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A Family of Approximation Algorithms for the Maximum Duo-Preservation String Mapping Problem
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28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Annual Symposium on Combinatorial Pattern Matching (CPM) - License:
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- Publication Date: 2017-06-30
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Bartlomiej Dudek, Pawel Gawrychowski, and Piotr Ostropolski-Nalewaja. A Family of Approximation Algorithms for the Maximum Duo-Preservation String Mapping Problem. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CPM.2017.10
https://doi.org/10.4230/LIPIcs.CPM.2017.10
Abstract
In the Maximum Duo-Preservation String Mapping problem we are given two strings and wish to map the letters of the former to the letters of the latter as to maximise the number of duos. A duo is a pair of consecutive letters that is mapped to a pair of consecutive letters in the same order. This is complementary to the well-studied Minimum Common String Partition problem, where the goal is to partition the former string into blocks that can be permuted and concatenated to obtain the latter string.
Maximum Duo-Preservation String Mapping is APX-hard. After a series of improvements, Brubach [WABI 2016] showed a polynomial-time 3.25-approximation algorithm. Our main contribution is that, for any eps>0, there exists a polynomial-time (2+eps)-approximation algorithm. Similarly to a previous solution by Boria et al. [CPM 2016], our algorithm uses the local search technique. However, this is used only after a certain preliminary greedy procedure, which gives us more structure and makes a more general local search possible. We complement this with a specialised version of the algorithm that achieves 2.67-approximation in quadratic time.
Keywords
- approximation scheme
- minimum common string partition
- local search
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References
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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(Complete):1-11, 2014. URL: http://dx.doi.org/10.1016/j.tcs.2014.02.017.
- Marek Chrobak, Petr Kolman, and Jiří Sgall. The greedy algorithm for the minimum common string partition problem. ACM Trans. Algorithms, 1(2):350-366, October 2005. URL: http://dx.doi.org/10.1145/1103963.1103971.
- 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.
- 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.
- Bin Fu, Haitao Jiang, Boting Yang, and Binhai Zhu. Exponential and polynomial time algorithms for the minimum common string partition problem. In Weifan Wang, Xuding Zhu, and Ding-Zhu Du, editors, Proceedings of the 5th International Conference on Combinatorial Optimization and Applications (COCOA 2011), volume 6831 of LNCS, pages 299-310. Springer, 2011. URL: http://dx.doi.org/10.1007/978-3-642-22616-8_24.
- 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.
- Isaac Goldstein and Moshe Lewenstein. Quick greedy computation for minimum common string partition. Theor. Comput. Sci., 542:98-107, July 2014. URL: http://dx.doi.org/10.1016/j.tcs.2014.05.006.
- Dan He. A novel greedy algorithm for the minimum common string partition problem. In Ion I. Mandoiu and Alexander Zelikovsky, editors, Proceedings of the 3rd International Symposium on Bioinformatics Research and Applications (ISBRA 2007), volume 4463 of LNCS, pages 441-452. Springer, 2007. URL: http://dx.doi.org/10.1007/978-3-540-72031-7_40.
- 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.
- Haim Kaplan and Nira Shafrir. The greedy algorithm for edit distance with moves. Inf. Process. Lett., 97(1):23-27, 2006. URL: http://dx.doi.org/10.1016/j.ipl.2005.08.010.
- Dana Shapira and James A. Storer. Edit distance with move operations. J. Discrete Algorithms, 5(2):380-392, 2007. URL: http://dx.doi.org/10.1016/j.jda.2005.01.010.