A Beam Search for the Longest Common Subsequence Problem Guided by a Novel Approximate Expected Length Calculation

The longest common subsequence problem (LCS) aims at finding a longest string that appears as subsequence in each of a given set of input strings. This is a well known NP -hard problem which has been tackled by many heuristic approaches. Among them, the best performing ones are based on beam search (BS) but differ significantly in various aspects. In this paper we compare the existing BS-based approaches by using a common BS framework making the differences more explicit. Furthermore, we derive a novel heuristic function to guide BS, which approximates the expected length of an LCS of random strings. In a rigorous experimental evaluation we compare all BS-based methods from the literature and investigate the impact of our new heuristic guidance. Results show in particular that our novel heuristic guidance leads frequently to significantly better solutions. New best solutions are obtained for a wide range of the existing benchmark instances.We gratefully acknowledge the financial support of this project by the Doctoral Program “Vienna Graduate School on Computational Optimization” funded by the Austrian Science Foundation (FWF) under contract no. W1260-N35. Moreover, Christian Blum acknowledges the support of LOGISTAR, a proyect from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 76914