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.
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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).
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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
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