Abstract
Given a set of two input strings and a pattern string, the constrained longest common subsequence problem deals with finding a longest string that is a subsequence of both input strings and that contains the given pattern string as a subsequence. This problem has various applications, especially in computational biology. In this work we consider the \(\mathcal {NP}\)–hard case of the problem in which more than two input strings are given. First, we adapt an existing A\(^*\) search from two input strings to an arbitrary number m of input strings (\(m \ge 2\)). With the aim of tackling large problem instances approximately, we additionally propose a greedy heuristic and a beam search. All three algorithms are compared to an existing approximation algorithm from the literature. Beam search turns out to be the best heuristic approach, matching almost all optimal solutions obtained by A\(^*\) search for rather small instances.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abboud, A., Backurs, A., Williams, V.V.: Tight hardness results for LCS and other sequence similarity measures. In: Proceedings of FOCS 2015 - the 56th Annual Symposium on Foundations of Computer Science, pp. 59–78. IEEE (2015)
Arslan, A.N., Eğecioğlu, Ö.: Algorithms for the constrained longest common subsequence problems. Int. J. Found. Comput. Sci. 16(06), 1099–1109 (2005)
Bezerra, F.N.: A longest common subsequence approach to detect cut and wipe video transitions. In: Proceedings of 17th Brazilian Symposium on Computer Graphics and Image Processing, pp. 154–160. IEEE Explore (2004). https://doi.org/10.1109/SIBGRA.2004.1352956
Blum, C., Blesa, M.J., López-Ibáñez, M.: Beam search for the longest common subsequence problem. Comput. Oper. Res. 36(12), 3178–3186 (2009)
Chin, F.Y., De Santis, A., Ferrara, A.L., Ho, N., Kim, S.: A simple algorithm for the constrained sequence problems. Inf. Process. Lett. 90(4), 175–179 (2004)
Djukanovic, M., Berger, C., Raidl, G.R., Blum, C.: An A\(^*\) search algorithm for the constrained longest common subsequence problem. Technical report AC-TR-20-004, Algorithms and Complexity Group, TU Wien (2020). http://www.ac.tuwien.ac.at/files/tr/ac-tr-20-004.pdf
Djukanovic, M., Raidl, G.R., Blum, C.: A heuristic approach for solving the longest common square subsequence problem. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2019. LNCS, vol. 12013, pp. 429–437. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45093-9_52
Djukanovic, M., Raidl, G.R., Blum, C.: A beam search for the longest common subsequence problem guided by a novel approximate expected length calculation. In: Nicosia, G., Pardalos, P., Umeton, R., Giuffrida, G., Sciacca, V. (eds.) LOD 2019. LNCS, vol. 11943, pp. 154–167. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-37599-7_14
Gotthilf, Z., Hermelin, D., Lewenstein, M.: Constrained LCS: hardness and approximation. In: Ferragina, P., Landau, G.M. (eds.) CPM 2008. LNCS, vol. 5029, pp. 255–262. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69068-9_24
Hart, P., Nilsson, N., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)
Huang, K., Yang, C., Tseng, K.: Fast algorithms for finding the common subsequences of multiple sequences. In: Proceedings of ICS 2004 - the 3rd IEEE International Computer Symposium, pp. 1006–1011 (2004)
Mousavi, S.R., Tabataba, F.: An improved algorithm for the longest common subsequence problem. Comput. Oper. Res. 39(3), 512–520 (2012)
Storer, J.: Data Compression: Methods and Theory. Computer Science Press, Rockville (1988)
Tsai, Y.T.: The constrained longest common subsequence problem. Inf. Process. Lett. 88(4), 173–176 (2003)
Wang, Q., Pan, M., Shang, Y., Korkin, D.: A fast heuristic search algorithm for finding the longest common subsequence of multiple strings. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence. AAAI Press (2010)
Acknowledgments
This work was partially funded by the Doctoral Program Vienna Graduate School on Computational Optimization, Austrian Science Foundation Project No. W1260-N35. This work was also supported by project CI-SUSTAIN funded by the Spanish Ministry of Science and Innovation (PID2019-104156GB-I00).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Djukanovic, M., Berger, C., Raidl, G.R., Blum, C. (2020). On Solving a Generalized Constrained Longest Common Subsequence Problem. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-62867-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-62866-6
Online ISBN: 978-3-030-62867-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)