL: http://dx.doi.org/10.4230/LIPIcs.CPM.2017.10.
  19. Guillaume Fertin, Anthony Labarre, Irena Rusu, Eric Tannier, and Stéphane Vialette. Combinatorics of Genome Rearrangements. Computational molecular biology. MIT Press, 2009. URL: http://dx.doi.org/10.7551/mitpress/9780262062824.001.0001.
  20. Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh. Efficient computation of representative families with applications in parameterized and exact algorithms. J. ACM, 63(4):29:1-29:60, 2016. URL: http://dx.doi.org/10.1145/2886094.
  21. Avraham Goldstein, Petr Kolman, and Jie Zheng. Minimum common string partition problem: Hardness and approximations. Electron. J. Comb., 12, 2005. URL: http://www.combinatorics.org/Volume_12/Abstracts/v12i1r50.html.
  22. Dan Gusfield. Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, 1997. URL: http://dx.doi.org/10.1017/CBO9780511574931.
  23. Haitao Jiang, Binhai Zhu, Daming Zhu, and Hong Zhu. Minimum common string partition revisited. J. Comb. Optim., 23(4):519-527, 2012. URL: http://dx.doi.org/10.1007/s10878-010-9370-2.
  24. Jacob T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. J. ACM, 27(4):701-717, 1980. URL: http://dx.doi.org/10.1145/322217.322225.
  25. Hadas Shachnai and Meirav Zehavi. Representative families: A unified tradeoff-based approach. J. Comput. Syst. Sci., 82(3):488-502, 2016. URL: http://dx.doi.org/10.1016/j.jcss.2015.11.008.
  26. Krister M. Swenson, Mark Marron, Joel V. Earnest-DeYoung, and Bernard M. E. Moret. Approximating the true evolutionary distance between two genomes. ACM J. Exp. Algorithmics, 12, 2008. URL: http://dx.doi.org/10.1145/1227161.1402297.
  27. Yao Xu, Yong Chen, Taibo Luo, and Guohui Lin. A local search 2.917-approximation algorithm for duo-preservation string mapping, 2017. URL: http://arxiv.org/abs/1702.01877.
  28. Richard Zippel. Probabilistic algorithms for sparse polynomials. In Edward W. Ng, editor, Proceedings of an International Symposiumon on Symbolic and Algebraic Manipulation (EUROSAM 1979), volume 72 of LNCS, pages 216-226. Springer, 1979. URL: http://dx.doi.org/10.1007/3-540-09519-5_73.
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